# Homo Deus Lab — Interactive Scientific Simulations

> Open-source library of 1,082 interactive scientific simulations across 217 topics.
> Physics, chemistry, biology, engineering, mathematics, computer science, earth sciences, and more.
> Each simulation runs a live Canvas 2D engine with adjustable parameters, computed outputs, and educational content.
> Website: https://homo-deus.com
> GitHub: github.com/homo-techno/simulations

## applied-science (2 topics, 10 simulations)

### Agriculture & Crop Science (5 simulations)
- [Crop Rotation & Soil Nutrient Cycles](/lab/agriculture/crop-rotation): Simulate multi-year crop rotation strategies to see how nitrogen fixation, nutrient depletion, and fallow periods affect long-term soil health and yield
- [Crop Yield Prediction & Weather Simulator](/lab/agriculture/yield-prediction): Predict crop yields based on temperature, rainfall, and growing degree days — see how weather variability impacts harvest outcomes
- [Integrated Pest Management Model](/lab/agriculture/pest-control): Simulate pest population dynamics under integrated pest management — balancing biological control, pesticide application, and economic thresholds
- [Irrigation Water Efficiency Simulator](/lab/agriculture/irrigation-optimization): Optimize irrigation schedules by balancing water application, evapotranspiration, and root zone soil moisture to maximize crop water use efficiency
- [Soil NPK Nutrient Balance Simulator](/lab/agriculture/soil-nutrients): Model the balance of nitrogen, phosphorus, and potassium in soil to understand Liebig's law of the minimum and optimize fertilizer application

### Forensic Science & Criminal Investigation (5 simulations)
- [Blood Spatter Angle Analysis](/lab/forensic-science/blood-spatter): Reconstruct the impact angle and origin of bloodstains from droplet geometry — the trigonometry behind bloodstain pattern analysis
- [Bullet Trajectory & Forensic Ballistics](/lab/forensic-science/ballistics): Simulate bullet trajectories accounting for gravity, drag, and wind to reconstruct shooting positions and distances in forensic investigations
- [DNA Fingerprinting & Match Probability](/lab/forensic-science/dna-fingerprinting): Calculate the probability of a random DNA profile match using STR loci allele frequencies — the statistical backbone of forensic genetics
- [Fingerprint Minutiae Matching Simulator](/lab/forensic-science/fingerprint-matching): Score fingerprint similarity by comparing minutiae points — ridge endings, bifurcations, and their spatial relationships used in automated fingerprint identification
- [Time of Death Estimation (Henssge Nomogram)](/lab/forensic-science/time-of-death): Estimate postmortem interval from body temperature using the Henssge cooling model — the standard forensic method for time-of-death determination

## arts (1 topics, 5 simulations)

### Music Theory & Sound (5 simulations)
- [Chord Progression & Harmony Simulator](/lab/music-theory/chord-progressions): Build and analyze chord progressions using Roman numeral analysis — explore voice leading, harmonic tension, and resolution in real time
- [Circle of Fifths Explorer](/lab/music-theory/circle-of-fifths): Navigate the circle of fifths to visualize key signatures, relative majors and minors, and the 3:2 frequency ratio that structures all of Western harmony
- [Musical Scales & Modes Explorer](/lab/music-theory/scale-modes): Explore the seven diatonic modes from bright Ionian to dark Locrian — visualize interval patterns, semitone positions, and modal color on a keyboard and circle
- [Polyrhythm & Time Signature Simulator](/lab/music-theory/rhythm-patterns): Layer two independent rhythmic cycles to create polyrhythms — watch how 3:2, 4:3, and complex ratios generate emergent rhythmic patterns
- [Tuning Systems Comparison](/lab/music-theory/tuning-systems): Compare equal temperament and just intonation side by side — hear and see the cent differences between pure frequency ratios and the compromises of modern tuning

## behavioral-science (1 topics, 5 simulations)

### Psychology & Cognition (5 simulations)
- [Cognitive Load & Working Memory Capacity](/lab/psychology/cognitive-load): Explore the limits of working memory — visualize how cognitive load affects performance and discover Miller's magical number 7±2
- [Dunning-Kruger Effect Simulator](/lab/psychology/dunning-kruger): Visualize the Dunning-Kruger curve — see how low performers drastically overestimate their ability while top performers slightly underestimate theirs
- [Milgram Obedience Experiment Simulation](/lab/psychology/milgram-obedience): Simulate Milgram's shocking obedience experiment — watch how authority pressure drives compliance rates to 65% even when participants believe they're harming others
- [Spacing Effect & Optimal Study Intervals](/lab/psychology/spacing-effect): Discover why spaced repetition crushes cramming — simulate memory retention curves and find the optimal study schedule for long-term learning
- [Stroop Effect Reaction Time Test](/lab/psychology/stroop-effect): Measure how conflicting word-color information slows your brain — the classic Stroop effect demonstrates automatic reading interference with color naming

## biology (16 topics, 79 simulations)

### Behavioral Ecology & Animal Strategy (5 simulations)
- [Hawk-Dove Evolutionary Game](/lab/behavioral-ecology/hawk-dove-game): Play the hawk-dove game — adjust resource value, injury cost, display cost, and initial hawk fraction to watch evolutionary dynamics converge to the ESS mixed strategy
- [Kin Selection & Hamilton's Rule](/lab/behavioral-ecology/kin-selection): Model kin selection and altruism — adjust relatedness, benefit to recipient, cost to altruist, and group size to explore when self-sacrifice evolves through inclusive fitness
- [Optimal Foraging Theory](/lab/behavioral-ecology/optimal-foraging): Simulate optimal foraging decisions — adjust prey energy value, handling time, encounter rate, and travel cost to find when a forager should be selective vs. generalist
- [Predator-Prey Behavioral Strategy](/lab/behavioral-ecology/predator-prey-strategy): Simulate predator-prey behavioral arms races — adjust predator speed, prey vigilance, group size, and escape probability to model the landscape of fear and optimal anti-predator behavior
- [Territory Defense Economics](/lab/behavioral-ecology/territory-defense): Model territory defense trade-offs — adjust territory size, resource density, defense cost, and intruder pressure to find the economically optimal territory size

### Biochemistry & Molecular Dynamics (5 simulations)
- [ATP Synthesis Energy Cycle](/lab/biochemistry/atp-cycle): Visualize the ATP-ADP energy cycle — the universal currency of cellular energy that powers every living process from muscle contraction to DNA replication
- [Chemical Reaction Rate & Arrhenius Equation](/lab/biochemistry/reaction-rate): Explore how temperature governs chemical reaction rates through the Arrhenius equation — visualize the exponential relationship between temperature and rate constant
- [Michaelis-Menten Enzyme Kinetics](/lab/biochemistry/enzyme-kinetics): Simulate enzyme kinetics using the Michaelis-Menten model — explore how substrate concentration, Km, and Vmax determine reaction velocity
- [pH Buffer Equilibrium](/lab/biochemistry/ph-buffer): Explore how buffer solutions resist pH changes — simulate acid/base titration and the Henderson-Hasselbalch equation in real time
- [Protein Folding Energy Landscape](/lab/biochemistry/protein-folding): Visualize the protein folding energy landscape — a rugged funnel where polypeptide chains navigate toward their minimum-energy native state

### Biomechanics & Human Movement (5 simulations)
- [Gait Cycle Analysis](/lab/biomechanics/gait-analysis): Simulate the human gait cycle — explore how walking speed, stride length, leg length, and cadence affect stance phase, swing phase, and ground reaction forces
- [Joint Reaction Forces](/lab/biomechanics/joint-loading): Simulate joint reaction forces — explore how body weight, muscle force, lever arms, and joint angle determine compressive and shear loads on the hip and knee
- [Muscle Force-Velocity Relationship](/lab/biomechanics/muscle-force): Simulate the Hill muscle model — explore how contraction velocity, activation level, fiber length, and maximum isometric force determine muscle output
- [Postural Balance & Stability](/lab/biomechanics/balance-stability): Simulate human balance — explore how center-of-mass position, base-of-support width, body height, and perturbation magnitude determine stability margin and fall risk
- [Vertical Jump Projectile Analysis](/lab/biomechanics/projectile-jump): Simulate the biomechanics of vertical jumping — explore how takeoff velocity, body mass, push-off depth, and air time determine jump height and ground reaction forces

### Biophysics & Molecular Mechanics (5 simulations)
- [DNA Mechanics & Elasticity](/lab/biophysics/dna-mechanics): Simulate DNA stretching mechanics — explore the worm-like chain model, persistence length, and force-extension behavior of double-stranded DNA
- [Ion Channel Gating Dynamics](/lab/biophysics/ion-channels): Simulate voltage-gated ion channel kinetics — explore how membrane voltage, gating charge, and temperature control channel opening probability and conductance
- [Membrane Transport & Nernst Potential](/lab/biophysics/membrane-transport): Simulate ion transport across biological membranes — explore how concentration gradients, membrane permeability, and voltage drive the Nernst and Goldman equations
- [Molecular Motors & Kinesin Stepping](/lab/biophysics/molecular-motors): Simulate molecular motor stepping along microtubules — explore how ATP concentration, load force, and temperature govern kinesin velocity and processivity
- [Protein Folding Energy Landscape](/lab/biophysics/protein-folding): Simulate the protein folding energy landscape — explore how temperature, hydrophobic forces, and chain length determine folding kinetics and native state stability

### Biotechnology & Genetic Engineering (5 simulations)
- [Bioreactor Growth Dynamics & Scale-Up](/lab/biotechnology/bioreactor-design): Simulate microbial and cell culture growth in bioreactors — model Monod kinetics, substrate consumption, oxygen transfer, and scale-up from bench to production
- [CRISPR-Cas9 Gene Editing Efficiency](/lab/biotechnology/crispr-editing): Simulate CRISPR-Cas9 gene editing — explore guide RNA design, on-target efficiency, off-target probability, and indel outcomes for different genomic targets
- [Gel Electrophoresis DNA Separation](/lab/biotechnology/gel-electrophoresis): Simulate gel electrophoresis — visualize how DNA fragments separate by size through an agarose matrix under an electric field, with band migration and ladder comparison
- [Gene Expression & Transcription Regulation](/lab/biotechnology/gene-expression): Simulate gene expression dynamics — explore promoter strength, mRNA degradation, protein synthesis rates, and feedback regulation in a single-gene expression model
- [PCR Amplification & Thermal Cycling](/lab/biotechnology/pcr-amplification): Simulate polymerase chain reaction — visualize exponential DNA amplification through thermal cycling, explore primer annealing, and calculate copy numbers across cycles

### Chronobiology & Biological Rhythms (5 simulations)
- [Circadian Rhythm Oscillator](/lab/chronobiology/circadian-rhythm): Simulate the 24-hour circadian clock — adjust light exposure, clock period, and coupling strength to see how the body's master oscillator entrains to the day-night cycle
- [Jet Lag Recovery Model](/lab/chronobiology/jet-lag-model): Model jet-lag recovery after crossing time zones — adjust the number of zones crossed, direction of travel, and light strategy to predict how many days until re-entrainment
- [Seasonal Affective Disorder Model](/lab/chronobiology/seasonal-affective): Model how photoperiod changes drive seasonal mood variation — adjust latitude, light therapy dose, and melatonin sensitivity to explore SAD mechanisms
- [Sleep Cycle Architecture](/lab/chronobiology/sleep-cycle): Visualize sleep architecture through the night — adjust sleep duration, REM pressure, and slow-wave drive to see how NREM and REM stages cycle in 90-minute ultradian rhythms
- [Ultradian Rhythm Oscillator](/lab/chronobiology/ultradian-rhythm): Explore ultradian rhythms — the 90–120 minute cycles of alertness, hormone release, and cognitive performance that pattern your waking and sleeping hours

### Ecology (5 simulations)
- [Ecological Succession](/lab/ecology/ecological-succession): Watch a landscape recover from disturbance — from bare ground through pioneer species to mature forest, with biodiversity and biomass tracking over time.
- [Food Web & Trophic Cascades](/lab/ecology/food-web): Interactive food web model showing how species removal triggers trophic cascades — watch energy flow through the network and see which species are truly keystone.
- [Island Biogeography Theory](/lab/ecology/island-biogeography): Explore MacArthur-Wilson theory of island biogeography — watch species immigrate and go extinct until equilibrium is reached.
- [Population Growth & Carrying Capacity](/lab/ecology/carrying-capacity): Watch a population grow through exponential and logistic phases — explore how carrying capacity limits growth and how harvesting affects sustainability.
- [Species-Area Relationship](/lab/ecology/species-area): Explore the power-law relationship between habitat area and species richness — see why halving habitat doesn't halve biodiversity, and calculate extinction debt.

### Epidemiology & Disease Dynamics (5 simulations)
- [Basic Reproduction Number R₀ Dynamics](/lab/epidemiology/r-number): Manipulate the basic reproduction number R₀ and observe how interventions like masking, distancing, and vaccination drive the effective reproduction number below 1
- [Contact Tracing Network Simulation](/lab/epidemiology/contact-tracing): Watch a disease spread through a social network and see how contact tracing identifies and isolates infectious individuals to break transmission chains
- [Epidemic Curve Flattening Strategies](/lab/epidemiology/epidemic-curve): Model SIR epidemic dynamics and observe how timing and intensity of interventions flatten the curve to keep cases below healthcare capacity
- [Herd Immunity Threshold Calculator](/lab/epidemiology/herd-immunity): Calculate the herd immunity threshold for any disease — visualize how vaccination coverage protects unvaccinated individuals through population-level immunity
- [Vaccine Efficacy & Trial Design](/lab/epidemiology/vaccine-efficacy): Design a vaccine clinical trial — set sample sizes, observe attack rates in treatment and control groups, and calculate efficacy with confidence intervals

### Evolution & Population Genetics (4 simulations)
- [Genetic Drift Simulator](/lab/evolution/genetic-drift): Wright-Fisher model demonstrating how random sampling in finite populations causes allele frequencies to fluctuate, leading to fixation or loss
- [Mutation Accumulation & Cancer Risk Simulator](/lab/evolution/mutation-accumulation): Armitage-Doll multi-hit model showing how somatic mutations accumulate with age and drive cancer incidence, with animated DNA visualization
- [Natural Selection Simulator](/lab/evolution/natural-selection): Interactive Hardy-Weinberg selection model showing how fitness differences drive allele frequency changes across generations
- [Predator-Prey Dynamics Simulator](/lab/evolution/predator-prey): Lotka-Volterra model showing oscillating population dynamics between predator and prey species with phase portrait visualization

### Genetics (5 simulations)
- [CRISPR-Cas9 Gene Editing](/lab/genetics/crispr-mechanism): Visualize CRISPR-Cas9 in action — guide RNA targets a DNA sequence, Cas9 cuts the double strand, and the cell repairs via NHEJ or HDR pathways
- [DNA Replication Fork](/lab/genetics/dna-replication): Watch DNA unwind and replicate — visualize the replication fork with helicase, primase, and DNA polymerase synthesizing leading and lagging strands in real time
- [Genetic Code & Protein Translation](/lab/genetics/genetic-code): Decode mRNA into proteins — watch ribosomes translate codons into amino acids, introduce mutations, and discover how frameshift errors devastate protein structure
- [Hardy-Weinberg Equilibrium](/lab/genetics/hardy-weinberg): Explore population genetics — watch allele frequencies evolve across generations under genetic drift, natural selection, and the Hardy-Weinberg equilibrium principle
- [Punnett Square & Mendelian Inheritance](/lab/genetics/mendelian-inheritance): Simulate Mendelian inheritance with interactive Punnett squares — predict offspring genotype ratios, test complete vs incomplete dominance, and validate results with chi-squared analysis

### Immunology & Immune Response (5 simulations)
- [Antibody-Antigen Binding Kinetics](/lab/immunology/antibody-binding): Simulate antibody-antigen binding — explore how affinity, concentration, and valence affect immune complex formation and pathogen neutralization
- [Autoimmune Threshold & Tolerance Breakdown](/lab/immunology/autoimmune-threshold): Simulate autoimmune dynamics — explore how self-reactivity levels, regulatory T-cell suppression, and molecular mimicry affect the threshold between tolerance and autoimmune disease
- [Cytokine Cascade & Signaling Networks](/lab/immunology/cytokine-cascade): Simulate cytokine signaling cascades — explore how initial stimulus, amplification gain, and negative feedback shape immune signaling dynamics
- [T-Cell Activation & Clonal Expansion](/lab/immunology/t-cell-response): Simulate T-cell immune response — explore how antigen dose, costimulation strength, and cytokine environment shape clonal expansion and memory formation
- [Vaccine-Induced Immunity Timeline](/lab/immunology/vaccine-immunity): Simulate vaccine immune response — explore how antigen dose, adjuvant strength, and booster timing affect antibody titers and protection duration

### Marine Biology & Ocean Life (5 simulations)
- [Bioluminescence & Light Production](/lab/marine-biology/bioluminescence): Simulate the biochemistry and ecology of bioluminescence — watch luciferin-luciferase reactions produce light and see how organisms use it for communication, camouflage, and predation.
- [Coral Reef Growth & Bleaching](/lab/marine-biology/coral-reef): Watch a coral reef grow, compete for space, and bleach under thermal stress — modeling the symbiotic relationship between coral polyps and zooxanthellae algae that sustains reef ecosystems.
- [Deep Sea Pressure & Adaptation](/lab/marine-biology/deep-sea-pressure): Visualize how hydrostatic pressure increases with ocean depth and how deep-sea organisms adapt their biochemistry — from flexible membranes to piezolyte molecules that resist crushing forces.
- [Fish Schooling & Collective Behavior](/lab/marine-biology/fish-schooling): Watch fish schools emerge from simple individual rules — alignment, cohesion, and separation create mesmerizing collective motion that confuses predators and improves foraging.
- [Ocean Currents & Thermohaline Circulation](/lab/marine-biology/ocean-currents): Visualize global ocean circulation driven by temperature and salinity differences — the thermohaline conveyor belt that distributes heat, nutrients, and marine life across the planet.

### Medical Science (5 simulations)
- [Cardiovascular Blood Flow](/lab/medical-science/blood-circulation): Model the cardiovascular system — visualize cardiac output, blood pressure waveforms, and the hemodynamics of circulation
- [Drug Pharmacokinetics (ADME)](/lab/medical-science/pharmacokinetics): Model drug absorption, distribution, metabolism, and elimination — visualize plasma concentration curves, therapeutic windows, and multi-dose accumulation
- [Immune Response Dynamics](/lab/medical-science/immune-response): Model the innate and adaptive immune response to infection — compare naive and vaccinated immune dynamics with pathogen clearance curves
- [Tumor Growth Dynamics](/lab/medical-science/tumor-growth): Model tumor progression with Gompertzian growth — explore immune surveillance, treatment timing, and the race between growth and therapy
- [Viral Replication Cycle](/lab/medical-science/virus-replication): Simulate the viral lifecycle — binding, entry, replication, assembly, and budding — and watch the immune system fight back

### Neuroscience (5 simulations)
- [Hebbian Learning Rule](/lab/neuroscience/hebbian-learning): Neurons that fire together wire together — watch synaptic connections strengthen in real time as correlated neurons form memory assemblies.
- [Neural Action Potential](/lab/neuroscience/action-potential): Watch a neuron fire — see how ion channels open and close to produce the all-or-nothing electrical spike that carries information in the brain.
- [Neural Firing Patterns](/lab/neuroscience/neuron-firing-patterns): Explore the five distinct firing patterns neurons use to encode information — from steady tonic firing to complex bursting rhythms.
- [Simple Perceptron Training](/lab/neuroscience/neural-network): Train a perceptron to classify points — watch the decision boundary rotate and shift as gradient descent finds the optimal separation.
- [Synaptic Plasticity & LTP/LTD](/lab/neuroscience/synaptic-plasticity): Explore spike-timing-dependent plasticity — see how millisecond differences in spike timing determine whether synapses strengthen or weaken.

### Nutrition Science (5 simulations)
- [Calorie Balance & Metabolic Rate Calculator](/lab/nutrition-science/calorie-balance): Calculate your Basal Metabolic Rate and simulate how calorie surplus or deficit drives weight change over weeks and months
- [Glycemic Index & Blood Sugar Response Simulator](/lab/nutrition-science/glycemic-index): Simulate how different glycemic index values affect blood sugar curves over time, comparing high-GI and low-GI meals
- [Hydration & Electrolyte Balance Model](/lab/nutrition-science/hydration-model): Model water intake, sweat loss, and electrolyte balance to understand how hydration affects performance and health
- [Macronutrient Ratio Optimizer](/lab/nutrition-science/macronutrient-ratio): Visualize how protein, carbohydrate, and fat ratios affect total calories, thermic effect, and body composition outcomes
- [Vitamin Absorption & Bioavailability Simulator](/lab/nutrition-science/vitamin-absorption): Explore how fat-soluble and water-soluble vitamins are absorbed differently, and how meal composition affects bioavailability

### Population Dynamics (5 simulations)
- [Age-Structured Population Model](/lab/population-dynamics/age-structure): Model how age-specific birth and death rates shape a population's age distribution over generations using Leslie matrix dynamics
- [Demographic Transition Stages](/lab/population-dynamics/demographic-transition): Simulate the four stages of demographic transition — from high birth/death rates to low rates — and watch population explode then stabilize
- [Malthusian vs Logistic Growth](/lab/population-dynamics/malthusian-growth): Compare unlimited exponential growth against resource-limited logistic growth — see why Malthus was right about the math but wrong about the outcome
- [Population Pyramid Dynamics](/lab/population-dynamics/population-pyramid): Build animated population pyramids — watch how birth rates, mortality, and migration reshape the age-sex distribution over decades
- [SIR Epidemic Model Simulator](/lab/population-dynamics/sir-epidemic): Simulate how infectious diseases spread through populations using the SIR model — adjust transmission and recovery rates to flatten the curve

## chemistry (9 topics, 45 simulations)

### Astrochemistry & Molecular Space (5 simulations)
- [Deuterium Enrichment in Cold Clouds](/lab/astrochemistry/isotope-fractionation): Simulate isotope fractionation reactions that enrich cold molecular clouds in deuterium, tracing the chemical heritage of our solar system
- [Grain Surface Ice Chemistry](/lab/astrochemistry/ice-mantle): Model the growth of molecular ice mantles on interstellar dust grains through accretion, surface reactions, and thermal desorption
- [Interstellar Molecular Cloud Chemistry](/lab/astrochemistry/molecular-cloud): Simulate gas-phase ion-molecule reaction networks inside a dense molecular cloud and watch molecular abundances evolve over millions of years
- [Photodissociation Region (PDR) Chemistry](/lab/astrochemistry/photodissociation-region): Explore UV-driven chemistry at the boundary between ionized gas and molecular clouds where photodissociation and photoionization shape the chemical structure
- [Rotational Spectral Line Identification](/lab/astrochemistry/spectral-line-id): Match observed radio/submillimeter spectral lines to molecular species using rotational transition frequencies and quantum numbers

### Brewing Science & Beer Chemistry (5 simulations)
- [Carbonation & Henry's Law](/lab/brewing-science/carbonation): Simulate beer carbonation — calculate CO2 volumes, equilibrium pressure, and priming sugar dose using Henry's law and temperature dependence
- [Hop Utilization & IBU Calculation](/lab/brewing-science/hop-utilization): Simulate hop bitterness extraction — calculate IBU from alpha acids, boil time, wort gravity, and hop form using the Tinseth model
- [Mash Conversion & Enzyme Kinetics](/lab/brewing-science/mash-conversion): Simulate starch-to-sugar conversion during mashing — explore how temperature, pH, and time affect alpha- and beta-amylase activity
- [Water Chemistry & Mash pH](/lab/brewing-science/water-chemistry): Simulate brewing water adjustments — calculate mash pH from grain bill, water mineral content, and acid or salt additions
- [Yeast Attenuation & Fermentation](/lab/brewing-science/yeast-attenuation): Simulate yeast fermentation — predict apparent and real attenuation, final gravity, and alcohol content from OG and yeast characteristics

### Chemical Kinetics & Reaction Rates (5 simulations)
- [Arrhenius Equation & Activation Energy](/lab/chemical-kinetics/arrhenius-equation): Explore how temperature and activation energy control reaction rate constants through the Arrhenius equation with interactive energy diagrams
- [Catalysis Energy Diagram & Turnover](/lab/chemical-kinetics/catalysis-mechanism): Visualize how catalysts lower activation energy, compare catalyzed vs uncatalyzed reaction profiles, and calculate turnover frequency
- [Dynamic Equilibrium & Le Chatelier's Principle](/lab/chemical-kinetics/equilibrium-kinetics): Visualize forward and reverse reaction rates reaching dynamic equilibrium, and observe Le Chatelier shifts when conditions change
- [Radical Chain Reactions & Explosion Limits](/lab/chemical-kinetics/chain-reaction): Model radical chain propagation, branching factors, and the transition from steady combustion to thermal explosion
- [Reaction Order & Concentration Decay](/lab/chemical-kinetics/reaction-order): Compare zero, first, and second-order kinetics side by side — concentration decay, half-life dependence, and integrated rate law plots

### Electrochemistry & Cell Design (5 simulations)
- [Battery Discharge Curve Simulator](/lab/electrochemistry/battery-discharge): Visualize battery discharge curves — explore how load current, internal resistance, and capacity affect voltage over time for different cell chemistries
- [Cyclic Voltammetry Simulator](/lab/electrochemistry/cyclic-voltammetry): Simulate cyclic voltammetry scans — sweep electrode potential and observe the characteristic duck-shaped voltammogram revealing redox peak positions and reversibility
- [Electrochemical Impedance Spectroscopy](/lab/electrochemistry/impedance-spectroscopy): Explore Nyquist plots and impedance spectra — adjust solution resistance, charge transfer resistance, and double-layer capacitance to model electrode behavior
- [Electrolysis & Faraday's Laws](/lab/electrochemistry/electrolysis): Simulate electrolysis — see how current, time, and molar mass determine the mass deposited at an electrode according to Faraday's laws
- [Nernst Equation & Cell Potential](/lab/electrochemistry/nernst-equation): Calculate electrochemical cell potential under non-standard conditions using the Nernst equation — adjust temperature, ion concentrations, and electron transfer count

### Photochemistry & Light-Driven Reactions (5 simulations)
- [Beer-Lambert Law & Absorption Spectra](/lab/photochemistry/photon-absorption): Simulate photon absorption through solutions using the Beer-Lambert law — explore how concentration, path length, and molar absorptivity affect transmittance
- [Fluorescence Quantum Yield Simulator](/lab/photochemistry/quantum-yield): Simulate fluorescence quantum yield — explore radiative and non-radiative decay rates, Stokes shift, and emission spectra
- [Photosynthesis Light Reactions & Electron Transport](/lab/photochemistry/photosynthesis-light): Simulate the light reactions of photosynthesis — model electron flow through PSII, cytochrome b6f, and PSI to produce ATP and NADPH
- [TiO₂ Photocatalytic Degradation](/lab/photochemistry/photocatalysis): Model TiO2 photocatalytic degradation of organic pollutants — explore UV intensity, catalyst loading, and Langmuir-Hinshelwood kinetics
- [UV Weathering & Polymer Degradation](/lab/photochemistry/uv-degradation): Model UV-induced polymer degradation — predict material lifetime from UV dose, stabilizer concentration, and temperature using Arrhenius kinetics

### Polymer Science & Plastics (5 simulations)
- [Glass Transition Temperature (Tg)](/lab/polymer-science/glass-transition): Simulate the glass transition — explore how temperature, cooling rate, plasticizer content, and molecular weight control the shift from rubbery to glassy polymer behavior
- [Polymer Crystallinity & Spherulite Growth](/lab/polymer-science/polymer-crystallinity): Simulate crystallization in semicrystalline polymers — explore how undercooling, nucleation density, and chain regularity control spherulite growth and crystallinity fraction
- [Polymerization Kinetics & Chain Growth](/lab/polymer-science/polymerization-kinetics): Simulate free-radical polymerization — explore how initiator concentration, rate constants, and temperature control molecular weight and conversion over time
- [Rubber Elasticity & Entropic Springs](/lab/polymer-science/rubber-elasticity): Simulate rubber elasticity — explore how crosslink density, temperature, chain length, and strain produce the unique stress-strain behavior of elastomeric networks
- [Viscoelasticity & Stress Relaxation](/lab/polymer-science/viscoelasticity): Simulate viscoelastic behavior — explore how elastic modulus, viscosity, strain rate, and temperature produce creep, relaxation, and hysteresis in polymers

### Stereochemistry & Molecular Chirality (5 simulations)
- [Chirality Center: R/S Configuration & CIP Rules](/lab/stereochemistry/chirality-center): Assign R/S configuration at a chiral center using Cahn-Ingold-Prelog priority rules with interactive 3D-style visualization
- [Conformational Analysis & Newman Projections](/lab/stereochemistry/conformational-analysis): Visualize Newman projections and rotational energy barriers for ethane and substituted alkanes with animated dihedral rotation
- [Enantiomer Separation & Chiral Resolution](/lab/stereochemistry/enantiomer-separation): Simulate chiral resolution methods and calculate enantiomeric excess from chromatographic peak areas with real-time visualization
- [Fischer Projection & Sugar Stereochemistry](/lab/stereochemistry/fischer-projection): Build Fischer projections of aldoses and explore D/L notation with interactive carbon chain configuration and sugar classification
- [Optical Rotation & Polarimetry](/lab/stereochemistry/optical-rotation): Measure specific rotation and optical activity of chiral compounds using a virtual polarimeter with animated light polarization

### Surface Chemistry & Adsorption (5 simulations)
- [BET Isotherm & Multilayer Adsorption](/lab/surface-chemistry/bet-isotherm): Simulate the BET multilayer adsorption model — explore how relative pressure and BET constant determine surface area and layer formation
- [Contact Angle & Wettability](/lab/surface-chemistry/contact-angle): Simulate wettability using Young's equation — explore how surface energies determine contact angle and droplet shape
- [Heterogeneous Catalysis & Sabatier Principle](/lab/surface-chemistry/heterogeneous-catalysis): Simulate heterogeneous catalysis — explore the volcano plot, Sabatier principle, and how binding energy controls catalytic activity
- [Langmuir Isotherm & Monolayer Adsorption](/lab/surface-chemistry/langmuir-isotherm): Simulate the Langmuir adsorption isotherm — explore how pressure, binding energy, and temperature control monolayer surface coverage
- [Surface Tension, Laplace Pressure & Capillary Rise](/lab/surface-chemistry/surface-tension): Simulate surface tension effects — explore Laplace pressure in bubbles and capillary rise in narrow tubes

### Tribochemistry & Surface Reactions (5 simulations)
- [Flash Temperature at Sliding Contacts](/lab/tribochemistry/flash-temperature): Simulate transient flash temperatures at asperity contacts — explore how sliding velocity, friction coefficient, load, and thermal conductivity determine the extreme temperature spikes that drive trib
- [Friction Energy Dissipation](/lab/tribochemistry/friction-energy): Simulate frictional energy budgets — explore how normal load, sliding velocity, and friction coefficient partition energy into heat, plastic deformation, and chemical activation at a tribological cont
- [Mechanochemical Reaction Kinetics](/lab/tribochemistry/mechanochemical-reaction): Simulate mechanochemical bond activation — explore how shear stress, temperature, and contact pressure lower reaction barriers and drive tribochemical transformations at sliding interfaces
- [Tribofilm Growth Dynamics](/lab/tribochemistry/tribofilm-growth): Simulate protective tribofilm formation — explore how contact pressure, temperature, additive concentration, and sliding cycles govern the nucleation and growth of tribochemical surface films
- [Wear Debris Generation & Morphology](/lab/tribochemistry/wear-debris): Simulate wear particle formation — explore how load, hardness ratio, sliding distance, and wear mechanism govern the size, shape, and volume of debris ejected from tribological contacts

## computer-science (13 topics, 64 simulations)

### AI Risk & Alignment (4 simulations)
- [AI Governance Race Dynamics Simulator](/lab/ai-risk/ai-governance-race): Model the multi-actor AI development race where competitive pressure, safety investment, and international coordination determine catastrophic risk. Explore how race dynamics create collective action 
- [Alignment Tax Calculator](/lab/ai-risk/alignment-tax): Quantify the tradeoff between AI capability and safety. The 'alignment tax' is the capability cost of building safe AI systems. This simulator models how alignment overhead affects capability growth, 
- [Intelligence Explosion Simulator](/lab/ai-risk/intelligence-explosion): Explore recursive self-improvement dynamics and the conditions under which artificial intelligence undergoes slow, exponential, or hyperbolic (FOOM) takeoff. Based on I.J. Good's intelligence explosio
- [Mesa-Optimization & Goodhart's Law Simulator](/lab/ai-risk/mesa-optimization): Visualize how optimizing a proxy objective diverges from the true objective under distribution shift, and how mesa-optimizers can become deceptively aligned when capability exceeds oversight. Combines

### Animation Physics & Simulation (5 simulations)
- [Bezier Curve Animation Paths Simulator](/lab/animation-physics/bezier-curves): Design and visualize cubic Bezier curves used for animation easing, motion paths, and vector graphics — drag control points and see De Casteljau's algorithm in action
- [Cloth Simulation With Constraints Simulator](/lab/animation-physics/cloth-simulation): Drape a particle-based cloth mesh over obstacles using distance constraints and Verlet integration — the technique behind capes, flags, and fabric in real-time graphics
- [Particle System Effects Simulator](/lab/animation-physics/particle-effects): Spawn, animate, and blend thousands of particles to create fire, smoke, sparks, and explosions — the visual effects system powering every game engine
- [Ragdoll Physics Joint Constraints Simulator](/lab/animation-physics/ragdoll-physics): Build and simulate a ragdoll skeleton with angular joint constraints — the physics system that makes characters tumble, collapse, and react to impacts in games
- [Spring Dynamics & Verlet Integration Simulator](/lab/animation-physics/spring-dynamics): Simulate spring-mass systems using Verlet integration — the stable numerical method behind hair, jelly, and soft-body physics in games and film

### Automata Theory & Formal Languages (5 simulations)
- [Cellular Automata & Emergent Complexity](/lab/automata-theory/cellular-automata): Explore 1D and 2D cellular automata — watch simple local rules generate fractals, gliders, and Turing-complete computation from random initial conditions
- [Deterministic Finite Automaton (DFA)](/lab/automata-theory/finite-automaton): Build and animate a deterministic finite automaton — watch states transition on input symbols, visualize acceptance and rejection of strings in real time
- [Pushdown Automaton & Context-Free Parsing](/lab/automata-theory/pushdown-automaton): Animate a pushdown automaton with a visible stack — trace how it recognizes nested parentheses, palindromes, and context-free grammars symbol by symbol
- [Regular Expressions & Pattern Matching](/lab/automata-theory/regular-expressions): Visualize how a regular expression compiles to an NFA and matches strings — watch states activate as the engine processes each character
- [Turing Machine & Universal Computation](/lab/automata-theory/turing-machine): Program a single-tape Turing machine — watch the head read, write, and move across an infinite tape as it computes step by step

### Computer Science (5 simulations)
- [A* Pathfinding Visualizer](/lab/computer-science/pathfinding): Watch A*, Dijkstra, and BFS explore a grid to find the shortest path — see how heuristics dramatically reduce search space
- [Binary Search vs Linear Search](/lab/computer-science/binary-search): Race binary search against linear search to see why halving the search space is exponentially faster than scanning one by one
- [Conway's Game of Life](/lab/computer-science/game-of-life): Watch complexity emerge from four simple rules — gliders, oscillators, and spaceships in the most famous cellular automaton
- [Hash Table Collision Visualization](/lab/computer-science/hash-table): See how hash functions map keys to buckets and how collisions are resolved through chaining or open addressing
- [Sorting Algorithm Race](/lab/computer-science/sorting-algorithms): Watch sorting algorithms race in real time — see why O(n log n) beats O(n²) as arrays grow larger

### Cryptocurrency & Blockchain (5 simulations)
- [Blockchain Mining Simulator](/lab/cryptocurrency/blockchain-mining): Mine blocks interactively — adjust hash rate, difficulty, and block size to see how miners compete to extend the blockchain
- [Consensus Algorithm Visualizer](/lab/cryptocurrency/consensus-algorithm): Watch distributed nodes reach consensus — simulate message passing, Byzantine faults, and finality in real-time network animations
- [Cryptographic Hash Function Explorer](/lab/cryptocurrency/hash-function): Explore cryptographic hash functions — visualize the avalanche effect, collision resistance, and bit distribution as you modify inputs character by character
- [Merkle Tree Builder](/lab/cryptocurrency/merkle-tree): Build a Merkle tree from transactions — visualize hash propagation, verify inclusion proofs, and understand how blockchains compress transaction integrity
- [Proof-of-Work Puzzle](/lab/cryptocurrency/proof-of-work): Solve proof-of-work puzzles interactively — watch nonce iteration, hash computation, and difficulty target comparison in real time

### Cryptography (5 simulations)
- [Caesar Cipher Visualizer](/lab/cryptography/caesar-cipher): Explore the oldest known encryption — rotate alphabet rings and watch plaintext transform into ciphertext with this interactive Caesar cipher.
- [Cryptographic Hash Visualizer](/lab/cryptography/hash-function): See why cryptographic hashes are one-way streets — watch the avalanche effect flip half the bits from a single input change.
- [Diffie-Hellman Key Exchange](/lab/cryptography/diffie-hellman): Watch Alice and Bob agree on a shared secret over a public channel — the magic of Diffie-Hellman key exchange visualized step by step.
- [One-Time Pad / Perfect Secrecy](/lab/cryptography/one-time-pad): The only provably unbreakable cipher — see how XOR with a random key creates perfect secrecy, and why key reuse destroys it.
- [RSA Public Key Encryption](/lab/cryptography/rsa-encryption): Watch how two prime numbers create a public-private key pair and encrypt a message step by step using RSA.

### Data Science & Machine Learning (5 simulations)
- [Decision Tree Classifier](/lab/data-science/decision-tree): Watch a decision tree carve feature space into regions — see how splits are chosen to maximize information gain and classify data
- [Gradient Descent Optimization](/lab/data-science/gradient-descent): Watch gradient descent navigate a loss landscape — see how learning rate and momentum affect convergence to the minimum of a function
- [K-Means Clustering Algorithm](/lab/data-science/k-means-clustering): Watch K-means discover clusters in real time — see centroids shift and data points reassign as the algorithm converges to a partition
- [Linear Regression & Least Squares Fit](/lab/data-science/linear-regression): Watch a regression line snap to data points in real time — explore how least squares minimization finds the best-fit line through noisy data
- [PCA Dimensionality Reduction](/lab/data-science/pca-reduction): Watch PCA compress high-dimensional data into its essential components — see eigenvectors emerge and variance explained accumulate

### Game Design & Systems (5 simulations)
- [2D Physics Engine (Rigid Body Collisions)](/lab/game-design/physics-engine): Simulate rigid body physics with gravity, elasticity, and friction — see how real-time collision detection and resolution work under the hood
- [Dynamic Difficulty Adjustment Curve](/lab/game-design/difficulty-curve): Visualize how difficulty curves shape player engagement — from linear ramps to adaptive systems that respond to player skill
- [Loot Table Probability & Drop Rates](/lab/game-design/loot-tables): Simulate thousands of loot drops to visualize how weighted probability tables create the reward psychology behind every RPG and looter game
- [Navigation Mesh Pathfinding (A*)](/lab/game-design/pathfinding-navmesh): Visualize A* pathfinding on a navigation mesh grid — watch how obstacles, heuristics, and grid size affect NPC pathfinding in real time
- [Procedural Terrain Generation (Perlin Noise)](/lab/game-design/procedural-generation): Generate infinite terrain landscapes using layered Perlin noise — the algorithm behind Minecraft, No Man's Sky, and countless open-world games

### Logic Circuits & Digital Systems (5 simulations)
- [Boolean Logic Gates Simulator](/lab/logic-circuits/boolean-gates): Visualize AND, OR, NOT, XOR, and NAND gates in real time — toggle inputs and watch outputs change instantly to build intuition for digital logic
- [Finite State Machine Simulator](/lab/logic-circuits/finite-automaton): Design and run finite automata — define states and transitions, feed input strings, and watch the machine accept or reject patterns in real time
- [Half Adder & Full Adder Circuit Simulator](/lab/logic-circuits/half-adder): Watch binary addition happen gate-by-gate — see carry bits propagate through half adders and full adders to build multi-bit arithmetic
- [SR & JK Flip-Flop Memory Circuit Simulator](/lab/logic-circuits/flip-flop): Observe how flip-flops store a single bit of memory — toggle Set, Reset, and Clock inputs to see state transitions in SR and JK circuits
- [Truth Table Generator & Evaluator](/lab/logic-circuits/truth-table): Generate and visualize truth tables for any combination of Boolean operations — see every possible input-output mapping at a glance

### Machine Learning & AI Algorithms (5 simulations)
- [Decision Tree Classifier Visualizer](/lab/machine-learning/decision-tree): Grow a decision tree on 2D data — adjust tree depth, split criteria, and data complexity to see how the tree partitions feature space
- [Gradient Descent Optimizer Visualizer](/lab/machine-learning/gradient-descent): Watch gradient descent navigate a 2D loss landscape — adjust learning rate, momentum, and surface shape to see convergence, oscillation, and divergence
- [K-Means Clustering Visualizer](/lab/machine-learning/clustering): Watch k-means clustering assign points to clusters — adjust k, data distribution, and initialization to see centroid convergence and Voronoi partitions
- [Neural Network Forward Pass Visualizer](/lab/machine-learning/neural-network): Build a neural network and watch activations propagate — adjust layer sizes, activation functions, and input values to see how networks transform data
- [Overfitting & Bias-Variance Tradeoff](/lab/machine-learning/overfitting): Explore overfitting by fitting polynomials to noisy data — adjust model complexity, data size, and noise to see training vs test error diverge

### Neuromorphic Computing (5 simulations)
- [Memristor Crossbar Array](/lab/neuromorphic-computing/memristor-crossbar): Simulate a memristive crossbar array — explore how conductance states, voltage pulses, and array size enable analog matrix-vector multiplication for neural networks
- [Neuromorphic Vision (Event Camera)](/lab/neuromorphic-computing/neuromorphic-vision): Simulate a neuromorphic event camera — explore how contrast threshold, pixel bandwidth, and latency enable microsecond-resolution motion capture with minimal data
- [Reservoir Computing (Echo State Network)](/lab/neuromorphic-computing/reservoir-computing): Simulate a reservoir computer — explore how recurrent network size, spectral radius, and input scaling transform temporal signals into linearly separable representations
- [Spike-Timing-Dependent Plasticity (STDP)](/lab/neuromorphic-computing/stdp-learning): Simulate STDP learning — explore how the relative timing of pre- and post-synaptic spikes strengthens or weakens synaptic connections
- [Spiking Neuron Model (LIF)](/lab/neuromorphic-computing/spiking-neuron): Simulate a leaky integrate-and-fire neuron — explore how input current, membrane time constant, and threshold voltage shape spike trains in neuromorphic hardware

### Quantum Computing & Qubits (5 simulations)
- [Quantum Entanglement & Bell States](/lab/quantum-computing/quantum-entanglement): Simulate quantum entanglement between two qubits — explore Bell states, CHSH inequality violations, and spooky action at a distance with real-time correlation analysis
- [Quantum Error Correction Codes](/lab/quantum-computing/quantum-error-correction): Simulate quantum error correction — explore how surface codes, Shor codes, and Steane codes detect and fix bit-flip and phase-flip errors on encoded logical qubits
- [Quantum Gates & Circuit Operations](/lab/quantum-computing/quantum-gates): Simulate quantum gate operations on a qubit — apply Hadamard, Pauli, and phase gates and watch the state vector rotate on the Bloch sphere in real time
- [Qubit Bloch Sphere Visualization](/lab/quantum-computing/qubit-bloch-sphere): Visualize a single qubit state on the Bloch sphere — explore how polar and azimuthal angles map to superposition amplitudes and measurement probabilities
- [Shor's Algorithm & Integer Factoring](/lab/quantum-computing/shor-algorithm): Simulate Shor's quantum factoring algorithm — explore how quantum Fourier transforms find the period of modular exponentiation to factor integers exponentially faster than classical methods

### Swarm Intelligence & Collective Behavior (5 simulations)
- [Ant Colony Optimization Pathfinding](/lab/swarm-intelligence/ant-colony): Watch virtual ants find the shortest path using pheromone trails — explore how evaporation rate, colony size, and pheromone influence shape emergent optimization
- [Bee Foraging & Waggle Dance Optimization](/lab/swarm-intelligence/bee-foraging): Model honey bee foraging strategy — explore how scout bees, waggle dance recruitment, and nectar quality drive optimal resource allocation across multiple food sources
- [Boid Flocking: Emergent Collective Motion](/lab/swarm-intelligence/boid-flocking): Simulate Reynolds' boid flocking — explore how three simple rules (separation, alignment, cohesion) generate realistic bird-flock and fish-school behavior
- [Firefly Algorithm: Light-Based Optimization](/lab/swarm-intelligence/firefly-algorithm): Visualize firefly agents synchronizing and converging on optima — explore how brightness attraction, light absorption, and randomness drive multi-modal optimization
- [Particle Swarm Optimization on Function Landscapes](/lab/swarm-intelligence/particle-swarm): Visualize particles swarming across a 2D fitness landscape — explore how inertia, cognitive pull, and social pull guide the swarm toward global optima

## cosmology (3 topics, 21 simulations)

### Astronomy (6 simulations)
- [Cosmic Microwave Background](/lab/astronomy/cosmic-microwave): Explore the cosmic microwave background radiation — the oldest light in the universe — and its blackbody spectrum that reveals conditions moments after the Big Bang.
- [Exoplanet Transit Detection](/lab/astronomy/exoplanet-transit): Simulate how astronomers detect exoplanets by measuring the tiny dip in starlight as a planet crosses in front of its host star.
- [Galaxy Rotation Curves & Dark Matter](/lab/astronomy/galaxy-rotation): Visualize how galaxy rotation curves deviate from Newtonian predictions, providing compelling evidence for dark matter halos surrounding galaxies.
- [Hertzsprung-Russell Diagram](/lab/astronomy/hr-diagram): Explore the HR diagram — the astronomer's most powerful tool. Plot hundreds of stars by temperature and luminosity, and watch how cluster age determines the main sequence turnoff point.
- [Hubble's Law & Universe Expansion](/lab/astronomy/hubble-expansion): Explore how galaxies recede faster with distance, revealing the expansion of the universe through Hubble's Law and the cosmological redshift.
- [Star Life Cycle](/lab/astronomy/stellar-evolution): Watch a star evolve from birth to death. Adjust mass and metallicity to see how different stars live, age, and ultimately end as white dwarfs, neutron stars, or black holes.

### Black Holes (4 simulations)
- [Gravitational Lensing Simulator](/lab/black-holes/gravitational-lensing): Visualize how massive objects bend light, creating Einstein rings and gravitational arcs from distant sources
- [Hawking Radiation Simulator](/lab/black-holes/hawking-radiation): Explore how black holes emit thermal radiation and slowly evaporate, with temperature, luminosity, and lifetime calculations
- [Schwarzschild Radius Calculator](/lab/black-holes/schwarzschild-radius): Interactive simulator for calculating the event horizon size of a black hole using the Schwarzschild metric
- [Tidal Forces & Spaghettification Simulator](/lab/black-holes/tidal-forces): Visualize how tidal forces near a black hole stretch and compress objects, leading to the phenomenon of spaghettification

### Fermi Paradox (11 simulations)
- [Civilization Self-Destruction Probability](/lab/fermi-paradox/self-destruction): Estimating the probability of a technological civilization's self-destruction across various scenarios
- [Dark Forest Game Theory](/lab/fermi-paradox/dark-forest): Game theory: why civilizations may hide from each other in the cosmos
- [Drake Equation Calculator](/lab/fermi-paradox/drake-equation): Interactive calculator for estimating the number of civilizations in the Galaxy using the Drake Equation
- [Earth's Light Cone Visualization](/lab/fermi-paradox/light-cone): How far our radio signals have traveled into space in over 100 years
- [Galaxy Colonization Simulation](/lab/fermi-paradox/galaxy-colonization): Visualization of a galactic colonization wave traveling at 0.1–2% the speed of light
- [Grabby Aliens Expansion Model](/lab/fermi-paradox/grabby-aliens): Robin Hanson's model: how 'grabby' civilizations divide the universe among themselves
- [Great Filter Probability Cascade](/lab/fermi-paradox/great-filter): Probability funnel: from dead matter to a starfaring civilization
- [Humanity's Radio Bubble Scale](/lab/fermi-paradox/radio-bubble): Scale visualization: the size of our radio bubble relative to the Galaxy and the universe
- [Kardashev Scale Slider](/lab/fermi-paradox/kardashev-scale): Interactive scale of civilizations classified by energy consumption level (Type I, II, III)
- [SETI Detection Probability (Monte Carlo)](/lab/fermi-paradox/seti-monte-carlo): Monte Carlo simulation: what is the probability of detecting an extraterrestrial signal with SETI?
- [Zoo Hypothesis Decision Tree](/lab/fermi-paradox/zoo-hypothesis): Decision tree: classifying hypotheses about why the aliens are silent

## earth-science (3 topics, 11 simulations)

### Climate Science (4 simulations)
- [Carbon Cycle Simulator](/lab/climate-science/carbon-cycle): Model the global carbon cycle as a box model with atmosphere, ocean, land, and fossil fuel reservoirs. Explore how emission rates, ocean uptake, and deforestation determine atmospheric CO₂ concentrati
- [Greenhouse Effect Simulator](/lab/climate-science/greenhouse-effect): Explore how CO₂ concentration, solar radiation, and albedo determine Earth's surface temperature through the greenhouse effect. Based on the Stefan-Boltzmann radiation law with optical depth parameter
- [Ice-Albedo Feedback Simulator](/lab/climate-science/ice-albedo-feedback): Visualize the ice-albedo positive feedback loop: warming melts ice, exposing dark ocean and land, which absorbs more radiation, causing further warming. Compare temperature trajectories with and witho
- [Sea Level Rise Simulator](/lab/climate-science/sea-level-rise): Model multi-component sea level rise from thermal expansion, glacier melt, and ice sheet disintegration. Visualize how warming scenarios translate to coastline flooding and understand why ice sheet co

### Earth Science (2 simulations)
- [Coriolis Effect & Weather Patterns Simulator](/lab/earth-science/coriolis-effect): Watch how Earth's rotation deflects moving objects — explore the Coriolis effect that creates hurricanes, trade winds, and the great ocean circulation patterns
- [Seismic Wave Propagation Simulator](/lab/earth-science/earthquake-waves): Trace P-waves and S-waves through Earth's layered interior — watch how seismic waves reveal the planet's hidden structure from crust to core

### Oceanography & Marine Science (5 simulations)
- [Coral Bleaching & Temperature Stress Simulator](/lab/oceanography/coral-bleaching): Model coral bleaching events — adjust sea surface temperature, duration, and recovery time to see threshold effects on reef health
- [Global Ocean Circulation Patterns](/lab/oceanography/ocean-currents): Visualize global ocean currents driven by wind, Coriolis force, and temperature gradients — watch gyres form and heat move from equator to poles
- [Lunar Tidal Forces & Cycles](/lab/oceanography/tidal-forces-moon): Visualize how the Moon's gravity creates tidal bulges on Earth — explore spring tides, neap tides, and the 12.42-hour tidal cycle
- [Ocean Wave Dynamics & Dispersion](/lab/oceanography/wave-dynamics): Model ocean wave propagation — adjust wind speed, fetch, and depth to see how waves form, grow, disperse, and break approaching shore
- [Thermohaline Conveyor Belt Simulator](/lab/oceanography/thermohaline-circulation): Trace the global thermohaline circulation — watch dense cold water sink in the North Atlantic and travel the ocean floor for a thousand-year journey

## earth-sciences (23 topics, 115 simulations)

### Biogeochemistry & Nutrient Cycles (5 simulations)
- [Global Carbon Cycle Model](/lab/biogeochemistry/carbon-cycle): Model Earth's carbon cycle — explore how fossil fuel emissions, photosynthesis, ocean absorption, and volcanism control atmospheric CO₂ and climate over decades to millennia
- [Nitrogen Cycle & Fixation Model](/lab/biogeochemistry/nitrogen-cycle): Model the nitrogen cycle — explore biological fixation, nitrification, denitrification, and anthropogenic inputs that drive eutrophication and N₂O emissions
- [Ocean Biological Carbon Pump](/lab/biogeochemistry/ocean-carbon-pump): Model the ocean biological carbon pump — explore how phytoplankton productivity, sinking particle flux, and deep ocean circulation sequester carbon from the atmosphere
- [Phosphorus Cycle & Weathering](/lab/biogeochemistry/phosphorus-cycle): Model the phosphorus cycle — explore weathering inputs, biological uptake, sedimentation, and anthropogenic mining that control phosphorus availability and eutrophication
- [Sulfur Cycle & Redox Chemistry](/lab/biogeochemistry/sulfur-cycle): Model the sulfur cycle — explore volcanic emissions, biological reduction, acid rain formation, and ocean sulfate dynamics across oxidation states from S²⁻ to SO₄²⁻

### Dendrochronology & Tree-Ring Science (5 simulations)
- [Annual Ring Width & Climate Proxy](/lab/dendrochronology/ring-width): Simulate annual tree-ring growth as a function of temperature, precipitation, and tree age — explore how climate signals are encoded in ring widths
- [Crossdating & Master Chronology](/lab/dendrochronology/crossdating): Simulate crossdating by sliding two ring-width series to find the optimal match position using correlation analysis
- [Fire History from Scar Analysis](/lab/dendrochronology/fire-scar): Simulate fire scar frequency analysis — explore how fire return intervals, drought cycles, and suppression affect wildfire regimes recorded in tree rings
- [Radiocarbon Calibration with Tree Rings](/lab/dendrochronology/radiocarbon-calibration): Simulate the calibration of radiocarbon dates using the tree-ring calibration curve to convert 14C years to calendar years
- [Temperature Reconstruction from Ring-Width Index](/lab/dendrochronology/climate-reconstruction): Simulate paleoclimate temperature reconstruction using linear regression transfer functions between ring-width indices and instrumental temperature

### Environmental Science & Pollution (5 simulations)
- [Air Quality Index (AQI) Simulator](/lab/environmental-science/air-quality): Model air quality under varying pollutant concentrations — compute AQI from PM2.5, ozone, NO₂, and SO₂ levels and visualize health impact zones
- [Biodiversity Index Calculator](/lab/environmental-science/biodiversity-index): Calculate Shannon, Simpson, and species richness indices — visualize species abundance distributions and compare ecosystem health metrics
- [Carbon Cycle & CO₂ Flux Simulator](/lab/environmental-science/carbon-cycle): Model the global carbon cycle — adjust emission rates, deforestation, and ocean uptake to see how atmospheric CO₂ evolves over decades
- [Soil Contamination & Plume Transport](/lab/environmental-science/soil-contamination): Simulate contaminant transport through soil — model advection, dispersion, and adsorption of pollutant plumes in groundwater systems
- [Water Treatment Process Simulator](/lab/environmental-science/water-treatment): Design a multi-stage water treatment plant — adjust coagulation, filtration, and disinfection parameters to see removal efficiency for turbidity, pathogens, and contaminants

### Fluvial Geomorphology & River Dynamics (5 simulations)
- [Alluvial Fan Deposition & Morphology](/lab/fluvial-geomorphology/alluvial-fan): Simulate alluvial fan formation — explore how sediment supply, discharge, and slope control fan radius, gradient, and depositional patterns
- [Hydraulic Geometry & Channel Scaling](/lab/fluvial-geomorphology/hydraulic-geometry): Simulate hydraulic geometry relationships — explore how discharge controls channel width, depth, and velocity through power-law scaling
- [Knickpoint Retreat & Bedrock Incision](/lab/fluvial-geomorphology/knickpoint-retreat): Simulate knickpoint retreat — explore how bedrock strength, stream power, and drainage area control the upstream migration of waterfalls and river knickpoints
- [Meander Migration & Channel Evolution](/lab/fluvial-geomorphology/meander-migration): Simulate river meander migration — explore how flow velocity, bank erodibility, and channel curvature drive lateral channel movement and oxbow lake formation
- [Stream Power & Erosion Potential](/lab/fluvial-geomorphology/stream-power): Simulate stream power — explore how discharge, channel slope, and width determine a river's erosive capacity and sediment transport potential

### Geomorphology & Landscape Evolution (5 simulations)
- [Alluvial Fan Formation & Sediment Deposition](/lab/geomorphology/alluvial-fan): Simulate alluvial fan growth — explore how sediment supply, water discharge, and slope control fan morphology, radius, and depositional patterns
- [Coastal Erosion & Cliff Retreat](/lab/geomorphology/coastal-erosion): Simulate wave-driven coastal erosion — explore how wave energy, rock strength, and sea level control cliff retreat rates and shore platform development
- [Glacial Erosion & U-Valley Formation](/lab/geomorphology/glacial-landforms): Simulate glacial valley carving — explore how ice thickness, sliding velocity, and bedrock hardness produce characteristic U-shaped valley cross-sections
- [Hillslope Diffusion & Soil Creep](/lab/geomorphology/hillslope-diffusion): Simulate hillslope evolution via diffusive soil creep — explore how diffusivity, slope, and uplift shape hill profiles over geological time
- [River Erosion & Channel Incision](/lab/geomorphology/river-erosion): Simulate stream power erosion — explore how river discharge, slope, and rock erodibility control channel incision rates and valley formation

### Geophysics & Earth Structure (5 simulations)
- [Earth's Magnetic Field & Geodynamo](/lab/geophysics/magnetic-field): Visualize Earth's dipolar magnetic field, explore how core convection speed, core radius, and conductivity affect field strength, and observe field line geometry from pole to equator.
- [Gravity Anomaly Modeling](/lab/geophysics/gravity-anomaly): Model Bouguer and free-air gravity anomalies over subsurface density contrasts, visualizing how buried structures like ore bodies, basins, and plutons create measurable gravitational signatures.
- [Isostatic Equilibrium](/lab/geophysics/isostasy): Explore Airy and Pratt isostasy models showing how continental and oceanic crust float on the denser mantle, with adjustable crustal thickness, density, and surface topography.
- [Mantle Convection Simulation](/lab/geophysics/mantle-convection): Simulate thermally driven convection in Earth's mantle, exploring how Rayleigh number, viscosity, and internal heating control convection cell geometry, surface heat flow, and plate velocities.
- [Seismic Wave Propagation](/lab/geophysics/seismic-waves): Visualize P-wave and S-wave propagation through Earth's layered interior, showing refraction, reflection, and shadow zones created by the liquid outer core.

### Glaciology & Ice Dynamics (5 simulations)
- [Glacier Flow & Ice Deformation](/lab/glaciology/glacier-flow): Simulate glacier flow dynamics — explore how ice thickness, slope, temperature, and Glen's flow law govern the creep and sliding of glaciers through mountain valleys
- [Ice Core Paleoclimate Analysis](/lab/glaciology/ice-core-analysis): Simulate ice core analysis — explore how trapped gas bubbles and isotope ratios in Antarctic and Greenland ice cores reveal 800,000 years of climate history
- [Iceberg Calving Dynamics](/lab/glaciology/iceberg-calving): Simulate iceberg calving from tidewater glaciers — explore how ice cliff height, water depth, crevasse penetration, and ocean temperature control the fracture and release of icebergs
- [Permafrost Thaw & Carbon Release](/lab/glaciology/permafrost-thaw): Simulate permafrost thaw dynamics — explore how rising temperatures, active layer deepening, and thermokarst formation drive carbon and methane release from frozen ground
- [Sea Ice Extent & Polar Feedback](/lab/glaciology/sea-ice-extent): Simulate Arctic and Antarctic sea ice extent — explore how temperature, albedo feedback, ocean heat transport, and seasonal cycles govern polar ice coverage

### Hydrology & Water Systems (5 simulations)
- [Evapotranspiration & Water Budget](/lab/hydrology/evapotranspiration): Simulate evapotranspiration rates using the Penman-Monteith method — explore temperature, solar radiation, wind speed, and humidity to estimate water loss from vegetated surfaces
- [Flood Wave Routing & Attenuation](/lab/hydrology/flood-routing): Simulate flood wave propagation through a river channel — explore inflow peak, channel storage, travel time, and weighting factor to predict downstream hydrograph attenuation
- [Groundwater Flow & Aquifer Dynamics](/lab/hydrology/groundwater-flow): Simulate groundwater flow through porous media — explore hydraulic conductivity, head gradient, porosity, and aquifer thickness to visualize Darcy flow and drawdown cones
- [Integrated Watershed Model](/lab/hydrology/watershed-model): Simulate an integrated watershed water balance — explore precipitation, land use, soil type, and slope to track partitioning between runoff, infiltration, ET, and baseflow
- [Rainfall-Runoff Response Model](/lab/hydrology/rainfall-runoff): Simulate how precipitation transforms into surface runoff — explore rainfall intensity, soil infiltration capacity, curve number, and basin lag to predict hydrograph shape

### Isotope Geochemistry (5 simulations)
- [Cosmogenic Nuclide Exposure Dating](/lab/isotope-geochemistry/cosmogenic-nuclide): Simulate cosmogenic nuclide production and exposure age calculation — explore how cosmic ray flux, altitude, latitude, and erosion rate control surface exposure dating
- [Isochron Method & Age Determination](/lab/isotope-geochemistry/isochron-method): Simulate the isochron method — explore how multiple samples with different Rb/Sr ratios define a line whose slope reveals the rock's age
- [Isotope Mixing Models](/lab/isotope-geochemistry/isotope-mixing): Simulate isotopic mixing between two or three end-members — explore how mixing proportions and end-member compositions produce hyperbolic mixing arrays in isotope space
- [Radiometric Dating & Decay Curves](/lab/isotope-geochemistry/radiometric-dating): Simulate radioactive decay and age determination — explore how half-life, parent-daughter ratios, and decay constants constrain the ages of rocks and minerals
- [Stable Isotope Fractionation](/lab/isotope-geochemistry/stable-isotope-fractionation): Simulate equilibrium and kinetic isotope fractionation — explore how temperature, mass difference, and reaction kinetics partition stable isotopes between phases

### Limnology & Freshwater Science (5 simulations)
- [Dissolved Oxygen Depth Profile](/lab/limnology/oxygen-profile): Model how dissolved oxygen varies with depth in a stratified lake, from supersaturated surface waters to anoxic hypolimnion
- [Eutrophication & Algal Bloom Dynamics](/lab/limnology/eutrophication): Model nutrient loading from agricultural runoff and watch algal blooms develop, collapse, and create oxygen dead zones in a lake
- [Lake Sediment Core Dating & Proxy Records](/lab/limnology/sediment-core): Explore how lake sediment layers record environmental history through radiometric dating, pollen, diatoms, and geochemical proxies
- [Lake Thermal Stratification & Turnover](/lab/limnology/thermal-stratification): Visualize how temperature layers form in lakes through seasonal heating and wind mixing, including spring and fall turnover events
- [Lake Water Balance & Residence Time](/lab/limnology/water-budget): Calculate a lake's water budget from precipitation, evaporation, inflow, and outflow — and determine how long water stays in the lake

### Meteorology & Weather Systems (5 simulations)
- [Atmospheric Pressure & Barometric Formula Simulator](/lab/meteorology/atmospheric-pressure): Explore how atmospheric pressure decreases with altitude using the barometric formula, and understand the physics behind weather systems
- [Cloud Classification & Altitude Simulator](/lab/meteorology/cloud-types): Explore the 10 cloud genera classified by altitude and formation process — from low stratus to towering cumulonimbus
- [Cold & Warm Front Dynamics Simulator](/lab/meteorology/weather-fronts): Visualize the collision of cold and warm air masses, observe frontal lifting, and see how precipitation forms along weather fronts
- [Hurricane Structure & Saffir-Simpson Scale Simulator](/lab/meteorology/hurricane-structure): Explore hurricane anatomy from eye to rainbands, adjust sea-surface temperature and wind shear to see how hurricanes intensify or weaken
- [Tornado Formation & Mesocyclone Simulator](/lab/meteorology/tornado-formation): Watch a mesocyclone develop from wind shear and updraft interaction, and see how tornadoes form from rotating supercell thunderstorms

### Ocean Acoustics & Underwater Sound (5 simulations)
- [Ocean Acoustic Tomography](/lab/ocean-acoustics/acoustic-tomography): Simulate acoustic tomography of the ocean — send sound pulses between transceiver pairs and reconstruct temperature fields from travel time perturbations
- [Ocean Ambient Noise Spectrum](/lab/ocean-acoustics/ambient-noise): Simulate the ocean ambient noise spectrum — explore how wind speed, shipping density, sea state, and rain contribute to the underwater noise floor across frequency
- [SOFAR Channel & Deep Sound Propagation](/lab/ocean-acoustics/sofar-channel): Simulate the SOFAR (Sound Fixing and Ranging) channel — explore how the ocean's sound speed minimum traps acoustic energy and allows propagation over thousands of kilometers
- [Sonar Equation & Detection Range](/lab/ocean-acoustics/sonar-equation): Simulate the sonar equation — balance source level, transmission loss, target strength, noise level, and detection threshold to determine maximum sonar detection range
- [Underwater Acoustic Ray Tracing](/lab/ocean-acoustics/ray-tracing): Simulate acoustic ray tracing in a layered ocean — launch sound rays at various angles and watch them refract through the sound speed profile, revealing shadow zones and convergence zones

### Paleoceanography & Ocean History (5 simulations)
- [CCD Depth & Lysocline](/lab/paleoceanography/carbonate-compensation): Explore the carbonate compensation depth — the ocean floor below which calcium carbonate dissolves faster than it accumulates, controlled by CO₂, temperature, and ocean chemistry
- [Eustatic Sea Level Reconstruction](/lab/paleoceanography/sea-level-curve): Reconstruct eustatic sea-level curves from ice volume, thermal expansion, and tectonic factors — visualize how global sea level has changed over geological time
- [Oceanic Anoxic Events & Black Shale](/lab/paleoceanography/ocean-anoxia): Model the conditions that trigger oceanic anoxic events — explore how warming, nutrient loading, and circulation stagnation create oxygen-free oceans and deposit organic-rich black shales
- [Thermohaline Conveyor Belt & Shutdown Events](/lab/paleoceanography/thermohaline-history): Model the Atlantic thermohaline circulation and its sensitivity to freshwater forcing — explore how meltwater pulses triggered abrupt climate events like the Younger Dryas
- [δ18O & Ice Volume Proxy](/lab/paleoceanography/oxygen-isotope): Simulate how oxygen isotope ratios in foraminifera shells record past ice volume and ocean temperature — explore the relationship between δ18O, global ice sheets, and deep-sea temperatures

### Paleoclimate & Ancient Atmospheres (5 simulations)
- [CO₂ Proxy Reconstruction from Ice Cores](/lab/paleoclimate/co2-proxy): Reconstruct atmospheric CO₂ from ice core data — explore how bubble depth, temperature, and accumulation rate affect the CO₂ record over 800,000 years
- [Glacial-Interglacial Cycles & Ice Volume](/lab/paleoclimate/ice-age-cycles): Model the growth and retreat of continental ice sheets — explore how orbital forcing, CO₂ feedback, and albedo combine to produce glacial-interglacial oscillations
- [Milankovitch Cycles & Orbital Forcing](/lab/paleoclimate/milankovitch-cycles): Visualize Earth's orbital variations — eccentricity, obliquity, and precession — and their combined effect on insolation patterns over hundreds of thousands of years
- [Thermohaline Ocean Circulation & AMOC](/lab/paleoclimate/ocean-circulation): Model the Atlantic Meridional Overturning Circulation — explore how salinity, temperature, and freshwater forcing control deep water formation and heat transport
- [Volcanic Winter & Aerosol Cooling](/lab/paleoclimate/volcanic-winter): Simulate the climate impact of major volcanic eruptions — explore how sulfur emissions, plume height, and latitude affect global temperature through stratospheric aerosol forcing

### Paleomagnetism & Ancient Magnetic Fields (5 simulations)
- [Apparent Polar Wander Path](/lab/paleomagnetism/apparent-polar-wander): Trace apparent polar wander paths — explore how plate velocity, rotation rate, continent latitude, and geological time combine to produce the sweeping pole tracks that prove continental drift
- [Declination & Inclination Stereographic Projection](/lab/paleomagnetism/declination-inclination): Visualize paleomagnetic field directions on a stereographic projection — explore how declination, inclination, latitude, and Fisher precision parameter define field direction distributions and confide
- [Geomagnetic Polarity Reversal](/lab/paleomagnetism/magnetic-reversal): Simulate geomagnetic field reversals — explore how dipole strength, reversal rate, transition duration, and field asymmetry govern the polarity flip recorded in volcanic rocks and ocean sediments
- [Paleointensity & Ancient Field Strength](/lab/paleomagnetism/paleointensity): Simulate paleointensity determination — explore how NRM/TRM ratios, laboratory field strength, thermal alteration, and the Arai plot diagram reveal the strength of Earth's ancient magnetic field
- [Virtual Geomagnetic Pole (VGP)](/lab/paleomagnetism/virtual-geomagnetic-pole): Compute virtual geomagnetic poles from paleomagnetic directions — explore how site latitude, declination, and inclination map to pole positions on the globe using the geocentric axial dipole hypothesi

### Paleoseismology & Ancient Earthquakes (5 simulations)
- [Earthquake Recurrence Interval Simulator](/lab/paleoseismology/recurrence-interval): Simulate earthquake recurrence statistics — explore how mean interval, coefficient of variation, elapsed time, and record length affect probability estimates and hazard forecasts
- [Fault Slip Rate Calculator & Simulator](/lab/paleoseismology/slip-rate): Simulate long-term fault slip rate determination — explore how offset features, dating uncertainty, geodetic rates, and fault geometry constrain tectonic loading and earthquake potential
- [Fault Trench Stratigraphy Simulator](/lab/paleoseismology/fault-trenching): Simulate fault trench excavation — explore how displacement, sedimentation rate, number of events, and erosion affect the stratigraphic record of past earthquakes
- [Liquefaction Evidence Analysis Simulator](/lab/paleoseismology/liquefaction-evidence): Simulate earthquake-induced liquefaction — explore how peak ground acceleration, soil density, water table depth, and sand layer thickness determine liquefaction potential and feature size
- [Paleomagnitude Estimation Simulator](/lab/paleoseismology/magnitude-estimation): Simulate paleoearthquake magnitude estimation — explore how surface displacement, rupture length, fault type, and depth constrain magnitude from geological evidence

### Petrology & Rock Formation (5 simulations)
- [Igneous Crystallization & Bowen's Series](/lab/petrology/igneous-crystallization): Simulate magma cooling and watch minerals crystallize in Bowen's reaction series — explore how temperature, cooling rate, and silica content control igneous rock texture and composition
- [Metamorphic Grade & Facies Diagram](/lab/petrology/metamorphic-grade): Simulate pressure–temperature paths through metamorphic facies — explore how burial depth, geothermal gradient, and protolith composition determine metamorphic grade and mineral assemblages
- [Mineral Identification & Optical Properties](/lab/petrology/mineral-identification): Simulate polarized light microscopy — explore how birefringence, extinction angle, crystal system, and refractive index help identify rock-forming minerals in thin section
- [Sediment Transport & Deposition](/lab/petrology/sediment-transport): Simulate sediment entrainment and deposition in a river channel — explore how flow velocity, grain size, channel slope, and water depth control erosion, transport, and sedimentation
- [The Rock Cycle: Transform & Recycle](/lab/petrology/rock-cycle): Simulate the complete rock cycle — explore how weathering rate, tectonic uplift, burial depth, and heat flow drive transformations between igneous, sedimentary, and metamorphic rocks

### Plate Tectonics & Continental Drift (5 simulations)
- [Continental Drift: Plate Reconstruction & Pangaea](/lab/plate-tectonics/continental-drift): Reconstruct Earth's tectonic plates through deep time — watch continents assemble into Pangaea and drift apart to their present positions
- [Hotspot Volcanism: Mantle Plumes & Island Chains](/lab/plate-tectonics/hotspot-volcanism): Simulate a mantle plume creating a volcanic island chain as a tectonic plate drifts overhead — the Hawaiian model
- [Mantle Convection: Rayleigh-Bénard Cells in the Mantle](/lab/plate-tectonics/mantle-convection): Simulate thermal convection in Earth's mantle — Rayleigh number, convection cell patterns, and heat transport from core to surface
- [Mid-Ocean Ridge: Seafloor Spreading & Magnetic Stripes](/lab/plate-tectonics/mid-ocean-ridge): Simulate seafloor spreading at a mid-ocean ridge — new crust formation, magnetic polarity reversals, and symmetric stripe patterns
- [Subduction Zone: Oceanic-Continental Convergence](/lab/plate-tectonics/subduction-zone): Simulate an oceanic plate subducting beneath a continental plate — trench formation, volcanic arc, and Benioff zone seismicity

### Sedimentology & Stratigraphy (5 simulations)
- [Compaction & Porosity: Athy's Law of Burial](/lab/sedimentology/compaction-porosity): Model porosity reduction with burial depth using Athy's exponential compaction law — understand how sediments transform into rock and predict reservoir quality at depth
- [Grain Settling: Stokes Law & Reynolds Number](/lab/sedimentology/grain-settling): Simulate particle settling through water using Stokes law — explore how grain size, density, and fluid viscosity control settling velocity and sediment sorting
- [Sediment Transport: Shields Parameter & Bedload](/lab/sedimentology/sediment-transport): Calculate the Shields parameter and critical shear stress for sediment entrainment — determine when a river or current begins to move sand, gravel, or cobbles along the bed
- [Stratigraphic Column: Walther's Law & Facies](/lab/sedimentology/stratigraphic-column): Build a stratigraphic column by varying sea level and sediment supply — observe how laterally adjacent facies stack vertically according to Walther's law of facies succession
- [Turbidite Sequence: Bouma Divisions & Graded Bedding](/lab/sedimentology/turbidite-sequence): Model turbidite deposition showing the Bouma sequence — visualize how flow velocity decay produces graded bedding, parallel lamination, ripple cross-lamination, and hemipelagic drape

### Seismology & Earthquake Science (5 simulations)
- [Earthquake Magnitude & Energy Calculator](/lab/seismology/earthquake-magnitude): Simulate earthquake magnitude scales — explore how seismogram amplitude, epicentral distance, depth, and frequency content determine Richter, moment, and body-wave magnitudes
- [Fault Mechanics & Stress Accumulation](/lab/seismology/fault-mechanics): Simulate earthquake fault mechanics — explore how tectonic stress rate, fault friction, normal stress, and recurrence interval govern the seismic cycle and rupture potential
- [Seismic Refraction & Ray Tracing](/lab/seismology/seismic-refraction): Simulate seismic wave refraction through layered Earth — explore how layer velocities, thicknesses, source offset, and interface dip control travel-time curves and head-wave arrivals
- [Seismogram Waveform Analysis](/lab/seismology/seismogram-analysis): Simulate a three-component seismogram — explore how epicentral distance, magnitude, focal depth, and station noise affect P-wave, S-wave, and surface wave arrivals
- [Soil Liquefaction Risk Assessment](/lab/seismology/liquefaction): Simulate seismic liquefaction susceptibility — explore how earthquake magnitude, PGA, soil density, and water table depth determine factor of safety and liquefaction potential

### Soil Science & Pedology (5 simulations)
- [Soil Compaction Under Mechanical Load](/lab/soil-science/compaction-model): Model how applied pressure compacts soil — visualize pore space collapse, bulk density increase, and the Proctor compaction curve at varying moisture contents
- [Soil Erosion by Water (USLE Model)](/lab/soil-science/erosion-model): Calculate annual soil loss using the Universal Soil Loss Equation — visualize how rainfall, slope, soil type, cover, and conservation practices interact to drive erosion
- [Soil Nutrient Cycle & Decomposition](/lab/soil-science/nutrient-cycle): Model the nitrogen and carbon cycles in soil — trace how organic matter decomposes, minerals are released, plants absorb nutrients, and microbes drive the whole system
- [Soil Texture Classification (USDA Triangle)](/lab/soil-science/soil-classification): Plot sand, silt, and clay percentages on the USDA texture triangle — instantly classify soil type and estimate hydraulic properties
- [Water Percolation & Infiltration Rate](/lab/soil-science/percolation-rate): Model water infiltration through soil layers — visualize the wetting front advancing through porous media with Darcy's law and the Green-Ampt model

### Volcanology & Magma Dynamics (5 simulations)
- [Eruption Column & Plume Height](/lab/volcanology/eruption-column): Model volcanic eruption columns — explore how mass discharge rate, vent radius, exit velocity, and atmospheric conditions control plume height and umbrella cloud spread
- [Lava Flow Advance & Cooling](/lab/volcanology/lava-flow): Simulate lava flow advance down a slope — model flow velocity, cooling rate, crust formation, and maximum runout distance as functions of effusion rate, viscosity, slope angle, and ambient conditions
- [Magma Viscosity & Rheology](/lab/volcanology/magma-viscosity): Simulate magma viscosity as a function of temperature, silica content, water content, and crystal fraction — visualize flow behavior from basaltic to rhyolitic compositions
- [Pyroclastic Density Currents](/lab/volcanology/pyroclastic-flow): Simulate pyroclastic density currents — model flow velocity, runout distance, dynamic pressure, and temperature as functions of collapse height, particle concentration, slope, and entrainment
- [Volcanic Explosivity Index (VEI)](/lab/volcanology/volcanic-explosivity): Calculate the Volcanic Explosivity Index from eruption volume, column height, duration, and mass discharge rate — compare with historical eruptions from Strómboli to Yellowstone

### Wildfire Science & Fire Behavior (5 simulations)
- [Crown Fire Transition & Torching Index](/lab/wildfire-science/crown-fire): Simulate crown fire initiation — explore how canopy base height, foliar moisture, and fireline intensity determine the transition from surface to crown fire
- [Dead Fuel Moisture & Ignition Threshold](/lab/wildfire-science/fuel-moisture): Simulate dead fuel moisture response to temperature and humidity — explore how timelag classes and ignition thresholds determine fire danger
- [Fire Weather Index System](/lab/wildfire-science/fire-weather): Simulate the Canadian Fire Weather Index — explore how temperature, humidity, wind, and rain combine into composite fire danger ratings
- [Gaussian Plume Smoke Transport](/lab/wildfire-science/smoke-dispersion): Simulate smoke dispersion from wildfire using a Gaussian plume model — explore how wind speed, atmospheric stability, and source strength shape downwind concentrations
- [Rothermel Fire Spread Model](/lab/wildfire-science/fire-spread): Simulate wildfire spread rate using the Rothermel model — explore how wind speed, fuel load, moisture, and slope drive fire behavior

## economics (2 topics, 10 simulations)

### Behavioral Economics (5 simulations)
- [Endowment Effect & WTP vs WTA](/lab/behavioral-economics/endowment-effect): Explore why owning something makes it feel more valuable — visualize the gap between willingness-to-pay and willingness-to-accept in Thaler's classic mug experiment
- [Loss Aversion Experiment](/lab/behavioral-economics/loss-aversion): Experience Kahneman & Tversky's prospect theory viscerally — watch how losses loom larger than gains and fair gambles feel negative
- [Mental Accounting](/lab/behavioral-economics/mental-accounting): See how identical dollars are treated differently based on their source — windfall vs earned money flows to different mental accounts in predictably irrational ways
- [Nudge Architecture](/lab/behavioral-economics/nudge-effects): See how default options, framing, and social proof dramatically shift behavior without restricting choice — the power of nudge architecture
- [Social Proof & Information Cascades](/lab/behavioral-economics/social-proof-cascade): Watch how rational individuals ignoring their own information creates cascading herd behavior — sometimes converging on the wrong answer

### Finance & Markets (5 simulations)
- [Black-Scholes Option Pricing Model](/lab/finance/black-scholes): Calculate fair option prices using the Black-Scholes model — the formula that earned a Nobel Prize and transformed derivatives trading forever
- [Bond Yield Curve & Term Structure](/lab/finance/bond-yield-curve): Visualize and model the yield curve — how interest rates vary across bond maturities and what the shape signals about the economy
- [Cryptocurrency Mining Profitability](/lab/finance/crypto-mining): Calculate whether crypto mining is profitable — factoring in hash rate, electricity costs, block rewards, difficulty, and hardware efficiency
- [Monte Carlo Simulation for Option Pricing](/lab/finance/monte-carlo-pricing): Price options by simulating thousands of random stock price paths — the brute-force method that can handle any payoff structure
- [Value at Risk (VaR) Portfolio Analysis](/lab/finance/portfolio-var): Measure portfolio risk with Value at Risk — quantify the maximum expected loss at a given confidence level over a time horizon

## engineering (53 topics, 265 simulations)

### Additive Manufacturing & 3D Printing (5 simulations)
- [Binder Jetting & Saturation Control](/lab/additive-manufacturing/binder-jetting): Simulate binder jetting — control binder saturation, droplet spacing, layer thickness, and powder packing to optimize green part density before sintering
- [FDM Extrusion & Layer Deposition](/lab/additive-manufacturing/fdm-printing): Simulate fused deposition modeling — control nozzle temperature, layer height, print speed, and extrusion width to visualize thermoplastic filament deposition and interlayer bonding
- [SLA Photopolymer Curing](/lab/additive-manufacturing/sla-curing): Model stereolithography UV curing — control laser power, exposure time, resin absorption, and layer thickness to optimize photopolymerization depth and resolution
- [SLM Melt Pool Dynamics](/lab/additive-manufacturing/slm-melting): Model selective laser melting of metal powder — visualize melt pool formation, solidification, and how laser power, scan speed, and hatch spacing control density and microstructure
- [Support Structure Optimization](/lab/additive-manufacturing/support-optimization): Optimize support structures for 3D printing — balance overhang angle, support density, material usage, and removal difficulty for any geometry

### Aerospace Engineering & Flight (5 simulations)
- [Airfoil Lift & Drag Simulator](/lab/aerospace/lift-drag): Visualize lift and drag forces on an airfoil — adjust angle of attack, airspeed, and air density to see force vectors and the lift-to-drag ratio
- [Atmospheric Re-entry Heating Simulator](/lab/aerospace/reentry-heating): Model the extreme heating during atmospheric re-entry — adjust velocity, altitude, nose radius, and ballistic coefficient to see heat flux and temperature profiles
- [Rocket Staging & Delta-V Calculator](/lab/aerospace/rocket-staging): Simulate multi-stage rocket performance — adjust exhaust velocity, mass ratios, and stage count to see delta-v accumulation and payload fraction
- [Supersonic Flow & Shock Wave Simulator](/lab/aerospace/supersonic-flow): Visualize supersonic flow past a wedge — adjust Mach number, wedge angle, and altitude to see oblique shocks, expansion fans, and downstream conditions
- [Wing Planform & Aspect Ratio Designer](/lab/aerospace/wing-design): Design wing planforms — adjust span, sweep, taper, and aspect ratio to see how geometry affects lift distribution, induced drag, and structural loads

### Antenna Design & Radiation Patterns (5 simulations)
- [Half-Wave Dipole Radiation Pattern](/lab/antenna-design/dipole-antenna): Simulate a half-wave dipole antenna — explore how frequency, length, and orientation shape the radiation pattern
- [Horn Antenna: Aperture & Beamwidth](/lab/antenna-design/horn-antenna): Simulate a pyramidal horn antenna — explore how aperture dimensions and flare angle control beamwidth and gain
- [Linear Antenna Array & Beam Steering](/lab/antenna-design/antenna-array): Simulate a linear phased array — explore how element count, spacing, and progressive phase shift steer and shape the beam
- [Microstrip Patch Antenna & Bandwidth](/lab/antenna-design/patch-antenna): Simulate a rectangular microstrip patch antenna — explore how dimensions, substrate, and feed position control resonance and bandwidth
- [Yagi-Uda Array: Gain & Directivity](/lab/antenna-design/yagi-uda): Simulate a Yagi-Uda antenna array — explore how element count, spacing, and length ratios control gain and front-to-back ratio

### Architecture & Structural Design (5 simulations)
- [Arch & Dome Force Analysis](/lab/architecture/arch-forces): Visualize how arches and domes redirect gravity loads into compression — adjust span, rise, and load to see thrust lines and force vectors
- [Building Solar Orientation & Daylighting](/lab/architecture/solar-orientation): Optimize building orientation for solar gain and daylighting — simulate sun paths across seasons and latitudes to maximize natural light and energy efficiency
- [Golden Section in Architecture](/lab/architecture/golden-section): Explore the golden ratio (1.618) in architectural proportions — overlay golden rectangles, spirals, and Le Corbusier's Modulor on building facades
- [Room Acoustics & Reverberation Simulator](/lab/architecture/acoustic-design): Calculate reverberation time (RT60) using the Sabine equation — adjust room dimensions, materials, and absorption to design spaces that sound right
- [Structural Load Distribution Simulator](/lab/architecture/structural-loads): Visualize how loads distribute through beams, columns, and supports — adjust span, load position, and material to see shear force and bending moment diagrams

### Astrodynamics & Spacecraft Orbits (5 simulations)
- [Gravity Assist & Planetary Slingshot](/lab/astrodynamics/gravity-assist): Simulate a gravity assist flyby — explore how approach velocity, periapsis distance, planet mass, and deflection angle determine the free delta-v gained from a planetary encounter
- [Hohmann Transfer Orbit](/lab/astrodynamics/hohmann-transfer): Simulate a Hohmann transfer between two circular orbits — explore how orbital radii, central body mass, and burn timing determine delta-v and transfer time
- [Lagrange Points & Three-Body Equilibrium](/lab/astrodynamics/lagrange-points): Simulate the five Lagrange points in a two-body gravitational system — explore how mass ratio, orbital radius, and perturbation velocity affect stability and halo orbits
- [Orbital Decay & Atmospheric Drag](/lab/astrodynamics/orbital-decay): Simulate orbital decay from atmospheric drag — explore how altitude, ballistic coefficient, solar activity, and spacecraft area determine orbital lifetime and re-entry timeline
- [Orbital Rendezvous & Docking](/lab/astrodynamics/orbital-rendezvous): Simulate orbital rendezvous between two spacecraft — explore how phase angle, altitude difference, thrust timing, and relative velocity determine approach trajectory and docking conditions

### Biomass Energy & Biofuel Technology (5 simulations)
- [Anaerobic Digestion & Methane Yield](/lab/biomass-energy/biogas-digestion): Model anaerobic digestion of organic waste — explore how temperature, retention time, and feedstock composition affect biogas production and methane concentration
- [Biomass Pyrolysis & Biochar Production](/lab/biomass-energy/pyrolysis): Simulate thermal decomposition of biomass in the absence of oxygen — explore how temperature, heating rate, and residence time determine the yields of biochar, bio-oil, and syngas
- [Cellulosic Ethanol Conversion](/lab/biomass-energy/bioethanol): Model cellulosic bioethanol production — explore how enzyme loading, fermentation temperature, and feedstock composition affect sugar yield and ethanol conversion efficiency
- [Syngas Gasification & Equivalence Ratio](/lab/biomass-energy/gasification): Model biomass gasification — explore how equivalence ratio, temperature, and steam-to-biomass ratio control syngas composition (H₂, CO, CO₂, CH₄) and cold gas efficiency
- [Wood Pellet Boiler Efficiency](/lab/biomass-energy/pellet-combustion): Model wood pellet combustion in automated boilers — explore how excess air, pellet moisture, and boiler design affect thermal efficiency, emissions, and heat output

### Biomedical Imaging & Diagnostics (5 simulations)
- [CT Back-Projection & Hounsfield Units](/lab/biomedical-imaging/ct-reconstruction): Simulate filtered back-projection in computed tomography — explore how projection count, filter kernel, and tissue density map to Hounsfield units
- [MRI Spin Echo & Relaxation Times](/lab/biomedical-imaging/mri-signal): Simulate MRI spin-echo signal formation — explore how T1, T2, TR, and TE control tissue contrast in magnetic resonance imaging
- [PET Tracer Kinetics & SUV](/lab/biomedical-imaging/pet-tracer): Simulate PET tracer uptake and clearance — explore how injection dose, body weight, uptake rate, and decay constant determine standardized uptake values
- [Ultrasound Pulse-Echo & B-Mode Resolution](/lab/biomedical-imaging/ultrasound-imaging): Simulate ultrasound pulse-echo imaging — explore how frequency, depth, and tissue impedance affect B-mode resolution and penetration
- [X-ray Beer-Lambert Attenuation & Contrast](/lab/biomedical-imaging/xray-attenuation): Simulate X-ray attenuation through tissue layers — explore how photon energy, tissue thickness, and material density affect transmitted intensity and image contrast

### Chemical Engineering & Process Design (5 simulations)
- [Chemical Reaction Kinetics Simulator](/lab/chemical-engineering/reaction-kinetics): Visualize concentration vs. time profiles for a reversible reaction with Arrhenius temperature dependence in a CSTR or batch reactor
- [Distillation Column Simulator](/lab/chemical-engineering/distillation): Simulate a binary distillation column with adjustable reflux ratio, feed composition, and tray count to visualize separation efficiency on a McCabe-Thiele diagram
- [Fluid Mixing & Stirred Tank Simulator](/lab/chemical-engineering/fluid-mixing): Visualize turbulent mixing in a stirred tank reactor with adjustable impeller speed, fluid viscosity, and baffle configuration
- [Heterogeneous Catalyst Design Simulator](/lab/chemical-engineering/catalyst-design): Explore how catalyst particle size, porosity, surface area, and temperature affect reaction rate through effectiveness factor and Thiele modulus analysis
- [Shell-and-Tube Heat Exchanger Simulator](/lab/chemical-engineering/heat-exchanger): Design and visualize a counter-flow shell-and-tube heat exchanger with real-time temperature profiles and heat duty calculations

### Combustion & Flame Dynamics (5 simulations)
- [Combustion Efficiency Analysis](/lab/combustion/combustion-efficiency): Simulate combustion efficiency — explore how equivalence ratio, excess air, fuel type, and exhaust temperature determine thermal losses and overall efficiency
- [Detonation Wave Structure](/lab/combustion/detonation-wave): Simulate detonation wave propagation — explore Chapman-Jouguet velocity, pressure ratios, and cellular detonation structure in reactive gas mixtures
- [Flammability Limits & Explosion Envelopes](/lab/combustion/flammability-limits): Simulate flammability limits — explore how fuel concentration, temperature, pressure, and diluent gases define the boundaries where ignition is possible
- [Laminar Flame Speed Propagation](/lab/combustion/flame-speed): Simulate laminar flame speed — explore how equivalence ratio, initial temperature, pressure, and fuel type affect flame propagation velocity
- [Thermodynamic Engine Cycle (Otto & Diesel)](/lab/combustion/engine-cycle): Simulate the Otto and Diesel thermodynamic engine cycles — explore how compression ratio, heat addition, and working fluid properties determine thermal efficiency and work output

### Control Systems & Feedback (5 simulations)
- [Bode Plot Analyzer](/lab/control-systems/bode-plot): Visualize frequency response of transfer functions — plot magnitude and phase Bode diagrams to analyze gain margin, phase margin, and bandwidth
- [Nyquist Stability Diagram](/lab/control-systems/nyquist-stability): Plot the Nyquist contour of an open-loop transfer function — count encirclements of the critical point to determine closed-loop stability
- [PID Controller Tuner](/lab/control-systems/pid-controller): Tune a PID controller in real time — adjust proportional, integral, and derivative gains to minimize overshoot, settling time, and steady-state error
- [Root Locus Explorer](/lab/control-systems/root-locus): Trace how closed-loop poles move in the complex plane as gain varies — visualize stability boundaries, breakaway points, and asymptotic angles
- [State-Space Simulator](/lab/control-systems/state-space): Explore state-space representations of dynamic systems — visualize state trajectories, eigenvalue placement, and controllability in the phase plane

### Corrosion Science & Protection (5 simulations)
- [Cathodic Protection System Design](/lab/corrosion-science/cathodic-protection): Simulate cathodic protection — explore how anode material, current density, soil resistivity, and structure surface area determine protection coverage and anode lifetime
- [Corrosion Rate Prediction](/lab/corrosion-science/corrosion-rate): Simulate corrosion rate — explore how oxygen concentration, temperature, pH, and flow velocity affect uniform dissolution rate using the Butler-Volmer equation
- [Galvanic Corrosion Between Dissimilar Metals](/lab/corrosion-science/galvanic-corrosion): Simulate galvanic corrosion — explore how electrode potential difference, electrolyte conductivity, area ratio, and temperature drive corrosion current between coupled metals
- [Passivation Film Growth & Breakdown](/lab/corrosion-science/passivation-film): Simulate passive oxide film formation — explore how chromium content, pH, applied potential, and chloride concentration affect film stability and breakdown
- [Pitting Corrosion Initiation & Growth](/lab/corrosion-science/pitting-corrosion): Simulate pitting corrosion — explore how chloride concentration, temperature, alloy PREN, and applied potential control pit initiation probability and growth rate

### Desalination & Water Purification (5 simulations)
- [Electrodialysis Ion Transport Simulator](/lab/desalination/electrodialysis): Simulate electrodialysis desalination — explore how voltage, membrane pairs, feed salinity, and flow rate control ion removal and energy consumption
- [Forward Osmosis Draw Solution Simulator](/lab/desalination/forward-osmosis): Simulate forward osmosis desalination — explore how draw solution concentration, membrane properties, feed salinity, and temperature affect water flux and dilution
- [Multi-Stage Flash Distillation Simulator](/lab/desalination/msf-distillation): Simulate MSF distillation — explore how number of stages, top brine temperature, feed salinity, and steam ratio affect freshwater yield and thermal efficiency
- [Reverse Osmosis Membrane Simulator](/lab/desalination/reverse-osmosis): Simulate reverse osmosis desalination — explore how feed pressure, salinity, membrane permeability, and recovery ratio affect freshwater production and energy consumption
- [Solar Still Evaporation Simulator](/lab/desalination/solar-still): Simulate passive solar still desalination — explore how solar irradiance, basin depth, glass angle, and ambient temperature affect freshwater yield and thermal efficiency

### Distillation & Separation Processes (5 simulations)
- [Azeotropic Distillation & Entrainer](/lab/distillation/azeotrope): Investigate azeotropic behavior in binary systems — visualize how positive deviations from Raoult's law create minimum-boiling azeotropes that limit ordinary distillation, and explore entrainer-based 
- [Isothermal Flash Drum Calculation](/lab/distillation/flash-drum): Solve the isothermal flash problem for a binary mixture — determine vapor fraction, liquid and vapor compositions using the Rachford-Rice equation with animated phase envelope visualization
- [McCabe-Thiele Binary Distillation](/lab/distillation/mccabe-thiele): Construct a McCabe-Thiele diagram for binary distillation — step off theoretical stages between operating lines and the equilibrium curve to determine the number of ideal plates required for a given s
- [Raoult's Law & Ideal Solutions](/lab/distillation/raoults-law): Explore Raoult's law for ideal binary mixtures — visualize partial pressures, total pressure, and deviation from ideality as you adjust pure-component vapor pressures and composition
- [Vapor-Liquid Equilibrium T-xy Diagram](/lab/distillation/vle-diagram): Generate T-xy phase diagrams for binary mixtures using Antoine equation vapor pressures — visualize bubble-point and dew-point curves, tie lines, and the two-phase region

### Electrical Engineering (5 simulations)
- [Ohm's Law Circuit Simulator](/lab/electrical-engineering/ohms-law): Explore the fundamental relationship between voltage, current, and resistance — adjust any parameter and watch the others respond in real time
- [Operational Amplifier Configurations](/lab/electrical-engineering/op-amp): Explore inverting, non-inverting, and differential op-amp configurations — adjust feedback resistors to set precise gain and see the output waveform
- [RC Circuit Charging & Discharging](/lab/electrical-engineering/rc-circuit): Watch a capacitor charge and discharge through a resistor — visualize the exponential time constant τ = RC that governs every timing circuit
- [RL Circuit Transient Response](/lab/electrical-engineering/rl-circuit): Simulate an inductor-resistor circuit to visualize current buildup, back-EMF, and the L/R time constant that governs inductive transients
- [Transistor Amplifier Gain](/lab/electrical-engineering/transistor-amplifier): Design a common-emitter BJT amplifier — adjust bias resistors and load to see voltage gain, operating point, and signal clipping in real time

### Energy Systems & Power Engineering (5 simulations)
- [Battery Discharge Curves & Capacity](/lab/energy-systems/battery-discharge): Simulate battery voltage discharge curves under different loads — explore C-rates, Peukert's law, and how discharge rate affects usable capacity
- [Nuclear Reactor Control Rods & Criticality](/lab/energy-systems/nuclear-reactor): Simulate nuclear reactor control — adjust control rod insertion to maintain criticality and balance neutron multiplication for stable power output
- [Power Grid Frequency Stability](/lab/energy-systems/grid-frequency): Simulate power grid frequency regulation — balance generation and demand to keep the grid at 50/60 Hz and prevent blackouts
- [Solar Panel Efficiency & Angle Optimization](/lab/energy-systems/solar-panel-efficiency): Optimize solar panel tilt angle for maximum energy harvest — simulate irradiance, temperature effects, and seasonal variation across latitudes
- [Wind Turbine Power & Betz Limit](/lab/energy-systems/wind-turbine): Simulate wind turbine power output and explore the Betz limit — the theoretical maximum of 59.3% energy extraction from wind

### Ergonomics & Human Factors (5 simulations)
- [Ergonomic Workstation Design](/lab/ergonomics/workstation-design): Simulate workstation ergonomics — explore how user height, desk height, monitor distance, and chair settings affect posture angles and musculoskeletal comfort
- [NIOSH Lifting Equation Calculator](/lab/ergonomics/lifting-equation): Simulate the NIOSH lifting equation — explore how load weight, horizontal distance, vertical height, and asymmetry angle determine the recommended weight limit and lifting index
- [Repetitive Strain Injury Risk Assessment](/lab/ergonomics/repetitive-strain): Simulate repetitive strain injury risk — explore how repetition rate, force level, posture deviation, and recovery time determine cumulative trauma disorder probability
- [Thermal Comfort & PMV Model](/lab/ergonomics/thermal-comfort): Simulate thermal comfort using Fanger's PMV-PPD model — explore how air temperature, humidity, air velocity, and metabolic rate determine comfort perception and dissatisfaction percentage
- [Visual Ergonomics & Display Optimization](/lab/ergonomics/visual-ergonomics): Simulate visual ergonomics — explore how viewing distance, text size, screen luminance, and ambient lighting affect readability, eye strain, and visual comfort

### Fiber Optics & Optical Communication (5 simulations)
- [EDFA Gain & Noise Figure](/lab/fiber-optics/fiber-amplifier): Simulate an erbium-doped fiber amplifier — explore gain, noise figure, and ASE noise as pump power and signal wavelength change
- [Fiber Attenuation & OTDR Trace](/lab/fiber-optics/fiber-attenuation): Simulate optical power loss along a fiber link — build loss budgets and visualize OTDR backscatter traces with splice and connector events
- [Modal Dispersion & Pulse Broadening](/lab/fiber-optics/modal-dispersion): Simulate multimode pulse broadening — watch how different guided modes spread optical pulses over distance and limit bandwidth
- [Total Internal Reflection & Numerical Aperture](/lab/fiber-optics/total-internal-reflection): Simulate total internal reflection inside an optical fiber — explore critical angle, acceptance cone, and numerical aperture as core and cladding indices change
- [Wavelength-Division Multiplexing (WDM)](/lab/fiber-optics/wavelength-division): Simulate WDM channel packing — explore how channel spacing, channel count, and per-channel data rate determine total fiber capacity

### Fire Engineering & Life Safety (5 simulations)
- [Axisymmetric Fire Plume Model](/lab/fire-engineering/fire-plume): Simulate buoyant fire plumes — explore how heat release rate, fire diameter, and ceiling height determine plume temperature, velocity, and entrainment using Heskestad correlations
- [Evacuation Egress Time Calculator](/lab/fire-engineering/egress-time): Simulate building evacuation — explore how occupant load, exit width, travel distance, and pre-movement delay determine Required Safe Egress Time (RSET)
- [Flashover Prediction Model](/lab/fire-engineering/flashover-model): Simulate flashover conditions in a compartment — explore how ventilation, fuel load, and room geometry determine the critical heat release rate for flashover using Thomas and Babrauskas correlations
- [Smoke Layer Descent Model](/lab/fire-engineering/smoke-layer): Simulate smoke filling in a compartment — explore how fire size, room geometry, and ventilation determine the rate of hot smoke layer descent and available safe egress time
- [Sprinkler Activation Response Model](/lab/fire-engineering/sprinkler-activation): Simulate automatic sprinkler activation — explore how RTI, ceiling jet temperature, sprinkler spacing, and fire growth rate determine activation time using the lumped-mass thermal model

### Geotechnical Engineering & Soil Mechanics (5 simulations)
- [1D Terzaghi Consolidation Settlement](/lab/geotechnical-engineering/consolidation): Simulate one-dimensional consolidation of clay layers under load — visualize pore pressure dissipation, settlement over time, and the degree of consolidation using Terzaghi's theory
- [Axial Pile Load Capacity](/lab/geotechnical-engineering/pile-capacity): Estimate the axial load capacity of driven piles using static analysis — visualize tip resistance, skin friction distribution, and load transfer along the pile shaft
- [Rankine Earth Pressure on Retaining Walls](/lab/geotechnical-engineering/retaining-wall): Calculate active and passive earth pressures using Rankine theory — visualize pressure distributions, resultant forces, and the effect of soil properties on retaining wall design
- [Soil Liquefaction & Cyclic Stress Analysis](/lab/geotechnical-engineering/liquefaction): Evaluate soil liquefaction potential under seismic loading — calculate the cyclic stress ratio (CSR), cyclic resistance ratio (CRR), and factor of safety against liquefaction using the simplified proc
- [Terzaghi Bearing Capacity of Shallow Foundations](/lab/geotechnical-engineering/bearing-capacity): Calculate the ultimate bearing capacity of shallow foundations using Terzaghi's classical equation — visualize failure surfaces, pressure bulbs, and the contributions of cohesion, surcharge, and soil 

### Geothermal Energy Engineering (5 simulations)
- [Binary-Cycle ORC Power Plant](/lab/geothermal-energy/binary-cycle): Simulate a binary-cycle organic Rankine cycle plant — explore how brine temperature, working fluid, and condenser conditions affect power output and efficiency
- [Enhanced Geothermal System (EGS) Stimulation](/lab/geothermal-energy/egs-stimulation): Simulate hydraulic stimulation of hot dry rock — explore how injection pressure, flow rate, rock stress, and fracture density create engineered geothermal reservoirs
- [Geothermal Reservoir Thermal Model](/lab/geothermal-energy/reservoir-modeling): Simulate subsurface reservoir temperature — explore how depth, geothermal gradient, rock thermal conductivity, and fluid flow affect reservoir thermal state
- [Heat Extraction Optimization](/lab/geothermal-energy/heat-extraction): Simulate geothermal heat extraction — explore how flow rate, reservoir permeability, well spacing, and injection temperature affect thermal output and reservoir life
- [Wellbore Heat Loss Model](/lab/geothermal-energy/wellbore-heat-loss): Simulate heat loss in geothermal wellbores — explore how depth, flow velocity, insulation, and casing design affect the temperature of produced fluid at the surface

### Haptics Engineering (5 simulations)
- [Electrostatic Friction Display](/lab/haptics-engineering/electrostatic-friction): Simulate electrostatic friction modulation — explore how applied voltage, frequency, dielectric thickness, and finger contact mechanics control friction forces on touchscreen haptic displays
- [Force Feedback Control Loop](/lab/haptics-engineering/force-feedback): Simulate a force-feedback haptic device — explore how stiffness, damping, virtual wall position, and control loop gain affect stability and force rendering fidelity
- [Haptic Texture Rendering](/lab/haptics-engineering/texture-rendering): Simulate haptic texture rendering — explore how spatial frequency, amplitude, scanning velocity, and friction modulation create the sensation of touching different surface textures
- [Thermal Haptic Display](/lab/haptics-engineering/thermal-display): Simulate thermal haptic displays — explore how contact conductance, skin thermal properties, temperature difference, and contact area determine the perception of hot, cold, and material identity
- [Vibrotactile Feedback Design](/lab/haptics-engineering/vibrotactile-feedback): Simulate vibrotactile waveform design — explore how frequency, amplitude, envelope shape, and duty cycle create distinct tactile sensations in haptic actuators

### Heat Transfer & Thermal Analysis (5 simulations)
- [Convective Heat Transfer Coefficient Calculator](/lab/heat-transfer/convection-coefficient): Calculate convective heat transfer coefficients for forced and natural convection — explore how fluid velocity, surface geometry, and fluid properties determine cooling rates
- [Extended Surface Fin Efficiency Analyzer](/lab/heat-transfer/fin-efficiency): Analyze fin performance — explore how fin length, thickness, thermal conductivity, and convection coefficient determine efficiency and total heat dissipation
- [Heat Pipe Thermal Performance Simulator](/lab/heat-transfer/heat-pipe): Simulate heat pipe operation — explore how working fluid, wick structure, pipe dimensions, and heat load determine effective thermal conductivity and transport limits
- [Radiative Heat Exchange Between Surfaces](/lab/heat-transfer/radiation-exchange): Model thermal radiation exchange between two surfaces — explore how emissivity, temperature, and view factors determine radiative heat transfer rates
- [Steady-State Conduction Through a Composite Wall](/lab/heat-transfer/conduction-wall): Simulate heat conduction through a multi-layer wall — explore how thermal conductivity, wall thickness, and boundary temperatures create linear temperature profiles

### Hydraulics & Pipe Flow Systems (5 simulations)
- [Bernoulli Equation & Venturi Effect](/lab/hydraulics/bernoulli-theorem): Simulate Bernoulli's energy equation along a streamline — explore how cross-section changes in a venturi create pressure drops, velocity increases, and flow measurement
- [Darcy-Weisbach Friction & Moody Chart](/lab/hydraulics/pipe-friction): Simulate pipe friction losses — explore how flow velocity, pipe diameter, roughness, and Reynolds number determine head loss via Darcy-Weisbach and the Moody chart
- [Manning Equation & Open Channel Flow](/lab/hydraulics/open-channel): Simulate open channel flow — explore how channel slope, roughness, cross-section shape, and depth control flow velocity and discharge via Manning's equation
- [Pump Performance & System Curve](/lab/hydraulics/pump-curve): Simulate pump-system interaction — explore how pump head, efficiency, system resistance, and static lift determine the operating point and power consumption
- [Water Hammer & Joukowsky Equation](/lab/hydraulics/water-hammer): Simulate water hammer pressure transients — explore how valve closure time, flow velocity, pipe material, and wave speed generate dangerous pressure surges

### Hydrometallurgy & Aqueous Processing (5 simulations)
- [Electrowinning Cell Design](/lab/hydrometallurgy/electrowinning): Simulate an electrowinning cell for metal deposition — optimize current density, voltage, electrolyte composition, and energy consumption for copper, zinc, or nickel recovery
- [Ion-Exchange Breakthrough Curves](/lab/hydrometallurgy/ion-exchange): Simulate ion-exchange column chromatography for metal recovery — model breakthrough curves, resin capacity, and selectivity for hydrometallurgical separations
- [Leaching Kinetics & Shrinking-Core Model](/lab/hydrometallurgy/leaching-kinetics): Simulate acid leaching of metal ores using the shrinking-core model — explore how particle size, acid concentration, temperature, and diffusion control dissolution rates
- [Selective Precipitation & pH Control](/lab/hydrometallurgy/precipitation): Simulate selective metal precipitation by pH adjustment — explore solubility curves, precipitation windows, and co-precipitation risks for multi-metal solutions
- [Solvent Extraction & McCabe-Thiele](/lab/hydrometallurgy/solvent-extraction): Simulate counter-current solvent extraction for metal separation — design McCabe-Thiele diagrams, optimize organic/aqueous ratios, and predict stage efficiency

### Industrial Fermentation & Bioprocess Engineering (5 simulations)
- [Bioreactor Scale-Up](/lab/industrial-fermentation/scale-up): Simulate bioreactor scale-up from bench to production — compare scale-up criteria including constant P/V, tip speed, kLa, and mixing time across scales
- [Continuous Culture & Chemostat](/lab/industrial-fermentation/continuous-culture): Simulate continuous chemostat culture — explore steady-state biomass, substrate, and dilution rate effects including washout and oscillatory dynamics
- [Fed-Batch Fermentation Strategy](/lab/industrial-fermentation/fed-batch): Simulate fed-batch fermentation — optimize substrate feeding profiles to maximize biomass and product while avoiding overflow metabolism and substrate inhibition
- [Oxygen Transfer & kLa](/lab/industrial-fermentation/oxygen-transfer): Simulate oxygen mass transfer in bioreactors — calculate kLa, dissolved oxygen profiles, and the oxygen transfer rate as functions of agitation and aeration
- [Stirred-Tank Bioreactor Design](/lab/industrial-fermentation/bioreactor-design): Simulate stirred-tank bioreactor geometry — optimize vessel dimensions, impeller configuration, and power input for microbial and mammalian cell culture

### LiDAR & Remote Sensing (5 simulations)
- [Bathymetric LiDAR & Water Penetration](/lab/lidar-remote-sensing/bathymetric-lidar): Simulate bathymetric LiDAR — explore how laser wavelength, water clarity, depth, and bottom reflectance determine subaqueous mapping capability
- [Canopy Height Model & Forest Structure](/lab/lidar-remote-sensing/canopy-height): Simulate forest canopy height estimation from LiDAR — explore how first/last return differences, point density, and crown shape determine canopy height models
- [LiDAR Pulse Propagation & Return](/lab/lidar-remote-sensing/lidar-pulse): Simulate LiDAR laser pulse propagation — explore how pulse energy, beam divergence, atmospheric attenuation, and surface reflectance determine return signal strength
- [Point Density & Survey Design](/lab/lidar-remote-sensing/point-density): Simulate LiDAR survey planning — explore how pulse rate, scan angle, flying speed, and altitude determine point density and coverage for geospatial accuracy requirements
- [Terrain Classification & Ground Filtering](/lab/lidar-remote-sensing/terrain-classification): Simulate LiDAR point cloud classification — explore how slope threshold, height difference, and cell size parameters affect ground vs. non-ground filtering

### Materials Fatigue & Failure Analysis (5 simulations)
- [Fatigue Crack Propagation (Paris Law)](/lab/materials-fatigue/crack-propagation): Simulate fatigue crack growth using the Paris-Erdogan law — predict how crack length evolves with loading cycles and estimate remaining component life
- [Goodman Diagram (Mean Stress Effect)](/lab/materials-fatigue/goodman-diagram): Construct modified Goodman diagrams — evaluate fatigue safety under combined alternating and mean stress for different materials and loading conditions
- [Miner's Rule (Cumulative Damage)](/lab/materials-fatigue/miners-rule): Apply Palmgren-Miner's linear damage accumulation rule — predict fatigue failure under variable amplitude loading with multiple stress levels
- [S-N Curve (Wohler Curve) Simulator](/lab/materials-fatigue/sn-curve): Generate and analyze S-N curves — plot stress amplitude versus cycles to failure for different materials and loading conditions
- [Stress Concentration Factor (Kt)](/lab/materials-fatigue/stress-concentration): Analyze stress concentrations around geometric discontinuities — visualize how holes, notches, and fillets amplify local stress and reduce fatigue life

### Materials Science & Engineering (5 simulations)
- [Binary Phase Diagram Simulator](/lab/materials-science/phase-diagram): Explore a binary alloy phase diagram — adjust composition and temperature to see which phases are stable and apply the lever rule
- [Crystal Lattice Structure Simulator](/lab/materials-science/crystal-structure): Visualize and compare FCC, BCC, and HCP crystal lattice structures — see how atomic packing determines material properties
- [Heat Conduction & Thermal Diffusivity Simulator](/lab/materials-science/heat-conduction): Watch heat diffuse through a 1D bar in real time — adjust thermal conductivity, density, and heat capacity to see how temperature evolves
- [Polymer Chain Dynamics & Random Coil Simulator](/lab/materials-science/polymer-chains): Watch polymer chains writhe in Brownian motion — explore how chain length, temperature, and stiffness affect the random coil conformation
- [Stress-Strain Curve Simulator](/lab/materials-science/stress-strain): Stretch a virtual specimen to observe elastic deformation, yielding, strain hardening, necking, and fracture on an interactive stress-strain curve

### Membrane Science & Separation Technology (5 simulations)
- [Electrodialysis & Ion Transport](/lab/membrane-science/electrodialysis): Simulate electrodialysis — explore how voltage, membrane conductivity, and current density drive ion transport and current efficiency in desalination stacks
- [Gas Separation Membranes](/lab/membrane-science/gas-separation): Simulate gas permeation membranes — explore the permeability-selectivity tradeoff and Robeson upper bound for CO2/N2 and O2/N2 separation
- [Membrane Distillation](/lab/membrane-science/membrane-distillation): Simulate thermal membrane distillation — explore how temperature difference, membrane porosity, and pore size drive vapor flux across hydrophobic membranes
- [Reverse Osmosis Desalination](/lab/membrane-science/reverse-osmosis): Simulate RO desalination — explore how applied pressure, osmotic pressure, and membrane permeability govern water flux and salt rejection
- [Ultrafiltration & Molecular Weight Cutoff](/lab/membrane-science/ultrafiltration): Simulate ultrafiltration membranes — explore molecular weight cutoff, pore size, and solute rejection curves for protein and colloid separation

### Microfluidics & Lab-on-a-Chip (5 simulations)
- [Capillary-Driven Flow in Microchannels](/lab/microfluidics/capillary-flow): Simulate capillary-driven flow through rectangular microchannels — explore how contact angle, channel dimensions, and fluid viscosity govern the Washburn flow dynamics
- [Diffusion-Based Laminar Micromixing](/lab/microfluidics/laminar-mixing): Simulate diffusion-driven mixing in laminar microchannels — explore how channel length, flow velocity, and diffusion coefficient affect mixing efficiency
- [Digital Microfluidics: Electrowetting Control](/lab/microfluidics/electrowetting): Simulate electrowetting-on-dielectric droplet manipulation — control voltage, dielectric thickness, and droplet volume to explore contact angle modulation and droplet transport
- [Fluorescence-Activated Cell Sorting (FACS)](/lab/microfluidics/cell-sorting): Simulate microfluidic fluorescence-activated cell sorting — explore how flow speed, laser power, and sorting threshold affect purity and throughput
- [T-Junction Droplet Generation](/lab/microfluidics/droplet-generation): Simulate monodisperse droplet formation at a microfluidic T-junction — control flow rates, channel geometry, and interfacial tension to explore dripping and jetting regimes

### Mining Engineering & Extraction (5 simulations)
- [Crushing & Grinding Energy — Bond Work Index](/lab/mining-engineering/comminution): Simulate comminution energy — explore how Bond work index, feed size, product size, and throughput affect grinding power and energy consumption
- [Cutoff Grade & Economic Optimization](/lab/mining-engineering/ore-grade): Simulate cutoff grade decisions — explore how metal price, processing cost, recovery rate, and mining cost affect economic ore boundaries
- [Drill-and-Blast Pattern & Fragmentation](/lab/mining-engineering/blast-design): Simulate drill-and-blast patterns — explore how burden, spacing, hole diameter, and charge density affect rock fragmentation and powder factor
- [Mine Ventilation Network & Fan Selection](/lab/mining-engineering/ventilation-network): Simulate underground mine ventilation — explore how airway dimensions, length, roughness, and fan pressure affect airflow quantity and power consumption
- [Pit Slope Stability & Factor of Safety](/lab/mining-engineering/slope-stability): Simulate pit slope stability — explore how slope angle, cohesion, friction angle, and water pressure affect factor of safety against failure

### Nanotechnology & Nanoscale Physics (5 simulations)
- [Carbon Nanotube Mechanics & Properties](/lab/nanotechnology/carbon-nanotube): Simulate carbon nanotube mechanical behavior — explore how diameter, chirality, number of walls, and applied strain govern stiffness, strength, and buckling
- [Molecular Self-Assembly & Pattern Formation](/lab/nanotechnology/self-assembly): Simulate molecular self-assembly — explore how interaction strength, concentration, temperature, and molecular geometry drive spontaneous pattern formation at the nanoscale
- [Nanofiltration Membrane Transport](/lab/nanotechnology/nanofiltration): Simulate nanofiltration membrane performance — explore how pore size, pressure, solute radius, and membrane thickness govern rejection rate and permeate flux
- [Nanoparticle Synthesis & Nucleation Kinetics](/lab/nanotechnology/nanoparticle-synthesis): Simulate nanoparticle nucleation and growth — explore how supersaturation, temperature, surface energy, and reaction time govern particle size distribution
- [Quantum Dot Confinement & Emission](/lab/nanotechnology/quantum-dot): Simulate quantum dot optical properties — explore how dot radius, material band gap, effective mass, and temperature control emission wavelength and color

### Navigation & Positioning Systems (5 simulations)
- [Dead Reckoning & Position Propagation](/lab/navigation/dead-reckoning): Simulate dead reckoning — explore how speed error, heading error, drift time, and update interval cause position uncertainty to grow from a known starting point
- [GPS Trilateration & Satellite Positioning](/lab/navigation/gps-positioning): Simulate GPS positioning — explore how satellite geometry, clock bias, atmospheric delay, and signal noise affect position accuracy through trilateration
- [Inertial Navigation System (INS)](/lab/navigation/inertial-navigation): Simulate inertial navigation — explore how accelerometer bias, gyroscope drift, integration time, and initial alignment affect position and attitude errors
- [Kalman Filter & Sensor Fusion](/lab/navigation/kalman-filter): Simulate a Kalman filter — explore how process noise, measurement noise, initial uncertainty, and update rate affect optimal state estimation and sensor fusion
- [Map Matching & Road Snapping](/lab/navigation/map-matching): Simulate map matching — explore how GPS noise, road network density, heading constraint, and candidate search radius affect snapping GPS traces to road segments

### Nuclear Engineering & Reactor Physics (5 simulations)
- [Fuel Burnup & Isotope Evolution](/lab/nuclear-engineering/fuel-burnup): Track the depletion of U-235 and buildup of Pu-239, fission products, and xenon-135 over a multi-year fuel cycle
- [Gamma & Neutron Shielding Attenuation](/lab/nuclear-engineering/shielding-design): Calculate gamma-ray and neutron attenuation through multi-layer shielding materials with buildup factor corrections
- [One-Group Neutron Diffusion & Flux Profile](/lab/nuclear-engineering/neutron-diffusion): Solve the one-group neutron diffusion equation to visualize the spatial flux profile in a bare homogeneous slab reactor
- [Post-Shutdown Decay Heat Curve](/lab/nuclear-engineering/decay-heat): Calculate and visualize decay heat production after reactor shutdown using the ANS standard model for fission product decay
- [Reactor Criticality & Neutron Multiplication](/lab/nuclear-engineering/reactor-criticality): Simulate the effective multiplication factor k-eff and neutron population dynamics in a thermal reactor to explore sub-critical, critical, and super-critical states

### Ocean Engineering & Offshore Structures (5 simulations)
- [Catenary Mooring Line Analysis](/lab/ocean-engineering/mooring-design): Simulate catenary mooring line geometry and tension — explore how line weight, water depth, and pretension affect mooring system performance
- [Hull Resistance & Froude Number](/lab/ocean-engineering/ship-resistance): Simulate ship hull resistance as a function of speed, hull dimensions, and form — explore frictional and wave-making resistance components across Froude numbers
- [Morison Equation & Wave Forces](/lab/ocean-engineering/wave-loading): Simulate wave forces on a cylindrical offshore structure using the Morison equation — explore drag and inertia components across wave conditions
- [Oscillating Water Column Wave Energy Converter](/lab/ocean-engineering/wave-energy): Simulate an oscillating water column (OWC) wave energy converter — explore how chamber geometry, wave conditions, and turbine characteristics affect power extraction
- [Subsea Pipeline On-Bottom Stability](/lab/ocean-engineering/pipeline-stability): Simulate subsea pipeline on-bottom stability under wave and current loading — evaluate whether the pipe remains stable or requires concrete coating or trenching

### Optoelectronics & Photonic Devices (5 simulations)
- [Electro-Optic Modulator & Mach-Zehnder](/lab/optoelectronics/optical-modulator): Simulate a Mach-Zehnder optical modulator — explore how drive voltage, bias point, extinction ratio, and modulation frequency shape the output optical signal
- [Laser Diode L-I Characteristics](/lab/optoelectronics/laser-diode): Simulate a semiconductor laser diode — explore how injection current, temperature, cavity length, and mirror reflectivity affect threshold, output power, and spectral behavior
- [Optical Waveguide Mode Solver](/lab/optoelectronics/waveguide-design): Simulate a slab dielectric waveguide — explore how core thickness, core and cladding refractive indices, and wavelength determine guided modes and confinement
- [Photodetector Responsivity & Noise](/lab/optoelectronics/photodetector): Simulate a semiconductor photodetector — explore how wavelength, optical power, reverse bias, and bandwidth affect photocurrent, responsivity, NEP, and signal-to-noise ratio
- [Photonic Optical Switch](/lab/optoelectronics/optical-switch): Simulate a directional coupler optical switch — explore how coupling length, refractive index change, wavelength, and gap spacing control light routing between waveguide ports

### Photogrammetry & 3D Reconstruction (5 simulations)
- [Camera Calibration & Lens Distortion](/lab/photogrammetry/camera-calibration): Simulate camera calibration — explore how focal length, principal point offset, and radial distortion coefficients affect image geometry
- [Orthorectification & Map Projection](/lab/photogrammetry/orthorectification): Simulate orthorectification — explore how terrain elevation, camera tilt, and flight altitude affect geometric correction of aerial imagery
- [Point Cloud Generation & Visualization](/lab/photogrammetry/point-cloud): Generate and visualize 3D point clouds — explore how point density, noise level, and viewing angle affect reconstructed surface quality
- [Stereo Matching & Disparity Maps](/lab/photogrammetry/stereo-matching): Simulate stereo matching algorithms — explore how baseline distance, block size, and disparity range affect depth estimation from stereo image pairs
- [Structure from Motion Pipeline](/lab/photogrammetry/structure-from-motion): Simulate the SfM pipeline — explore how image count, feature matches, and bundle adjustment iterations affect 3D reconstruction quality

### Photovoltaics & Solar Energy (5 simulations)
- [Partial Shading & Bypass Diode Losses](/lab/photovoltaics/shading-loss): See how partial shading on even one cell can collapse an entire module's output — and how bypass diodes limit the damage by routing current around shaded cell strings
- [Solar Cell I-V Curve & Maximum Power Point](/lab/photovoltaics/iv-curve): Trace the current-voltage characteristic of a solar cell and find the maximum power point — the operating condition where a cell extracts the most energy from sunlight
- [Solar Module Layout & Array Optimization](/lab/photovoltaics/module-layout): Optimize solar module arrangement on a rooftop — balance row spacing, tilt angle, and azimuth to maximize energy density while avoiding inter-row shading
- [Solar Spectrum & Photon Energy Distribution](/lab/photovoltaics/solar-spectrum): Visualize the solar irradiance spectrum from UV to infrared and see which wavelengths a silicon cell can actually absorb — revealing why single-junction efficiency has a hard ceiling
- [Temperature Coefficient & Thermal Derating](/lab/photovoltaics/temperature-coefficient): Watch solar cell efficiency decline as temperature rises — simulate the physics of thermal derating across different cell technologies from silicon to perovskite

### Powder Metallurgy (5 simulations)
- [Atomization Process Simulator](/lab/powder-metallurgy/atomization): Interactive model of gas and water atomization showing how process parameters control powder particle size distribution, morphology, and yield
- [Hot Isostatic Pressing (HIP) Simulator](/lab/powder-metallurgy/hot-isostatic-pressing): Interactive model of HIP densification showing how temperature, pressure, and time eliminate residual porosity through creep and diffusion mechanisms
- [Metal Injection Molding (MIM) Simulator](/lab/powder-metallurgy/metal-injection-molding): Interactive model of the MIM process showing how powder loading, binder properties, and sintering conditions determine final part density, shrinkage, and properties
- [Powder Compaction Simulator](/lab/powder-metallurgy/powder-compaction): Interactive model of uniaxial die compaction showing how applied pressure, friction, and powder properties determine green density distribution
- [Sintering Kinetics Simulator](/lab/powder-metallurgy/sintering-kinetics): Interactive model of solid-state sintering showing neck growth, densification, and grain coarsening as functions of temperature, time, and particle size

### Power Systems & Electrical Grids (5 simulations)
- [Grid Frequency Stability](/lab/power-systems/grid-stability): Simulate grid frequency response after a generation-load imbalance — visualize inertia, governor response, and frequency nadir
- [Load Flow Analysis (Newton-Raphson)](/lab/power-systems/load-flow): Simulate power flow across a multi-bus electrical network using the Newton-Raphson method — visualize voltage profiles, line losses, and power distribution
- [Power Factor Correction](/lab/power-systems/power-factor): Visualize the relationship between real, reactive, and apparent power — calculate capacitor bank sizing for power factor correction
- [Symmetrical Fault Analysis](/lab/power-systems/fault-analysis): Calculate three-phase fault currents using Thevenin equivalent circuits — visualize fault propagation and protective relay coordination
- [Transformer Design & Efficiency](/lab/power-systems/transformer-design): Design a power transformer by specifying turns ratio, core material, and loading — visualize efficiency curves, losses, and voltage regulation

### Propulsion Systems & Thrust (5 simulations)
- [Brayton Cycle & Turbojet Thrust](/lab/propulsion/turbojet-cycle): Model the Brayton thermodynamic cycle — adjust compression ratio, turbine inlet temperature, and airspeed to compute turbojet thrust and thermal efficiency
- [Ion Thruster & Specific Impulse](/lab/propulsion/ion-thruster): Simulate electrostatic ion propulsion — adjust beam voltage, propellant flow, and grid geometry to see thrust, Isp, and power requirements
- [Propeller Thrust & Blade Element Theory](/lab/propulsion/propeller-thrust): Calculate propeller thrust using blade element theory — adjust blade count, pitch, RPM, and airspeed to visualize the advance ratio and efficiency curve
- [Ramjet Performance & Supersonic Inlet](/lab/propulsion/ramjet-performance): Model ram compression and combustion in a ramjet — adjust Mach number, combustion temperature, and altitude to compute thrust and propulsive efficiency
- [Tsiolkovsky Rocket Equation & Delta-V](/lab/propulsion/rocket-equation): Calculate delta-v from exhaust velocity and mass ratio — visualize the exponential propellant cost of velocity change

### Radar Systems & Detection (5 simulations)
- [Doppler Radar & Velocity Measurement](/lab/radar-systems/doppler-radar): Simulate Doppler radar — explore how target radial velocity creates frequency shifts used for velocity measurement, clutter rejection, and weather detection
- [Phased Array Beam Steering & Antenna Patterns](/lab/radar-systems/phased-array): Simulate a phased-array antenna — explore how element spacing, phase shifts, and array size control beam direction, sidelobe levels, and angular resolution
- [Pulse Compression & Chirp Radar](/lab/radar-systems/pulse-compression): Simulate pulse compression radar — explore how linear frequency modulation (chirp) achieves fine range resolution without sacrificing detection energy
- [Radar Cross Section & Target Detectability](/lab/radar-systems/radar-cross-section): Simulate radar cross section — explore how target size, shape, material, and frequency determine RCS and stealth characteristics
- [Radar Range Equation & SNR](/lab/radar-systems/radar-range): Simulate the radar range equation — explore how transmit power, antenna gain, target cross-section, and noise determine maximum detection range

### Renewable Energy & Clean Power (5 simulations)
- [Geothermal Power Plant Simulator](/lab/renewable-energy/geothermal): Model a geothermal power plant with adjustable reservoir temperature, well depth, flow rate, and plant type to calculate electrical output and thermal efficiency
- [Grid Energy Storage Simulator](/lab/renewable-energy/energy-storage): Compare battery energy storage systems by modeling charge/discharge cycles, round-trip efficiency, degradation, and levelized cost for lithium-ion, flow, and compressed air technologies
- [Hydrogen Fuel Cell Simulator](/lab/renewable-energy/hydrogen-fuel-cell): Model a PEM hydrogen fuel cell with adjustable current density, temperature, pressure, and membrane thickness to visualize the voltage-current characteristic and efficiency
- [Tidal Power Generation Simulator](/lab/renewable-energy/tidal-power): Model tidal stream energy extraction with variable current speed, turbine diameter, tidal range, and channel geometry to calculate power output over a tidal cycle
- [Wind Turbine Power Simulator](/lab/renewable-energy/wind-turbine): Simulate wind turbine power output with adjustable wind speed, blade pitch, rotor diameter, and air density to explore the Betz limit and power curves

### Robotics & Control Systems (5 simulations)
- [PID Controller Tuning Simulator](/lab/robotics/pid-controller): Tune a PID controller in real time — adjust proportional, integral, and derivative gains to minimize overshoot and settling time
- [Robot Arm Forward Kinematics Simulator](/lab/robotics/robot-arm): Manipulate joint angles of a multi-link robot arm and watch the end-effector trace its path — visualizing forward kinematics and the Denavit-Hartenberg convention
- [Robot Arm Inverse Kinematics Simulator](/lab/robotics/inverse-kinematics): Drag a target point and watch a 2-link robot arm solve inverse kinematics in real time — see the elbow-up and elbow-down solutions
- [Robot Path Planning (RRT/PRM) Simulator](/lab/robotics/path-planning): Compare RRT and PRM path-planning algorithms on a randomized obstacle map — watch the tree grow and find a collision-free path
- [Swarm Robotics Emergent Behavior Simulator](/lab/robotics/swarm-robotics): Watch simple local rules produce complex emergent swarm behavior — adjust cohesion, alignment, and separation to see flocking, clustering, and dispersion

### Signal Processing (5 simulations)
- [AM/FM Modulation & Demodulation](/lab/signal-processing/am-fm-modulation): Modulate and demodulate carrier waves using amplitude and frequency modulation — see how information rides on radio waves
- [FFT Spectrum Analyzer](/lab/signal-processing/fft-spectrum): Decompose any composite signal into its frequency components using the Fast Fourier Transform — see the spectrum update in real time as you change frequencies and amplitudes
- [Nyquist-Shannon Sampling Theorem](/lab/signal-processing/sampling-theorem): Visualize aliasing and perfect reconstruction — see why sampling rate must exceed twice the signal frequency to avoid information loss
- [Signal Convolution Visualizer](/lab/signal-processing/convolution): Watch convolution in action — slide one signal over another and see how the output is built point by point, the foundation of filtering and system response
- [Signal Noise Filtering](/lab/signal-processing/noise-filtering): Apply low-pass and high-pass filters to noisy signals — visualize how cutoff frequency and filter order affect signal clarity in real time

### Structural Engineering & Load Analysis (5 simulations)
- [Beam Bending & Deflection Analysis](/lab/structural-engineering/beam-bending): Simulate beam bending under distributed and point loads — visualize shear force diagrams, bending moment curves, and deflection shapes for simply supported and cantilever beams
- [Column Buckling & Euler Critical Load](/lab/structural-engineering/column-buckling): Simulate Euler column buckling — explore how length, end conditions, cross-section, and material properties determine the critical load at which a column becomes unstable
- [Reinforced Concrete Section Design](/lab/structural-engineering/concrete-reinforcement): Design reinforced concrete beam sections — calculate required steel area, check moment capacity, visualize the stress block, and verify ductility requirements
- [Seismic Response Spectrum Analysis](/lab/structural-engineering/seismic-design): Simulate earthquake response spectra — explore how natural period, damping ratio, soil type, and peak ground acceleration determine a structure's seismic demand
- [Truss Force Analysis & Member Sizing](/lab/structural-engineering/truss-analysis): Analyze planar truss structures — compute member forces using the method of joints, visualize tension and compression, and identify critical members under various loading conditions

### Telecommunications & Signal Transmission (5 simulations)
- [Antenna Radiation Pattern Simulator](/lab/telecommunications/antenna-radiation): Simulate antenna radiation patterns — explore how element count, spacing, and frequency shape directional gain in phased array antennas
- [Digital Modulation Constellation Viewer](/lab/telecommunications/modulation-schemes): Visualize digital modulation constellations — compare BPSK, QPSK, 16-QAM, and 64-QAM under varying noise and observe bit error rates
- [Forward Error Correction Simulator](/lab/telecommunications/error-correction): Simulate forward error correction — visualize how redundancy bits detect and correct transmission errors using Hamming, convolutional, and LDPC codes
- [Satellite Link Budget Analyzer](/lab/telecommunications/link-budget): Analyze satellite link budgets — compute path loss, received power, and link margin for LEO, MEO, and GEO communication links
- [Shannon Channel Capacity Calculator](/lab/telecommunications/channel-capacity): Compute the Shannon-Hartley channel capacity — explore how bandwidth, signal power, and noise determine the theoretical maximum data rate

### Textile Engineering & Fiber Science (5 simulations)
- [Dyeing Kinetics & Diffusion](/lab/textile-engineering/dyeing-kinetics): Simulate textile dyeing kinetics — explore how diffusion coefficient, fiber radius, dye bath concentration, and temperature control dye uptake over time
- [Fabric Drape & Bending Rigidity](/lab/textile-engineering/fabric-drape): Simulate fabric drape behavior — explore how bending rigidity, fabric weight, drape radius, and shear modulus affect the drape coefficient and fold formation
- [Fiber Tensile Strength & Stress-Strain](/lab/textile-engineering/fiber-strength): Simulate fiber tensile testing — explore how Young's modulus, yield strength, elongation at break, and fiber diameter determine mechanical performance
- [Weave Pattern Geometry & Structure](/lab/textile-engineering/weave-patterns): Simulate fundamental weave patterns — explore how warp density, weft density, float length, and weave type create distinct fabric structures
- [Yarn Twist & Strength Optimization](/lab/textile-engineering/yarn-twist): Simulate yarn twist mechanics — explore how twist level, fiber length, fiber strength, and yarn count affect yarn tensile strength and the critical twist angle

### Tissue Engineering & Regenerative Medicine (5 simulations)
- [Bioreactor Design & Perfusion Flow](/lab/tissue-engineering/bioreactor-design): Design a perfusion bioreactor by tuning flow rate, chamber geometry, and scaffold permeability to optimize shear stress and nutrient delivery
- [Cell Proliferation & Growth Kinetics](/lab/tissue-engineering/cell-proliferation): Model cell population growth with logistic kinetics, doubling time, and growth factor concentration effects on tissue constructs
- [Oxygen Diffusion & Tissue Viability](/lab/tissue-engineering/oxygen-diffusion): Visualize oxygen concentration gradients in tissue constructs and predict the critical thickness beyond which necrosis occurs
- [Scaffold Degradation & Tissue Ingrowth](/lab/tissue-engineering/degradation-rate): Balance scaffold degradation kinetics with new tissue formation to maintain mechanical integrity throughout the regeneration process
- [Scaffold Porosity & Cell Infiltration](/lab/tissue-engineering/scaffold-porosity): Model scaffold pore architecture and simulate cell infiltration depth as a function of pore size, porosity, and interconnectivity

### Transportation & Traffic Science (5 simulations)
- [Autonomous Emergency Braking Simulator](/lab/transportation/autonomous-braking): Simulate autonomous emergency braking (AEB) systems — see how sensor delay, vehicle speed, road friction, and deceleration affect total stopping distance
- [Queueing Theory (M/M/1) Simulator](/lab/transportation/queue-theory): Simulate an M/M/1 queue to explore how arrival rate and service rate determine waiting times, queue length, and system utilization
- [Route Optimization (TSP) Simulator](/lab/transportation/route-optimization): Visualize the traveling salesman problem — compare nearest-neighbor, 2-opt, and simulated annealing algorithms to find short routes through randomly placed cities
- [Traffic Flow Simulator](/lab/transportation/traffic-flow): Explore the fundamental diagram of traffic flow — adjust vehicle density to observe the transition from free flow to congested traffic and the emergence of phantom jams
- [Vehicle Fuel Efficiency Simulator](/lab/transportation/fuel-efficiency): Model how speed, drag coefficient, vehicle mass, and rolling resistance affect fuel consumption — find the optimal cruising speed for maximum efficiency

### Tribology & Friction Science (5 simulations)
- [Friction Coefficient & Contact Mechanics](/lab/tribology/friction-coefficient): Calculate static and kinetic friction coefficients for various material pairs — explore the effects of normal load, surface energy, contact area, and sliding velocity on friction behavior
- [Journal Bearing Design & Optimization](/lab/tribology/bearing-design): Design and optimize hydrodynamic journal bearings — calculate film thickness, eccentricity, power loss, and temperature rise using Sommerfeld number analysis
- [Lubrication Regimes & Stribeck Curve](/lab/tribology/lubrication-regimes): Explore the Stribeck curve — simulate the transition from boundary to mixed to hydrodynamic lubrication as a function of viscosity, speed, load, and surface roughness
- [Surface Roughness & Texture Analysis](/lab/tribology/surface-roughness): Analyze surface roughness parameters — simulate Ra, Rq, Rsk, and Rku for different manufacturing processes and explore their effect on contact mechanics and functional performance
- [Wear Rate & Archard Equation](/lab/tribology/wear-rate): Predict material wear rate using the Archard wear model — explore effects of normal load, sliding distance, hardness, and wear coefficient on volume loss and component lifetime

### Water Treatment & Purification (5 simulations)
- [Activated Carbon Adsorption & Breakthrough](/lab/water-treatment/activated-carbon): Model activated carbon adsorption using the Freundlich isotherm — adjust carbon dose, influent concentration, and flow rate to see breakthrough curves
- [Chlorination & CT Disinfection Kinetics](/lab/water-treatment/chlorination): Model chlorine disinfection using the CT concept — adjust dose, contact time, pH, and temperature to see log inactivation of pathogens
- [Coagulation, Jar Test & Zeta Potential](/lab/water-treatment/coagulation): Simulate coagulation chemistry — adjust coagulant dose, pH, and mixing intensity to model zeta potential reduction and floc formation
- [Sedimentation & Stokes Settling](/lab/water-treatment/sedimentation): Model particle settling using Stokes' law — adjust particle size, density, and basin geometry to calculate settling velocity and removal efficiency
- [UV Disinfection & Dose-Response](/lab/water-treatment/uv-disinfection): Model UV disinfection dose-response — adjust UV intensity, exposure time, and transmittance to calculate log inactivation of pathogens

### Wind Engineering & Structural Aerodynamics (5 simulations)
- [Atmospheric Boundary Layer Wind Profile](/lab/wind-engineering/wind-profile): Visualize how wind speed increases with height using power law and logarithmic atmospheric boundary layer profiles for different terrain categories
- [Bridge Deck Aeroelastic Flutter Analysis](/lab/wind-engineering/flutter-analysis): Determine the critical flutter speed of a bridge deck by analyzing the coupling between torsional and vertical vibration modes under aerodynamic forcing
- [Building Pressure Coefficient (Cp) Visualizer](/lab/wind-engineering/pressure-coefficient): Visualize pressure coefficient distribution around a rectangular building cross-section as wind angle changes
- [Pedestrian Wind Comfort Criteria Simulator](/lab/wind-engineering/wind-comfort): Assess pedestrian wind comfort at ground level using Lawson and Davenport criteria for walking, sitting, and standing activities
- [Vortex Shedding & Strouhal Number Simulator](/lab/wind-engineering/vortex-shedding): Observe vortex shedding from a bluff body and the dangerous lock-in phenomenon when shedding frequency matches structural natural frequency

## humanities (2 topics, 10 simulations)

### Linguistics & Language (5 simulations)
- [Language Family Tree & Divergence Simulator](/lab/linguistics/language-tree): Watch languages evolve and diverge from common ancestors in real time — explore how Proto-Indo-European split into hundreds of modern languages over thousands of years
- [Markov Chain Text Generator](/lab/linguistics/markov-text): Generate surprisingly coherent text from simple probability chains — see how statistical patterns in language create the illusion of understanding without any grammar rules
- [Phonetic Vowel Space Simulator](/lab/linguistics/phonetic-vowel-space): Explore the IPA vowel chart as an interactive acoustic space — see how tongue height, backness, and rounding map to formant frequencies across the world's languages
- [Word Embedding Vector Space Simulator](/lab/linguistics/word-embedding): Explore the geometric space where words become vectors — see how king minus man plus woman equals queen, and why meaning has direction
- [Zipf's Law Word Frequency Simulator](/lab/linguistics/zipfs-law): Visualize how word frequencies in natural language follow a power law — the nth most common word appears proportional to 1/n, a pattern universal across all human languages

### Philosophy & Thought Experiments (5 simulations)
- [Nozick's Experience Machine Thought Experiment](/lab/philosophy/experience-machine): Would you plug into a machine that gives you any experience you want? Simulate the trade-offs between pleasure, authenticity, and agency
- [Rawls' Veil of Ignorance Resource Allocation](/lab/philosophy/veil-of-ignorance): Design a just society from behind the veil of ignorance — allocate resources when you don't know which position you'll occupy
- [Ship of Theseus Identity Paradox](/lab/philosophy/ship-of-theseus): Watch the Ship of Theseus transform plank by plank — at what percentage of replacement does identity break?
- [Trolley Problem Ethical Dilemma Simulator](/lab/philosophy/trolley-problem): Explore the classic trolley problem and its variants — simulate utilitarian vs deontological outcomes across thousands of moral scenarios
- [Utility Monster & Utilitarian Paradox](/lab/philosophy/utility-monster): Simulate the Utility Monster paradox — when one being derives vastly more utility from resources, should everyone else sacrifice for it?

## interdisciplinary (1 topics, 5 simulations)

### Complexity Science (5 simulations)
- [Ant Colony Optimization](/lab/complexity-science/ant-colony): Watch virtual ants solve the traveling salesman problem using pheromone trails — emergent intelligence from simple insects finding near-optimal routes
- [Boids Flocking Algorithm](/lab/complexity-science/boids-flocking): Watch emergent flocking behavior arise from three simple rules — separation, alignment, and cohesion — with no leader and no central control
- [Edge of Chaos (1D Cellular Automata)](/lab/complexity-science/edge-of-chaos): Explore Wolfram's 256 elementary cellular automata — from dead uniformity through complex computation to pure chaos — and find the edge where Rule 110 achieves Turing completeness
- [Self-Organized Criticality (Abelian Sandpile)](/lab/complexity-science/sandpile): Watch a sandpile self-organize to criticality — where adding a single grain can trigger avalanches of any size, following a power law that explains earthquakes and market crashes
- [Turing Morphogenesis Patterns](/lab/complexity-science/turing-patterns): Simulate Alan Turing's activator-inhibitor model of biological pattern formation — watch spots, stripes, and labyrinths emerge from random noise

## life-sciences (18 topics, 90 simulations)

### Aquaculture & Fish Farming Science (5 simulations)
- [Ammonia-Nitrite-Nitrate Nitrogen Cycle](/lab/aquaculture/water-quality): Simulate the nitrification cycle in a fish pond showing ammonia production, bacterial conversion to nitrite and nitrate, and toxicity thresholds
- [Dissolved Oxygen Dynamics & Aeration](/lab/aquaculture/dissolved-oxygen): Simulate dissolved oxygen levels in a fish pond under varying temperature, biomass load, and aeration rates to prevent hypoxic events
- [Feed Conversion Ratio & Growth Modeling](/lab/aquaculture/feed-conversion): Model fish growth curves and feed conversion ratios under varying feeding rates, protein levels, and temperature regimes
- [Recirculating Aquaculture System (RAS) Biofilter Performance](/lab/aquaculture/recirculating-system): Design and simulate a RAS biofilter system showing water recirculation, ammonia removal efficiency, and energy requirements
- [Stocking Density & Carrying Capacity](/lab/aquaculture/stocking-density): Model the relationship between fish stocking density, biomass growth, carrying capacity, and mortality to optimize production without overcrowding

### Astrobiology & Origin of Life (5 simulations)
- [Circumstellar Habitable Zone Calculator](/lab/astrobiology/habitable-zone): Calculate the inner and outer edges of the habitable zone for any star based on luminosity, effective temperature, and albedo feedback
- [Extremophile Survival Boundaries](/lab/astrobiology/extremophile-limits): Explore the temperature, pH, radiation, and pressure limits of extremophile organisms and map their survival envelopes
- [Habitable Worlds Probability Estimator](/lab/astrobiology/drake-parameters): Estimate the probability of habitable worlds using stellar formation rates, planetary occurrence, and habitability constraints
- [Miller-Urey Prebiotic Chemistry Simulation](/lab/astrobiology/miller-urey): Simulate the Miller-Urey experiment — model amino acid synthesis rates from primitive atmospheric gases under electrical discharge
- [Spectral Biosignature Analysis](/lab/astrobiology/biosignature-detection): Analyze exoplanet transmission spectra for biosignature gases — oxygen, methane, ozone, and water vapor absorption features

### Bioinformatics & Computational Biology (5 simulations)
- [De Bruijn Graph Genome Assembly](/lab/bioinformatics/genome-assembly): Simulate genome assembly using de Bruijn graphs — explore how k-mer size, read length, and coverage depth affect assembly contiguity and correctness
- [Needleman-Wunsch Global Sequence Alignment](/lab/bioinformatics/sequence-alignment): Simulate the Needleman-Wunsch dynamic programming algorithm for global sequence alignment — explore how scoring parameters affect optimal alignments
- [Protein Folding Energy Landscape](/lab/bioinformatics/protein-folding): Simulate a protein folding energy landscape — explore how temperature, hydrophobic strength, and chain length affect the folding funnel and native state stability
- [RNA-seq Differential Gene Expression](/lab/bioinformatics/gene-expression): Simulate RNA-seq differential expression analysis — explore how fold change, sample size, and read depth affect statistical power to detect differentially expressed genes
- [UPGMA Phylogenetic Tree Construction](/lab/bioinformatics/phylogenetic-tree): Simulate UPGMA hierarchical clustering to build phylogenetic trees from distance matrices — explore how sequence divergence maps to evolutionary relationships

### Circadian Biology & Chronobiology (5 simulations)
- [Clock Gene Network Oscillator](/lab/circadian-biology/clock-gene-network): Simulate the molecular clock gene feedback loop — explore how CLOCK/BMAL1 activation, PER/CRY inhibition, and degradation rates generate ~24-hour oscillations
- [Jet Lag Recovery Model](/lab/circadian-biology/jet-lag-model): Simulate jet lag recovery dynamics — model how time zone shifts, travel direction, light exposure, and individual chronotype affect circadian re-entrainment speed
- [Light Entrainment & Zeitgeber Strength](/lab/circadian-biology/light-entrainment): Simulate circadian entrainment to the light-dark cycle — explore how photoperiod, light intensity, spectral composition, and intrinsic period determine phase angle and stability
- [Phase Response Curve (PRC)](/lab/circadian-biology/phase-response-curve): Simulate the circadian phase response curve to light pulses — explore how timing, intensity, and duration of light exposure advance or delay the biological clock
- [Social Jet Lag & Health Impact](/lab/circadian-biology/social-jet-lag): Simulate social jet lag — quantify the mismatch between biological and social clocks, and explore its effects on metabolic health, cognitive performance, and disease risk

### Cognitive Neuroscience (5 simulations)
- [Attention Network Selection Model](/lab/cognitive-neuroscience/attention-network): Simulate attentional filtering — explore how signal strength, distractor count, and top-down bias shape the selection of relevant stimuli
- [Mirror Neuron Activation Model](/lab/cognitive-neuroscience/mirror-neuron): Simulate mirror neuron firing — explore how action observation, motor familiarity, and social context modulate the mirror system response
- [Neural Oscillation & Brainwave Synchrony](/lab/cognitive-neuroscience/neural-oscillation): Simulate cortical oscillations — explore how frequency bands, phase coupling, and amplitude modulation produce EEG rhythms linked to cognition
- [Neuroplasticity & Synaptic Strength](/lab/cognitive-neuroscience/neuroplasticity): Simulate experience-dependent neuroplasticity — explore how learning rate, spike timing, and repetition drive long-term synaptic potentiation and depression
- [Working Memory Capacity Model](/lab/cognitive-neuroscience/working-memory): Simulate working memory capacity — explore how chunk size, rehearsal rate, and decay time limit the number of items held in conscious awareness

### Comparative Anatomy & Morphology (5 simulations)
- [Allometric Scaling Laws](/lab/comparative-anatomy/allometric-scaling): Explore how body mass drives organ size, metabolic rate, and lifespan across species using power-law scaling relationships
- [Cephalization Index & Brain Allometry](/lab/comparative-anatomy/cephalization-index): Compare brain-to-body mass ratios across species — quantify encephalization quotients and explore what drives cognitive complexity in the animal kingdom
- [Convergent Evolution & Analogous Forms](/lab/comparative-anatomy/convergent-evolution): Visualize how unrelated lineages independently evolve similar body plans — streamlined shapes in sharks, dolphins, and ichthyosaurs under identical hydrodynamic pressures
- [Homologous Structures & Skeletal Mapping](/lab/comparative-anatomy/homologous-structures): Map homologous bones across vertebrate forelimbs — compare human arms, bat wings, whale flippers, and horse legs to reveal the shared ancestral blueprint
- [Vestigial Organs & Evolutionary Regression](/lab/comparative-anatomy/vestigial-organs): Model the regression of vestigial structures over evolutionary time — trace how functional organs become rudimentary under relaxed selection pressure

### Endocrinology & Hormone Signaling (5 simulations)
- [Circadian Cortisol Rhythm Simulator](/lab/endocrinology/circadian-cortisol): Visualize the diurnal cortisol rhythm driven by the suprachiasmatic nucleus, showing peak morning levels and nocturnal nadir with adjustable circadian parameters
- [Glucose-Insulin Homeostasis Simulator](/lab/endocrinology/insulin-glucose): Interactive model of glucose-insulin dynamics showing how beta-cell secretion and tissue sensitivity maintain blood sugar within physiological range
- [Hormone-Receptor Binding Kinetics Simulator](/lab/endocrinology/hormone-receptor): Interactive model of ligand-receptor binding equilibrium showing how hormone concentration, receptor density, and affinity determine cellular signaling response
- [HPA Axis Feedback Simulator](/lab/endocrinology/hpa-axis): Model the hypothalamic-pituitary-adrenal axis negative feedback loop showing how CRH, ACTH, and cortisol levels respond to stress and regulate each other
- [Thyroid Regulation Simulator](/lab/endocrinology/thyroid-regulation): Model the TSH-T3-T4 feedback loop showing how the hypothalamic-pituitary-thyroid axis maintains metabolic homeostasis

### Entomology & Insect Science (5 simulations)
- [Caste Ratio: Eusocial Colony Caste Allocation](/lab/entomology/caste-ratio): Optimize eusocial colony fitness by adjusting worker-soldier caste ratios — explore the trade-off between foraging capacity and colony defense
- [Insect Flight: Wing Kinematics & Lift Generation](/lab/entomology/insect-flight): Simulate insect wing kinematics — explore how stroke frequency, wing span, and stroke amplitude generate aerodynamic lift at low Reynolds numbers
- [Insect Population Cycle: Outbreak Dynamics & Voltinism](/lab/entomology/population-cycle): Model insect population outbreaks using discrete logistic growth — explore how growth rate, carrying capacity, and generation count drive boom-bust cycles
- [Metamorphosis Timing: Degree-Day Development Model](/lab/entomology/metamorphosis-timing): Predict insect development timing using degree-day accumulation — model how temperature drives progression through egg, larval, pupal, and adult stages
- [Pollination Efficiency: Flower Visit Rate & Pollen Transfer](/lab/entomology/pollination-efficiency): Model pollination efficiency — explore how visit rate, transfer efficiency, flower density, and foraging time determine fruit set in pollinator-dependent crops

### Enzyme Kinetics & Catalysis (5 simulations)
- [Allosteric Regulation & Hill Equation](/lab/enzyme-kinetics/allosteric-regulation): Simulate allosteric cooperativity — explore how the Hill coefficient shapes the sigmoidal response curve and enables switch-like metabolic regulation
- [Competitive Inhibition](/lab/enzyme-kinetics/competitive-inhibition): Simulate competitive enzyme inhibition — explore how inhibitor concentration and Ki alter apparent Km while Vmax remains unchanged
- [Enzyme Temperature Response & Arrhenius Kinetics](/lab/enzyme-kinetics/enzyme-temperature): Simulate enzyme activity vs temperature — explore Arrhenius activation energy and thermal denaturation that create an optimal temperature peak
- [Michaelis-Menten Kinetics & Lineweaver-Burk](/lab/enzyme-kinetics/michaelis-menten): Simulate Michaelis-Menten enzyme kinetics — explore how Vmax, Km, and substrate concentration determine reaction velocity with Lineweaver-Burk linearization
- [Multi-Substrate Mechanisms](/lab/enzyme-kinetics/multi-substrate): Simulate ping-pong and sequential bi-substrate enzyme mechanisms — explore how two substrates interact with the enzyme in ordered and random pathways

### Ethology & Animal Behavior (5 simulations)
- [Fixed Action Pattern Simulator](/lab/ethology/fixed-action-pattern): Interactive model of innate behavioral sequences triggered by sign stimuli, showing how stimulus intensity and threshold determine the probability and completeness of fixed action patterns
- [Honeybee Waggle Dance Simulator](/lab/ethology/waggle-dance): Interactive visualization of Karl von Frisch's waggle dance communication system, showing how bees encode food source distance and direction through dance angle and duration
- [Imprinting & Critical Period Simulator](/lab/ethology/imprinting): Interactive model of Lorenz's filial imprinting showing how sensitive periods, stimulus exposure timing, and irreversibility shape early behavioral attachment
- [Kin Selection & Hamilton's Rule Simulator](/lab/ethology/kin-selection): Interactive model of Hamilton's rule (rB > C) showing how genetic relatedness drives the evolution of altruistic behavior among relatives
- [Optimal Foraging Theory Simulator](/lab/ethology/optimal-foraging): Interactive model of the marginal value theorem showing how animals optimize time allocation across food patches of varying quality

### Forensic Genetics & DNA Profiling (5 simulations)
- [DNA Degradation Kinetics & Fragment Size Distribution](/lab/forensic-genetics/degradation-kinetics): Model time-dependent DNA degradation under environmental conditions and predict recoverable fragment sizes for forensic STR analysis
- [DNA Mixture Deconvolution & Contributor Estimation](/lab/forensic-genetics/mixture-analysis): Analyze mixed DNA profiles by estimating contributor ratios, stochastic thresholds, and mixture likelihood ratios across STR loci
- [Forensic Population Statistics & Match Probability](/lab/forensic-genetics/population-statistics): Calculate random match probabilities, likelihood ratios, and database search statistics using Hardy-Weinberg expectations and population correction factors
- [Paternity Index & Likelihood Ratio](/lab/forensic-genetics/paternity-index): Calculate the combined paternity index and probability of paternity from STR genotype data using likelihood ratios across multiple loci
- [STR Loci & Allele Frequency Analysis](/lab/forensic-genetics/str-profiling): Visualize Short Tandem Repeat allele frequency distributions across forensic loci and calculate per-locus heterozygosity and discrimination power

### Mycology & Fungal Biology (5 simulations)
- [Decomposition Rate: Lignocellulose Decay & Carbon Cycling](/lab/mycology/decomposition-rate): Model fungal decomposition of lignocellulose — explore how moisture, temperature, and lignin content determine decay rate, half-life, and carbon flux
- [Fungal Pharmacology: Bioactive Compound Dose-Response](/lab/mycology/fungal-pharmacology): Model dose-response curves for fungal bioactive compounds — explore how dose, EC50, Hill coefficient, and maximum efficacy determine pharmacological response
- [Mycelial Growth: Radial Colony Expansion & Nutrient Uptake](/lab/mycology/mycelial-growth): Model radial mycelial colony expansion — explore how growth rate, nutrient concentration, temperature, and humidity drive hyphal extension and biomass accumulation
- [Spore Dispersal: Wind-Borne Spore Transport Model](/lab/mycology/spore-dispersal): Simulate wind-borne fungal spore dispersal — model how wind speed, release height, spore diameter, and turbulence determine transport distance and deposition patterns
- [Symbiosis Model: Mycorrhizal Nutrient Exchange](/lab/mycology/symbiosis-model): Model mycorrhizal symbiosis — explore how carbon allocation, phosphorus availability, root density, and fungal cover determine nutrient exchange and net plant benefit

### Paleoanthropology & Human Evolution (5 simulations)
- [Brain Size Evolution Over Time](/lab/paleoanthropology/cranial-capacity): Simulate cranial capacity evolution — explore how encephalization rate, dietary quality, and social group size correlate with brain volume across hominin species
- [K-Ar & U-Pb Radiometric Age Determination](/lab/paleoanthropology/radiometric-dating): Simulate radiometric dating — explore how parent isotope ratio, half-life, decay constant, and measurement precision determine age calculations for geological and fossil samples
- [Lithic Technology & Cognitive Evolution](/lab/paleoanthropology/tool-complexity): Simulate stone tool complexity — explore how reduction steps, planning depth, technique variety, and symmetry requirements reflect cognitive evolution in hominins
- [Out-of-Africa Dispersal Simulation](/lab/paleoanthropology/migration-model): Simulate hominin dispersal from Africa — explore how migration speed, population growth, carrying capacity, and climate barriers shape expansion patterns
- [Stable Isotope & Dental Diet Analysis](/lab/paleoanthropology/dietary-reconstruction): Simulate dietary reconstruction — explore how carbon-13, nitrogen-15 isotope ratios, dental microwear, and tooth morphology reveal ancient hominin diets

### Paleobotany & Fossil Plants (5 simulations)
- [Fossil Wood Growth Rings & Paleoclimate](/lab/paleobotany/wood-anatomy): Analyze growth ring patterns in petrified wood to reconstruct paleoclimate seasonality, temperature, and precipitation
- [Leaf Margin Analysis & Paleotemperature](/lab/paleobotany/leaf-margin): Estimate mean annual temperature from the percentage of entire-margined (smooth-edged) leaves in a fossil flora using leaf margin analysis
- [Phytolith Morphology & Habitat Reconstruction](/lab/paleobotany/phytolith-analysis): Classify silica phytolith morphotypes from sediment samples to reconstruct grassland versus forest habitats through geological time
- [Pollen Percentage Diagram & Vegetation Reconstruction](/lab/paleobotany/pollen-diagram): Build a pollen percentage diagram from simulated core data and reconstruct shifting vegetation zones through time
- [Stomatal Index & Paleo-CO2 Reconstruction](/lab/paleobotany/stomatal-density): Reconstruct ancient atmospheric CO2 concentrations from the stomatal index of fossil leaves using the inverse relationship between stomatal density and CO2

### Paleontology & Deep Time (5 simulations)
- [Continental Drift & Plate Tectonics Simulator](/lab/paleontology/plate-tectonics-evolution): Watch continents drift across the globe over 300 million years — from Pangaea to today's configuration and into the future
- [Dinosaur Body Size Scaling Laws Simulator](/lab/paleontology/dinosaur-size): Explore allometric scaling laws that governed dinosaur body size — from metabolic rate to bone strength and the physics of gigantism
- [Mass Extinction Events Timeline Simulator](/lab/paleontology/mass-extinction): Explore the Big Five mass extinctions across 500 million years — visualize species loss, recovery time, and the causes behind each catastrophe
- [Phylogenetic Tree Reconstruction Simulator](/lab/paleontology/phylogenetic-tree): Build phylogenetic trees from trait matrices using distance-based and parsimony methods — explore how evolutionary relationships are inferred
- [Radiometric Fossil Dating Methods Simulator](/lab/paleontology/fossil-dating): Explore how radioactive decay curves are used to determine the age of fossils and rocks — from carbon-14 to uranium-lead dating

### Parasitology & Host-Parasite Dynamics (5 simulations)
- [Anderson-May Host-Parasite Model](/lab/parasitology/host-parasite-model): Simulate the Anderson-May SIR framework with parasite load, showing how transmission rate, host recovery, and parasite-induced mortality shape endemic equilibria
- [Helminth Burden Distribution Simulator](/lab/parasitology/helminth-burden): Visualize the overdispersed distribution of worm burdens across a host population using the negative binomial model with adjustable aggregation
- [Mosquito Vectorial Capacity Simulator](/lab/parasitology/vector-capacity): Calculate vectorial capacity for mosquito-borne disease transmission incorporating biting rate, survival probability, vector competence, and extrinsic incubation period
- [Parasite Drug Resistance Evolution Simulator](/lab/parasitology/drug-resistance): Model the evolutionary dynamics of drug resistance in parasite populations showing how treatment pressure, fitness costs, and mutation rates drive resistance spread
- [Plasmodium Erythrocytic Cycle Simulator](/lab/parasitology/malaria-lifecycle): Model the intra-erythrocytic lifecycle of Plasmodium falciparum showing merozoite invasion, replication, and red blood cell lysis dynamics

### Speech Science & Phonetics (5 simulations)
- [Articulatory Speech Synthesis](/lab/speech-science/speech-synthesis): Synthesize vowel sounds from articulatory parameters — control tongue position, jaw opening, and lip rounding to shape the vocal tract and generate formant patterns
- [Pitch Tracking & Intonation](/lab/speech-science/pitch-tracking): Visualize fundamental frequency contours — explore how pitch patterns encode questions, statements, emotions, and tonal distinctions in speech
- [Speech Spectrogram Viewer](/lab/speech-science/spectrogram-viewer): Generate and read spectrograms of synthetic speech signals — visualize how frequency content evolves over time for different vowels and consonants
- [Voice Onset Time (VOT) Analyzer](/lab/speech-science/voice-onset-time): Visualize voice onset time — the critical timing difference between voiced and voiceless stop consonants across languages
- [Vowel Formant Analysis](/lab/speech-science/formant-analysis): Explore how the first two formant frequencies (F1 and F2) define vowel identity — map any vowel on the acoustic vowel space in real time

### Xenobiology & Alien Life (5 simulations)
- [Alternative Biochemistry Designer](/lab/xenobiology/alternative-biochemistry): Design non-carbon biochemistries — explore how solvent polarity, backbone element, and temperature range constrain the possibility space of alien life
- [Extremophile Survival Limits](/lab/xenobiology/extremophile-limits): Push extremophiles to their limits — model how temperature, pH, radiation dose, and salinity define the boundary of habitable space for life
- [Shadow Biosphere Detector](/lab/xenobiology/shadow-biosphere): Simulate detection of a hypothetical shadow biosphere — organisms with non-standard biochemistry hiding in plain sight on Earth
- [Silicon-Based Life Simulator](/lab/xenobiology/silicon-life): Model silicon-based metabolism — explore how temperature, pressure, and solvent conditions determine whether silicon chemistry can support living systems
- [XNA Polymer Designer](/lab/xenobiology/xna-polymers): Design xeno-nucleic acid polymers — explore how sugar backbone modifications affect base-pairing stability, replication fidelity, and information density

## mathematics (17 topics, 87 simulations)

### Biostatistics & Clinical Trials (5 simulations)
- [Adaptive Clinical Trial Design](/lab/biostatistics/clinical-trial-design): Simulate a multi-arm adaptive clinical trial with interim analyses — visualize efficacy boundaries, futility stopping, and arm-dropping decisions
- [Kaplan-Meier Survival Analysis](/lab/biostatistics/survival-analysis): Generate and compare Kaplan-Meier survival curves for treatment vs. control groups — visualize censoring, confidence intervals, and hazard ratios
- [Meta-Analysis Forest Plot](/lab/biostatistics/meta-analysis): Combine effect estimates from multiple studies into a pooled estimate — visualize forest plots, heterogeneity, and the impact of individual study weights
- [Regression Diagnostics & Residual Analysis](/lab/biostatistics/regression-diagnostics): Fit a regression model and diagnose violations — visualize residual plots, leverage, Cook's distance, and normality checks
- [Sample Size & Power Calculator](/lab/biostatistics/sample-size): Calculate the sample size needed to detect a treatment effect with specified power — visualize the relationship between effect size, sample size, and Type I/II error

### Computational Geometry (5 simulations)
- [Convex Hull Algorithm Visualizer](/lab/computational-geometry/convex-hull): Visualize convex hull construction — watch gift-wrapping and Graham scan algorithms build the tightest boundary around a point set step by step
- [Delaunay Triangulation Builder](/lab/computational-geometry/delaunay-triangulation): Construct Delaunay triangulations interactively — observe the empty circumcircle property, flip operations, and mesh quality metrics in real time
- [Line Sweep Intersection Detector](/lab/computational-geometry/line-sweep): Visualize the sweep-line algorithm for detecting segment intersections — watch the event queue and status structure in real time
- [Polygon Clipping Visualizer](/lab/computational-geometry/polygon-clipping): Visualize polygon clipping operations — see Sutherland-Hodgman and Weiler-Atherton algorithms clip subject polygons against convex and concave windows
- [Voronoi Diagram Generator](/lab/computational-geometry/voronoi-diagram): Generate interactive Voronoi diagrams — explore how seed point placement, distance metrics, and perturbation affect spatial partitioning

### Decision Theory (5 simulations)
- [Auction Theory Simulator](/lab/decision-theory/optimal-auction): Compare English, Dutch, first-price sealed, and Vickrey auctions — see revenue equivalence, bidding strategies, and efficiency in action
- [Kelly Criterion Betting](/lab/decision-theory/kelly-criterion): Visualize optimal bet sizing with the Kelly criterion — compare wealth trajectories for Kelly, over-betting, under-betting, and all-in strategies
- [Markowitz Portfolio Frontier](/lab/decision-theory/portfolio-optimization): Explore mean-variance portfolio optimization — visualize the efficient frontier, tangency portfolio, and diversification benefits
- [Multi-Armed Bandit (Explore vs Exploit)](/lab/decision-theory/multi-armed-bandit): Compare exploration strategies in the multi-armed bandit problem — random, epsilon-greedy, UCB1, and Thompson sampling
- [Prospect Theory & Loss Aversion](/lab/decision-theory/prospect-theory-gambles): Visualize the S-shaped value function of prospect theory — see how loss aversion, diminishing sensitivity, and reference dependence distort rational decision-making

### Game Theory (5 simulations)
- [Auction Theory Simulator](/lab/game-theory/auction-theory): Compare first-price, second-price (Vickrey), and English auctions — visualize bidding strategies, revenue, and efficiency with configurable bidder populations
- [Evolutionary Stable Strategy (ESS) Simulator](/lab/game-theory/evolutionary-stable-strategy): Simulate the Hawk-Dove game with replicator dynamics — watch population frequencies converge to the evolutionarily stable strategy predicted by V/C
- [Iterated Prisoner's Dilemma Simulator](/lab/game-theory/prisoners-dilemma): Simulate Axelrod-style tournaments with Tit-for-Tat, Always Defect, and Always Cooperate strategies competing across hundreds of rounds with configurable noise
- [Nash Equilibrium Visualizer](/lab/game-theory/nash-equilibrium): Explore mixed-strategy Nash equilibria in 2x2 bimatrix games with interactive best-response diagrams
- [Tragedy of the Commons Simulator](/lab/game-theory/tragedy-of-commons): Model resource depletion dynamics with competing herders — watch how cooperation percentage determines whether a shared resource collapses or sustains

### Geometry & Spatial Structures (5 simulations)
- [Hyperbolic Geometry & Poincaré Disk Tiling](/lab/geometry/hyperbolic-tiling): Explore hyperbolic tilings in the Poincaré disk model — visualize non-Euclidean geometry where parallel lines diverge and triangles have angle sums less than 180°
- [Platonic Solids Wireframe Rotation](/lab/geometry/platonic-solids): Rotate all five Platonic solids in 3D wireframe — tetrahedron, cube, octahedron, dodecahedron, and icosahedron — and explore their dual relationships
- [Projective Geometry & Perspective](/lab/geometry/projective-geometry): Explore projective transformations, vanishing points, and cross-ratios — the geometry behind perspective drawing, camera calibration, and algebraic geometry
- [Tessellation & Tiling Patterns](/lab/geometry/tessellation): Create tessellations with different polygon types and symmetry groups — explore how shapes tile the plane without gaps or overlaps
- [Voronoi Diagram & Delaunay Triangulation](/lab/geometry/voronoi-diagram): Generate Voronoi diagrams and their dual Delaunay triangulations from seed points — explore spatial partitioning, nearest-neighbor regions, and computational geometry

### Geostatistics & Spatial Analysis (5 simulations)
- [Indicator Kriging Probability Mapper](/lab/geostatistics/indicator-kriging): Map the probability of exceeding a critical cutoff grade using indicator kriging with binary-transformed spatial data
- [Moran's I & LISA Spatial Clustering Detector](/lab/geostatistics/spatial-clustering): Detect and visualize spatial clusters and outliers using global Moran's I statistic and Local Indicators of Spatial Association
- [Ordinary Kriging Interpolation Simulator](/lab/geostatistics/kriging): Watch ordinary kriging build optimal interpolated surfaces from scattered sample points using spatial correlation structure
- [Ore Body Block Estimation Simulator](/lab/geostatistics/block-model): Estimate ore grades in a 2D block model grid using kriging and classify blocks as ore or waste based on economic cutoff
- [Semivariogram Modeling & Range Estimation](/lab/geostatistics/variogram): Explore how spatial correlation decays with distance by fitting spherical, exponential, and Gaussian variogram models to scattered data

### Graph Theory & Networks (5 simulations)
- [Dijkstra's Shortest Path Simulator](/lab/graph-theory/shortest-path): Watch Dijkstra's algorithm explore a weighted graph step by step, revealing the shortest path from source to destination in real time
- [Eulerian & Hamiltonian Path Explorer](/lab/graph-theory/eulerian-path): Trace paths that visit every edge or every vertex exactly once — discover why Euler paths are easy to find but Hamiltonian paths are NP-hard
- [Graph Coloring & Chromatic Number](/lab/graph-theory/graph-coloring): Explore the graph coloring problem — assign colors to vertices so that no two adjacent vertices share a color and discover the chromatic number
- [Max Flow / Min Cut Simulator](/lab/graph-theory/network-flow): Push flow through a network from source to sink and discover the max-flow min-cut theorem — the duality that connects maximum throughput to minimum bottleneck
- [Minimum Spanning Tree Simulator](/lab/graph-theory/minimum-spanning-tree): Build the cheapest network connecting all nodes — watch Kruskal's algorithm sort edges and grow a minimum spanning tree step by step

### Information Theory (4 simulations)
- [Channel Capacity Explorer](/lab/information-theory/channel-capacity): Visualize Shannon's channel capacity theorem — the ultimate speed limit of communication. Explore how bandwidth, signal-to-noise ratio, and modulation scheme determine the maximum data rate, and see c
- [Data Compression Simulator](/lab/information-theory/data-compression): Visualize how Huffman coding compresses data by exploiting symbol frequency imbalance. Compare original size, compressed size, and the theoretical Shannon limit across different source types — from En
- [Error Correction Simulator](/lab/information-theory/error-correction): Watch error correction codes detect and fix transmission errors in real time. Compare uncoded transmission, triple repetition, and Hamming(7,4) codes to see how redundancy trades bandwidth for reliabi
- [Shannon Entropy Calculator](/lab/information-theory/shannon-entropy): Explore the foundational measure of information: Shannon entropy. Adjust symbol probabilities to see how uncertainty, redundancy, and optimal code lengths change. Discover why English text carries abo

### Mathematical Art (5 simulations)
- [L-System Fractal Plants](/lab/art-mathematics/l-system-plants): Grow fractal trees, ferns, bushes, and flowers using Lindenmayer systems — simple rewriting rules that produce stunningly realistic plant structures
- [Lissajous Figures](/lab/art-mathematics/lissajous): Draw beautiful Lissajous curves from two perpendicular oscillations — explore frequency ratios, phase shifts, and the figures used to calibrate oscilloscopes
- [Phyllotaxis / Sunflower Spiral](/lab/art-mathematics/phyllotaxis): Explore how the golden angle creates the optimal seed packing found in sunflowers, pinecones, and pineapples — and watch Fibonacci spirals emerge from pure mathematics
- [Reaction-Diffusion Patterns (Gray-Scott)](/lab/art-mathematics/reaction-diffusion): Watch organic patterns emerge from chemical equations — spots, stripes, spirals, and chaos generated by the Gray-Scott reaction-diffusion model that explains animal coat patterns
- [Spirograph / Hypotrochoid Curves](/lab/art-mathematics/spirograph): Generate mesmerizing spirograph curves by rolling one circle inside another — explore the geometry of hypotrochoid and epicycloid curves through interactive animation

### Mathematical Biology & Population Dynamics (5 simulations)
- [Fisher-KPP Traveling Wave Equation](/lab/mathematical-biology/fisher-wave): Simulate Fisher-KPP traveling wavefronts — explore how diffusion and logistic growth combine to produce advancing population fronts at a minimum speed
- [Galton-Watson Branching Process](/lab/mathematical-biology/branching-process): Simulate stochastic branching processes — explore how offspring distribution determines extinction probability, population growth, and genealogical tree structure
- [Lotka-Volterra Predator-Prey Dynamics](/lab/mathematical-biology/lotka-volterra): Simulate classic predator-prey oscillations — explore how birth rates, predation efficiency, and mortality shape population cycles in ecological systems
- [SIR Compartment Epidemic Model](/lab/mathematical-biology/sir-compartment): Simulate epidemic dynamics with the SIR model — explore how transmission rate, recovery rate, and population size determine outbreak size and herd immunity thresholds
- [Turing Reaction-Diffusion Patterns](/lab/mathematical-biology/turing-pattern): Simulate Turing morphogenesis — explore how activator-inhibitor diffusion ratios generate spots, stripes, and labyrinthine patterns from uniform initial conditions

### Mathematics (8 simulations)
- [2D Random Walk](/lab/mathematics/random-walk): Watch particles take random steps in two dimensions. Discover the square-root law of diffusion as walkers drift from the origin.
- [Central Limit Theorem Demo](/lab/mathematics/central-limit-theorem): See the Central Limit Theorem in action: sample from any distribution and watch the distribution of means converge to a perfect bell curve.
- [Fourier Series Visualizer](/lab/mathematics/fourier-series): Decompose any waveform into sine and cosine harmonics. Watch rotating circles (epicycles) construct square waves, sawtooth waves, and more.
- [Fractal Tree Generator](/lab/mathematics/fractal-tree): Grow recursive fractal trees by adjusting branch angles, depth, and length ratios. Explore self-similarity and fractal dimensions in botanical structures.
- [Golden Ratio & Fibonacci Spiral](/lab/mathematics/golden-ratio): Explore the golden ratio through interactive Fibonacci spirals and golden rectangle subdivisions. Watch how the ratio of consecutive Fibonacci numbers converges to phi.
- [Monte Carlo Pi Estimation](/lab/mathematics/pi-estimation): Estimate pi by throwing random darts at a square with an inscribed circle. Watch the approximation improve as more points accumulate.
- [Normal Distribution / Bell Curve](/lab/mathematics/normal-distribution): Visualize the Gaussian bell curve and explore the 68-95-99.7 rule. Adjust mean, standard deviation, and sample size to see how the distribution shapes data.
- [Sieve of Eratosthenes](/lab/mathematics/prime-sieve): Watch the ancient algorithm discover prime numbers in real time. Composite numbers are crossed off one by one as each new prime is found.

### Network Science (5 simulations)
- [Percolation Threshold Simulator](/lab/network-science/percolation-threshold): Interactive site percolation on a 2D square lattice demonstrating the critical phase transition at p_c where a giant connected cluster suddenly emerges
- [Power-Law Distribution Explorer](/lab/network-science/power-law-distribution): Interactive exploration of power-law distributions and Zipf's law across city sizes, word frequencies, wealth distribution, and earthquake magnitudes
- [Scale-Free Networks Simulator](/lab/network-science/scale-free-networks): Interactive Barabasi-Albert preferential attachment model showing how hub-dominated scale-free networks emerge and respond to targeted vs random attacks
- [SIR Epidemic Spreading Model](/lab/network-science/epidemic-spreading): Interactive SIR compartmental model showing how infectious diseases spread through populations, with vaccination and herd immunity dynamics
- [Small-World Network Model](/lab/network-science/small-world): Interactive Watts-Strogatz model demonstrating how a small amount of random rewiring creates the 'small-world' phenomenon with short paths and high clustering

### Number Theory & Prime Numbers (5 simulations)
- [Continued Fractions Explorer](/lab/number-theory/continued-fractions): Expand any real number into its continued fraction representation — visualize convergents approaching the target and discover best rational approximations
- [Goldbach's Conjecture Verifier](/lab/number-theory/goldbach-conjecture): Test Goldbach's conjecture interactively — decompose any even number into pairs of primes and visualize the number of representations
- [Modular Arithmetic & Clock Math](/lab/number-theory/modular-arithmetic): Explore modular arithmetic visually — compute modular exponentiation, visualize residue classes on a clock dial, and see congruence patterns
- [Prime Distribution & Number Theorem](/lab/number-theory/prime-distribution): Visualize how primes thin out along the number line — compare π(x) against N/ln(N) and the logarithmic integral Li(x) in real time
- [Sieve of Eratosthenes](/lab/number-theory/prime-sieve): Visualize the Sieve of Eratosthenes in real time — watch composite numbers get eliminated as primes are discovered up to any limit

### Operations Research & Optimization (5 simulations)
- [Economic Order Quantity & Inventory Costs](/lab/operations-research/inventory-model): Optimize inventory replenishment — explore how demand rate, ordering cost, and holding cost determine the economic order quantity and total cost
- [Job Scheduling & Makespan Optimization](/lab/operations-research/scheduling-problem): Schedule jobs on parallel machines — explore how job count, machine count, and heuristic choice affect makespan and load balance
- [Linear Programming & Feasible Region](/lab/operations-research/linear-programming): Visualize a 2D linear programming problem — adjust constraints and objective function to see the feasible region, corner points, and optimal solution
- [Markov Chain & Steady-State Analysis](/lab/operations-research/markov-chain): Visualize a discrete Markov chain — adjust transition probabilities and watch the state distribution converge to its steady-state equilibrium
- [Monte Carlo Simulation & Probability Estimation](/lab/operations-research/monte-carlo-simulation): Estimate pi and other quantities using random sampling — watch Monte Carlo convergence in real time as sample size grows

### Probability & Randomness (5 simulations)
- [Birthday Paradox Simulator](/lab/probability/birthday-paradox): Discover why only 23 people are needed for a 50% chance of a shared birthday — one of probability's most surprising results
- [Galton Board (Bean Machine)](/lab/probability/galton-board): Watch balls cascade through pegs to form a perfect bell curve — the physical demonstration of the Central Limit Theorem
- [Law of Large Numbers Visualizer](/lab/probability/law-of-large-numbers): Watch the running average converge to the true mean as samples accumulate — the foundation of all statistical inference
- [Monty Hall Problem Simulator](/lab/probability/monty-hall): Simulate thousands of Monty Hall games to prove why switching doors wins 2/3 of the time — the most counterintuitive result in probability
- [Secretary Problem (Optimal Stopping)](/lab/probability/secretary-problem): Explore the elegant 37% rule — reject the first third of candidates, then pick the next one who's the best so far

### Statistics & Inference (5 simulations)
- [Analysis of Variance (ANOVA)](/lab/statistics/anova): Compare means across multiple groups with one-way ANOVA — visualize between-group and within-group variance to understand the F-test
- [Chi-Squared Test for Independence](/lab/statistics/chi-squared): Build contingency tables and run chi-squared tests to determine whether two categorical variables are independent or associated
- [Confidence Intervals & Sample Size](/lab/statistics/confidence-intervals): Visualize how confidence intervals shrink with larger samples and see why a 95% CI does not mean 95% probability the parameter is inside
- [Hypothesis Testing & P-Values](/lab/statistics/hypothesis-testing): Simulate hypothesis tests to understand p-values, Type I and Type II errors, and why statistical significance doesn't mean practical significance
- [Regression to the Mean](/lab/statistics/regression-to-mean): Visualize why extreme observations tend to be followed by less extreme ones — the statistical phenomenon that fools coaches, doctors, and policymakers

### Topology & Surfaces (5 simulations)
- [Euler Characteristic V−E+F](/lab/topology/euler-characteristic): Compute the Euler characteristic for polyhedra and surfaces — the topological invariant that connects vertices, edges, and faces through V−E+F
- [Four Color Theorem Map Coloring](/lab/topology/topological-map): Color maps with the minimum number of colors so no two adjacent regions share a color — demonstrating the famous four color theorem interactively
- [Klein Bottle Immersion in 3D](/lab/topology/klein-bottle): Visualize the Klein bottle — a closed non-orientable surface that cannot exist in 3D without self-intersection — through its classic figure-eight immersion
- [Knot Invariants & Crossings](/lab/topology/knot-theory): Explore mathematical knots — closed curves in 3D space — and compute their invariants including crossing number, writhe, and unknotting number
- [Möbius Strip & Non-Orientability](/lab/topology/mobius-strip): Explore the Möbius strip — a surface with only one side and one edge — and discover why non-orientability breaks our intuition about inside and outside

## medical-science (1 topics, 5 simulations)

### Plasma Medicine (5 simulations)
- [Atmospheric Plasma Jet Dynamics](/lab/plasma-medicine/plasma-jet): Simulate a cold atmospheric plasma jet — explore how voltage, gas flow, and nozzle diameter shape the plasma plume geometry, temperature profile, and reactive species output
- [Cold Plasma Sterilization Kinetics](/lab/plasma-medicine/cold-plasma-sterilization): Simulate cold atmospheric plasma sterilization — explore how plasma power, exposure time, and gas composition affect microbial inactivation rates
- [Plasma-Assisted Dentistry](/lab/plasma-medicine/plasma-dentistry): Simulate plasma dental treatment — explore how plasma exposure, cavity depth, and bacterial biofilm thickness affect sterilization and dentin bond strength enhancement
- [Plasma-Assisted Wound Healing](/lab/plasma-medicine/plasma-wound-healing): Simulate plasma-accelerated wound closure — explore how treatment dose, wound area, and NO concentration drive fibroblast proliferation and tissue regeneration
- [Reactive Oxygen & Nitrogen Species (RONS)](/lab/plasma-medicine/reactive-species): Simulate RONS generation and diffusion — explore how plasma parameters, humidity, and target distance control the therapeutic cocktail of reactive species in plasma medicine

## medical-sciences (3 topics, 15 simulations)

### Epidemiological Modeling & Disease Spread (5 simulations)
- [Contact Tracing Network Visualization](/lab/epidemiological-modeling/contact-tracing): Trace infection paths through a social network — watch how identifying and isolating contacts breaks transmission chains and reduces outbreak size
- [Pandemic Waves & Seasonal Recurrence](/lab/epidemiological-modeling/pandemic-waves): Simulate how waning immunity, seasonal forcing, and behavioral changes combine to produce the recurring waves seen in real pandemics from 1918 influenza to COVID-19
- [SIR Compartmental Model Simulation](/lab/epidemiological-modeling/sir-model): Watch a classic SIR epidemic unfold — susceptible, infected, and recovered compartments evolve according to differential equations that govern disease dynamics
- [Superspreader Events & Overdispersion](/lab/epidemiological-modeling/superspreader-events): Explore how overdispersed transmission — where a small fraction of cases causes most infections — fundamentally changes epidemic dynamics and control strategies
- [Vaccination & Herd Immunity Threshold](/lab/epidemiological-modeling/vaccination-threshold): Calculate the critical vaccination coverage needed to achieve herd immunity — visualize how vaccine efficacy and R₀ determine whether an outbreak can take hold

### Pharmacology & Drug Kinetics (5 simulations)
- [Bioavailability & First-Pass Effect](/lab/pharmacology/bioavailability): Simulate oral bioavailability — explore how gut absorption fraction, first-pass hepatic extraction, gut wall metabolism, and formulation factor determine systemic drug exposure
- [Dose-Response Curve & EC50](/lab/pharmacology/dose-response): Simulate sigmoidal dose-response relationships — explore how EC50, Hill coefficient, efficacy ceiling, and baseline activity shape the pharmacodynamic curve
- [Drug Absorption & Plasma Concentration](/lab/pharmacology/drug-absorption): Simulate oral drug absorption — explore how absorption rate, dose, volume of distribution, and elimination rate shape the plasma concentration-time curve
- [Drug-Drug Interaction Modeling](/lab/pharmacology/drug-interaction): Simulate pharmacokinetic drug interactions — explore how enzyme inhibition, induction, and protein binding displacement alter plasma drug levels
- [Half-Life & Drug Elimination](/lab/pharmacology/half-life-elimination): Simulate drug elimination kinetics — explore how half-life, initial concentration, dosing interval, and number of doses affect steady-state accumulation

### Toxicology & Dose-Response (5 simulations)
- [Bioaccumulation & Biomagnification](/lab/toxicology/bioaccumulation): Simulate chemical bioaccumulation through trophic levels — explore how bioconcentration factor, trophic transfer efficiency, and elimination rate drive tissue concentration
- [LD50 Dose-Response Estimation](/lab/toxicology/ld50-estimation): Simulate LD50 dose-response curves — explore how dose, slope factor, and organism sensitivity shape the sigmoidal mortality relationship
- [Multi-Route Exposure Assessment](/lab/toxicology/exposure-assessment): Simulate chemical exposure through multiple routes — explore how inhalation, ingestion, and dermal absorption contribute to total daily intake and hazard quotient
- [Quantitative Risk Characterization](/lab/toxicology/risk-characterization): Simulate quantitative cancer and non-cancer risk assessment — explore how slope factor, exposure duration, and population size determine individual and population risk
- [Threshold Limit Values & Workplace Safety](/lab/toxicology/threshold-limit): Simulate occupational exposure limits — explore how TLV-TWA, STEL, ceiling values, and exposure duration determine workplace safety compliance

## physics (36 topics, 176 simulations)

### Acoustics & Sound Engineering (5 simulations)
- [Active Noise Cancellation](/lab/acoustics/noise-cancellation): Simulate active noise cancellation — explore how anti-phase signals, delay compensation, and filter adaptation reduce unwanted sound
- [Doppler Effect & Frequency Shift](/lab/acoustics/doppler-effect): Simulate the Doppler effect — explore how source velocity, observer velocity, and medium speed produce frequency shifts in sound waves
- [Room Acoustics & Reverberation](/lab/acoustics/room-acoustics): Simulate room acoustics and reverberation time — explore how room dimensions, surface absorption, and speaker position affect sound decay and clarity
- [Standing Wave Resonance Modes](/lab/acoustics/resonance-modes): Simulate standing wave resonance patterns — explore how mode number, tube length, boundary conditions, and damping shape resonant frequencies and node patterns
- [Ultrasound Beam Focusing & Imaging](/lab/acoustics/ultrasound): Simulate ultrasound beam propagation — explore how frequency, aperture, focal depth, and tissue attenuation affect beam width and imaging resolution

### Acousto-Optics & Light-Sound Interaction (5 simulations)
- [Acousto-Optic Deflector Resolution & Scan Range](/lab/acousto-optics/deflector-design): Design acousto-optic beam deflectors by calculating resolvable spots, scan angle, access time, and deflection efficiency across the operating bandwidth
- [Acousto-Optic Modulator Rise Time & Extinction](/lab/acousto-optics/aom-modulator): Model AOM switching dynamics including rise time, modulation bandwidth, extinction ratio, and insertion loss for laser beam modulation
- [Acousto-Optic Tunable Filter (AOTF) Spectral Response](/lab/acousto-optics/tunable-filter): Model AOTF wavelength selection, spectral resolution, and tuning range for hyperspectral imaging and spectroscopic applications
- [Bragg Acousto-Optic Diffraction Efficiency](/lab/acousto-optics/bragg-diffraction): Calculate diffraction efficiency, Bragg angle, and bandwidth for acousto-optic Bragg regime interaction in crystalline media
- [Raman-Nath Multi-Order Diffraction Pattern](/lab/acousto-optics/raman-nath): Simulate Raman-Nath acousto-optic diffraction showing multiple diffraction orders and their intensity distribution in the thin-grating regime

### Aeroacoustics & Flow-Generated Noise (5 simulations)
- [Aeolian Tones & Vortex Shedding](/lab/aeroacoustics/aeolian-tone): Simulate aeolian tones from vortex shedding past cylinders — explore how flow speed, cylinder diameter, and Reynolds number set the shedding frequency
- [Rotor & Propeller Noise](/lab/aeroacoustics/propeller-noise): Simulate propeller tonal and broadband noise — explore how blade count, RPM, diameter, and advance ratio shape the acoustic signature
- [Sonic Boom & Shock Wave Propagation](/lab/aeroacoustics/sonic-boom): Simulate sonic boom formation — explore how Mach number, altitude, and aircraft length determine the N-wave overpressure on the ground
- [Turbulent Boundary Layer Noise](/lab/aeroacoustics/boundary-layer-noise): Simulate turbulent boundary layer noise — explore how freestream velocity, boundary layer thickness, and surface roughness affect wall-pressure spectra
- [Turbulent Jet Mixing Noise](/lab/aeroacoustics/jet-noise): Simulate turbulent jet mixing noise — explore how exhaust velocity, jet diameter, and temperature ratio shape the acoustic spectrum and directivity

### Astrometry & Stellar Position Measurement (5 simulations)
- [Astrometric Binary Orbit Solver](/lab/astrometry/binary-orbit): Simulate a visual binary star system — trace the apparent elliptical orbit on the sky and derive stellar masses from the orbital period and semi-major axis using Kepler's third law
- [Astrometric Calibration & Error Budget](/lab/astrometry/astrometric-calibration): Simulate the astrometric calibration process — explore how atmospheric seeing, detector pixel scale, reference star count, and exposure time affect positional accuracy
- [Celestial Reference Frame Builder](/lab/astrometry/reference-frame): Simulate the construction of a celestial reference frame — explore how quasar anchor points, coordinate rotations, and precession corrections establish the ICRF coordinate system
- [Proper Motion & Stellar Kinematics](/lab/astrometry/proper-motion): Simulate stellar proper motion — watch how stars drift across the sky over decades and compute their true space velocities from angular motion and distance
- [Stellar Parallax & Distance Measurement](/lab/astrometry/parallax-measurement): Simulate stellar parallax — measure how a star's apparent position shifts against background stars as Earth orbits the Sun, and convert the parallax angle to distance in parsecs

### Chaos Theory (5 simulations)
- [Double Pendulum Simulator](/lab/chaos-theory/double-pendulum): Watch a double pendulum evolve in real time — a mechanical system that exhibits chaotic motion from simple Newtonian physics
- [Elementary Cellular Automaton](/lab/chaos-theory/cellular-automaton): Explore Wolfram's elementary cellular automata — simple local rules that generate complexity, from ordered patterns to computational universality
- [Logistic Map & Bifurcation Diagram](/lab/chaos-theory/logistic-map): Explore the logistic map — a deceptively simple equation that produces period-doubling cascades, chaos, and fractal structure
- [Lorenz Attractor Simulator](/lab/chaos-theory/lorenz-attractor): Visualize the Lorenz attractor and observe how tiny perturbations lead to exponential divergence — the hallmark of deterministic chaos
- [Mandelbrot Set Explorer](/lab/chaos-theory/mandelbrot-explorer): Navigate the infinite fractal boundary of the Mandelbrot set — where complex iteration reveals self-similar structures at every scale

### Classical Mechanics (5 simulations)
- [Elastic & Inelastic Collision Simulator](/lab/classical-mechanics/momentum-collision): Smash objects together and observe conservation of momentum and energy — from perfect elastic bounces to completely inelastic collisions where objects stick together
- [Friction on Inclined Plane Simulator](/lab/classical-mechanics/friction-incline): Slide a block down a ramp with adjustable friction — explore static vs kinetic friction, critical angles, and the physics of everyday surfaces
- [Projectile Motion with Air Resistance](/lab/classical-mechanics/projectile-motion): Launch projectiles through realistic air resistance and watch how drag transforms the perfect parabola of vacuum physics into the asymmetric arcs of the real world
- [Rotational Inertia & Angular Momentum Simulator](/lab/classical-mechanics/rotational-inertia): Spin objects of different shapes and mass distributions to discover rotational inertia — why figure skaters spin faster when they pull in their arms
- [Spring-Mass Harmonic Oscillator](/lab/classical-mechanics/spring-oscillator): Watch a spring-mass system oscillate in simple, damped, and driven modes — the fundamental model behind clocks, circuits, and quantum mechanics

### Color Science & Perception (5 simulations)
- [Additive & Subtractive Color Mixing](/lab/color-science/color-mixing): Mix colors additively (light) and subtractively (paint) — see how RGB and CMY create every color through opposite blending rules
- [Color Blindness Simulation](/lab/color-science/color-blindness): See the world through color-blind eyes — simulate protanopia, deuteranopia, and tritanopia to understand how 300 million people perceive color differently
- [Color Harmony & Complementary Palettes](/lab/color-science/color-harmony): Generate harmonious color palettes using complementary, triadic, split-complementary, and analogous rules from color theory
- [Color Temperature & Black Body Radiation](/lab/color-science/color-temperature): Explore how temperature determines color — from the warm glow of candlelight at 1800K to the cool blue of a clear sky at 10000K through Planck's black body law
- [Light Spectral Analysis & Wavelength](/lab/color-science/spectral-analysis): Decompose light into its spectral components — visualize wavelengths from 380nm violet to 700nm red and see how spectral power distributions create perceived colors

### Cosmology & the Expanding Universe (5 simulations)
- [Big Bang Nucleosynthesis & Primordial Abundances](/lab/cosmology/big-bang-nucleosynthesis): Simulate primordial nucleosynthesis — explore how baryon density and neutron lifetime determine the abundances of hydrogen, helium, deuterium, and lithium formed in the first minutes
- [CMB Power Spectrum & Anisotropies](/lab/cosmology/cosmic-microwave): Simulate the cosmic microwave background power spectrum — explore how baryon density, dark matter, and curvature shape the acoustic peaks
- [Cosmic Inflation & Exponential Expansion](/lab/cosmology/cosmic-inflation): Simulate cosmic inflation — explore how the inflaton field drives exponential expansion, solving the flatness and horizon problems
- [Dark Energy & Cosmic Acceleration](/lab/cosmology/dark-energy): Simulate the cosmological constant and dark energy — explore how the equation of state parameter drives the accelerating expansion of the universe
- [Hubble's Law & Redshift-Distance Relation](/lab/cosmology/hubble-expansion): Simulate Hubble's law — explore how recession velocity scales with distance and how the Hubble constant determines the age of the universe

### Cryogenics & Low-Temperature Physics (5 simulations)
- [Cryocooler Thermodynamic Cycle](/lab/cryogenics/cryocooler-cycle): Simulate a Gifford-McMahon cryocooler cycle — explore how pressure ratio, displacement volume, and cold-end temperature determine cooling power
- [Cryogenic Storage & Boil-Off](/lab/cryogenics/cryogenic-storage): Simulate cryogenic dewar boil-off — explore how insulation thickness, ambient temperature, liquid volume, and heat leak determine storage hold time
- [Superconductivity & Critical Temperature](/lab/cryogenics/superconductivity): Simulate superconducting phase transitions — explore how temperature, magnetic field, and material type determine zero-resistance states
- [Superfluidity & Quantum Vortices](/lab/cryogenics/superfluidity): Simulate superfluid helium-4 — explore how temperature, rotation speed, and container geometry produce quantized vortices and frictionless flow
- [Thermal Contraction of Materials](/lab/cryogenics/thermal-contraction): Simulate thermal contraction at cryogenic temperatures — explore how material type, length, and temperature range determine shrinkage and thermal stress

### Crystallography & Crystal Structure (5 simulations)
- [Crystal Defect Structure](/lab/crystallography/defect-structure): Simulate point defects in crystals — adjust vacancy concentration, interstitial fraction, temperature, and substitutional impurity level to see how defects affect lattice energy and diffusion
- [Crystal Symmetry Operations](/lab/crystallography/crystal-symmetry): Explore crystal symmetry — apply rotation, mirror, inversion, and glide operations to a 2D motif and watch how symmetry generates the full pattern from a single asymmetric unit
- [Miller Indices & Crystal Planes](/lab/crystallography/miller-indices): Visualize crystal planes using Miller indices — adjust h, k, l values and lattice parameter to see how planes slice through the unit cell and calculate interplanar spacing
- [Reciprocal Lattice Construction](/lab/crystallography/reciprocal-lattice): Build and explore the reciprocal lattice — adjust real-space lattice parameters and angle to see how the reciprocal lattice transforms, with Ewald sphere visualization
- [Unit Cell Geometry Explorer](/lab/crystallography/unit-cell): Explore unit cell structures — adjust lattice parameters, crystal system type, atomic radius, and packing to visualize cubic, tetragonal, and hexagonal unit cells in real time

### Electromagnetism (5 simulations)
- [Electric Field Lines](/lab/electromagnetism/electric-field-lines): Visualize electric field lines from point charges. See how positive and negative charges create field patterns, with equipotential lines and animated test charges.
- [Faraday's Law of Induction](/lab/electromagnetism/electromagnetic-induction): Watch a rotating coil generate electricity through electromagnetic induction. See how changing magnetic flux produces EMF, synchronized with real-time waveform plots.
- [LC Circuit Oscillator](/lab/electromagnetism/lc-circuit): Visualize energy oscillating between electric and magnetic fields in an LC circuit. Watch charge slosh between capacitor plates while current flows through the inductor.
- [Lorentz Force on Charged Particles](/lab/electromagnetism/lorentz-force): Watch charged particles spiral through magnetic fields. Visualize the Lorentz force creating circular and helical trajectories, with adjustable mass, charge, and field strength.
- [Magnetic Field Around Wires](/lab/electromagnetism/magnetic-field): Visualize magnetic field lines around current-carrying wires. See circular field patterns, parallel wire interactions, and the right-hand rule in action.

### Ferroelectrics & Piezoelectric Materials (5 simulations)
- [180 and 90 Degree Domain Wall Motion](/lab/ferroelectrics/domain-switching): Watch ferroelectric domains switch under an applied electric field — visualize 180-degree and 90-degree domain wall motion in real time
- [Ferroelectric-Paraelectric Phase Transition](/lab/ferroelectrics/curie-transition): Visualize the Curie transition where a ferroelectric loses its spontaneous polarization and becomes paraelectric above the Curie temperature
- [Piezoelectric d33 & Coupling Factor](/lab/ferroelectrics/piezoelectric-coefficient): Calculate the piezoelectric charge coefficient d33 and electromechanical coupling factor k for various ferroelectric materials
- [Piezoelectric Vibration Energy Harvester](/lab/ferroelectrics/energy-harvesting): Design a piezoelectric cantilever energy harvester — tune frequency, load resistance, and material properties to maximize power output from ambient vibrations
- [Polarization-Electric Field Hysteresis Loop](/lab/ferroelectrics/pe-hysteresis): Trace the classic P-E hysteresis loop of a ferroelectric material and extract remnant polarization, coercive field, and saturation polarization

### Fluid Dynamics (4 simulations)
- [Bernoulli's Principle & Lift Simulator](/lab/fluid-dynamics/bernoulli-principle): Explore how faster-moving air creates lower pressure, generating lift on an airfoil — the fundamental physics behind airplane wings and race car aerodynamics
- [Fick's Law of Diffusion Simulator](/lab/fluid-dynamics/diffusion-process): Watch particles spread from concentrated to dispersed through Brownian motion — visualizing Fick's law, random walks, and the square-root-of-time diffusion scaling
- [Laminar vs Turbulent Flow Simulator](/lab/fluid-dynamics/reynolds-number): Visualize the transition from smooth laminar flow to chaotic turbulence by adjusting velocity, pipe diameter, and fluid properties to compute the Reynolds number
- [Viscosity & Poiseuille Flow Simulator](/lab/fluid-dynamics/viscosity-flow): Explore how viscosity determines fluid flow rates through pipes — visualize parabolic velocity profiles and discover why small radius changes have enormous effects

### Magnetism & Magnetic Materials (5 simulations)
- [B-H Hysteresis Loop & Coercivity](/lab/magnetism/hysteresis-loop): Simulate magnetic hysteresis — explore how coercivity, remanence, and saturation magnetization shape the B-H curve of ferromagnetic materials
- [Crystal Magnetic Anisotropy & Easy Axis](/lab/magnetism/magnetic-anisotropy): Simulate magnetocrystalline anisotropy — explore how crystal symmetry, anisotropy constants, and applied field determine the easy axis and energy landscape
- [Curie Temperature: Ferromagnetic-Paramagnetic Transition](/lab/magnetism/curie-temperature): Simulate the Curie temperature phase transition — explore how temperature destroys long-range magnetic order in ferromagnetic materials
- [Magnetic Domain Wall Motion & Barkhausen Effect](/lab/magnetism/magnetic-domains): Simulate magnetic domain wall motion under applied field — explore how pinning sites, wall energy, and the Barkhausen effect shape magnetization
- [Solenoid Electromagnet Design & Force](/lab/magnetism/electromagnet-design): Design a solenoid electromagnet — explore how turns, current, core material, and geometry determine magnetic field strength and attractive force

### Nuclear Physics (4 simulations)
- [Nuclear Fission Chain Reaction Simulator](/lab/nuclear-physics/nuclear-fission): Simulate a nuclear fission chain reaction — watch neutrons split uranium atoms, adjust control rods and enrichment to balance criticality between sustained power and runaway explosion
- [Nuclear Fusion & Ignition Simulator](/lab/nuclear-physics/nuclear-fusion): Explore the extreme conditions needed for nuclear fusion — adjust plasma temperature, density, and confinement to chase the Lawson criterion and achieve ignition
- [Radioactive Decay & Half-Life Simulator](/lab/nuclear-physics/radioactive-decay): Watch unstable atoms decay in real time — visualize exponential decay curves, understand half-lives, and explore decay chains from parent to daughter nuclei
- [Radiometric Dating Calculator](/lab/nuclear-physics/half-life-dating): Calculate the age of rocks, fossils, and artifacts using radioactive isotope ratios — from Carbon-14 dating of ancient wood to Uranium-Lead dating of Earth's oldest minerals

### Optics & Instruments (5 simulations)
- [Fiber Optic Total Internal Reflection Simulator](/lab/optics-instruments/fiber-optics): Visualize how light propagates through optical fibers via total internal reflection, and explore how core size, refractive index, and bending affect signal transmission
- [Holography Interference Patterns Simulator](/lab/optics-instruments/holography): Visualize how reference and object beams interfere to create holographic fringe patterns, and explore how wavelength, angle, and film resolution affect hologram quality
- [Laser Cavity Modes & Gain Simulator](/lab/optics-instruments/laser-cavity): Simulate longitudinal cavity modes, gain threshold, and output spectrum of a Fabry-Perot laser resonator with adjustable cavity length, reflectivity, and gain medium
- [Microscope Resolution & Abbe Limit Simulator](/lab/optics-instruments/microscope-resolution): Explore how numerical aperture, wavelength, and immersion medium determine the resolving power of an optical microscope through the Abbe diffraction limit
- [Telescope Magnification & Resolution Simulator](/lab/optics-instruments/telescope-magnification): Simulate how objective diameter, focal length, and eyepiece choice affect a telescope's magnification, resolving power, and light-gathering ability

### Orbital Mechanics (4 simulations)
- [Gravity Assist Simulator](/lab/orbital-mechanics/gravity-assist): Visualize how spacecraft gain or lose speed by flying past planets, using the gravitational slingshot effect
- [Hohmann Transfer Orbit Calculator](/lab/orbital-mechanics/hohmann-transfer): Simulate the most fuel-efficient two-impulse maneuver to transfer between circular orbits, with animated spacecraft trajectory
- [Kepler Orbit Simulator](/lab/orbital-mechanics/kepler-orbits): Interactive simulation of elliptical planetary orbits using Kepler's laws, showing equal-area sweeps and velocity changes
- [Lagrange Points Visualizer](/lab/orbital-mechanics/lagrange-points): Explore the five equilibrium points of the restricted three-body problem with an interactive effective potential map

### Particle Physics (5 simulations)
- [Higgs Field & Symmetry Breaking](/lab/particle-physics/higgs-field): Visualize the Mexican hat potential and watch symmetry breaking as the Higgs field acquires a vacuum expectation value, giving mass to fundamental particles.
- [Pair Production & Annihilation](/lab/particle-physics/pair-production): Watch matter emerge from pure energy. A high-energy photon near a nucleus creates an electron-positron pair, demonstrating E=mc² in action.
- [Particle Collision Event Display](/lab/particle-physics/particle-collision): Simulate particle collisions like those at the Large Hadron Collider. Watch tracks radiate from the collision point, curved by magnetic fields, with energy deposits in calorimeters.
- [Quark Confinement & Color Force](/lab/particle-physics/quark-confinement): Visualize quark confinement and the color force. Pull quarks apart and watch the gluon flux tube stretch until it snaps, creating new quark-antiquark pairs.
- [Standard Model Particle Zoo](/lab/particle-physics/standard-model): Interactive visualization of all 17 fundamental particles in the Standard Model — quarks, leptons, gauge bosons, and the Higgs boson — with their masses, charges, and spins.

### Photonics & Optical Engineering (5 simulations)
- [Nonlinear Optical Effects](/lab/photonics/nonlinear-optics): Simulate self-phase modulation, four-wave mixing, and spectral broadening in optical fibers, visualizing how pulse intensity, fiber nonlinearity, and dispersion shape the output spectrum.
- [Optical Amplifier Gain Dynamics](/lab/photonics/optical-amplifier): Model erbium-doped fiber amplifier (EDFA) gain and noise characteristics as a function of pump power, signal wavelength, fiber length, and erbium concentration.
- [Optical Fiber Mode Propagation](/lab/photonics/optical-fiber-modes): Simulate guided mode profiles in step-index and graded-index optical fibers, visualizing how core diameter, numerical aperture, and wavelength determine single-mode vs multimode operation.
- [Photonic Crystal Band Structure](/lab/photonics/photonic-crystal): Visualize photonic band gaps in 1D and 2D periodic dielectric structures, showing how lattice period, refractive index contrast, and fill fraction create frequency ranges where light cannot propagate.
- [Waveguide Directional Coupler](/lab/photonics/waveguide-coupling): Simulate evanescent-field power transfer between two parallel optical waveguides, exploring coupling length, wavelength dependence, and cross-talk in integrated photonic circuits.

### Planetary Science & Solar System (5 simulations)
- [Albedo & Planetary Energy Balance](/lab/planetary-science/albedo-temperature): Calculate equilibrium temperature from stellar luminosity, orbital distance, albedo, and greenhouse effect — understand why Venus is hotter than Mercury despite being farther from the Sun
- [Impact Crater Scaling: Size vs Energy](/lab/planetary-science/crater-scaling): Calculate impact crater diameter from impactor size, velocity, and target properties — explore the physics of hypervelocity impacts that shaped planetary surfaces
- [Planetary Atmosphere: Scale Height & Escape Velocity](/lab/planetary-science/planetary-atmosphere): Model atmospheric structure using scale height and compare thermal velocity to escape velocity — understand why Mars lost its atmosphere while Earth kept its own
- [Roche Limit: Tidal Disruption Distance](/lab/planetary-science/roche-limit): Calculate the Roche limit — the critical distance where tidal forces tear apart a satellite — and visualize the disruption process that creates planetary rings
- [Tidal Heating & Io-Style Dissipation](/lab/planetary-science/tidal-heating): Simulate tidal heating in moons like Io — explore how orbital eccentricity, distance, and interior rigidity drive volcanic activity through gravitational flexing

### Plasma Physics & Fusion (5 simulations)
- [Debye Shielding & Charge Screening](/lab/plasma-physics/debye-shielding): Visualize how a plasma shields electric charges — watch the Debye cloud form around a test charge and see the exponential potential decay
- [Langmuir Plasma Oscillation Simulator](/lab/plasma-physics/langmuir-waves): Watch electrons oscillate collectively in a plasma — visualize Langmuir waves, the plasma frequency, and the Bohm-Gross dispersion relation
- [Magnetic Plasma Confinement Simulator](/lab/plasma-physics/plasma-confinement): Simulate charged particles spiraling along magnetic field lines — explore how magnetic mirrors and toroidal fields confine hot plasma for fusion
- [Plasma Frequency Simulator](/lab/plasma-physics/plasma-frequency): Visualize how electromagnetic waves interact with plasma — watch waves reflect below the plasma frequency and propagate above it
- [Tokamak Fusion Reactor Cross-Section](/lab/plasma-physics/tokamak-fusion): Explore the anatomy of a tokamak fusion reactor — visualize the magnetic field geometry, plasma cross-section, and the Lawson criterion for ignition

### Quantum Field Theory & Particle Physics (5 simulations)
- [Casimir Effect & Vacuum Force](/lab/quantum-field-theory/casimir-effect): Simulate the Casimir effect — explore how plate separation, area, and temperature determine the attractive force between conducting plates from quantum vacuum fluctuations
- [Feynman Diagram & Scattering Amplitude](/lab/quantum-field-theory/feynman-diagram): Simulate Feynman diagram scattering — explore how coupling strength, particle masses, and momentum transfer determine cross sections in quantum electrodynamics
- [Lamb Shift & Radiative Corrections](/lab/quantum-field-theory/lamb-shift): Simulate the Lamb shift — explore how quantum vacuum fluctuations and radiative corrections lift the degeneracy between hydrogen energy levels
- [Running Coupling Constants & Asymptotic Freedom](/lab/quantum-field-theory/running-coupling): Simulate running coupling constants — explore how electromagnetic, weak, and strong coupling strengths change with energy scale through renormalization group flow
- [Vacuum Fluctuations & Zero-Point Energy](/lab/quantum-field-theory/vacuum-fluctuation): Simulate quantum vacuum fluctuations — explore how field mode frequency, spatial extent, and observation time affect virtual particle pair creation and zero-point energy

### Quantum Mechanics (5 simulations)
- [Double-Slit Experiment Simulator](/lab/quantum-mechanics/double-slit): Watch quantum interference emerge photon by photon — adjust wavelength, slit geometry, and photon count to see the famous interference pattern build up from individual particle detections
- [Particle in a Box Simulator](/lab/quantum-mechanics/particle-in-a-box): Explore quantized energy levels and wave functions of a particle confined in an infinite square well — visualize standing waves, probability densities, and quantum superposition states
- [Quantum Entanglement & Bell's Inequality Simulator](/lab/quantum-mechanics/quantum-entanglement): Test Bell's inequality with entangled particle pairs — set detector angles for Alice and Bob and watch the CHSH parameter S reveal whether correlations exceed classical limits
- [Quantum Tunneling Simulator](/lab/quantum-mechanics/quantum-tunneling): Visualize how particles tunnel through potential energy barriers — adjust energy, barrier height, width, and particle mass to see transmission and reflection coefficients change in real time
- [Qubit Bloch Sphere Simulator](/lab/quantum-mechanics/qubit-bloch-sphere): Visualize qubit states on the Bloch sphere and apply quantum gates — see how Hadamard, Pauli-X, Pauli-Z, and T-gate transform the quantum state vector in 3D

### Quantum Optics & Photonics (5 simulations)
- [Cavity QED & Jaynes-Cummings Model](/lab/quantum-optics/cavity-qed): Simulate cavity quantum electrodynamics — explore vacuum Rabi oscillations, atom-photon coupling strengths, and the Jaynes-Cummings energy ladder in optical and microwave cavities
- [Entanglement Witness & Bell Inequality](/lab/quantum-optics/entanglement-witness): Simulate entanglement detection — explore Bell's CHSH inequality, witness operators, and the boundary between classical correlations and quantum entanglement
- [Hanbury Brown-Twiss Experiment](/lab/quantum-optics/hbt-experiment): Simulate the HBT experiment — explore photon bunching and antibunching by measuring intensity correlations g⁽²⁾(τ) for thermal, coherent, and single-photon sources
- [Photon Counting Statistics](/lab/quantum-optics/photon-statistics): Simulate photon number distributions — compare Poissonian (coherent), super-Poissonian (thermal), and sub-Poissonian (quantum) light sources in real time
- [Squeezed Light & Quantum Noise](/lab/quantum-optics/squeezed-light): Simulate squeezed states of light — visualize how squeezing reduces quantum noise in one quadrature below the vacuum level at the expense of the conjugate quadrature

### Radio Astronomy & Interferometry (5 simulations)
- [Aperture Synthesis Imaging](/lab/radio-astronomy/aperture-synthesis): Simulate aperture synthesis — explore how array configuration, observation duration, and declination affect UV coverage and synthesized beam quality
- [Interferometer Baseline & Resolution](/lab/radio-astronomy/interferometer-baseline): Simulate a two-element radio interferometer — explore how baseline length, wavelength, and source angle produce fringe patterns and angular resolution
- [Pulsar Timing & Period Analysis](/lab/radio-astronomy/pulsar-timing): Simulate pulsar radio emission — explore how spin period, period derivative, dispersion measure, and pulse width shape the observed timing profile
- [Radio Spectrum & Source Classification](/lab/radio-astronomy/radio-spectrum): Simulate radio source spectra — explore how spectral index, turnover frequency, and flux density characterize synchrotron, thermal, and self-absorbed emission
- [Radio Telescope Beam Pattern](/lab/radio-astronomy/radio-telescope): Simulate a parabolic radio telescope's beam pattern — explore how dish diameter, wavelength, and feed offset shape the primary beam and sidelobes

### Rheology & Flow Behavior (5 simulations)
- [Extensional Flow & Elongational Viscosity](/lab/rheology/extensional-flow): Simulate extensional flow of polymer solutions — explore how strain rate, relaxation time, and extensibility govern filament thinning and elongational viscosity
- [Rheometry & Oscillatory Testing](/lab/rheology/rheometry): Simulate oscillatory rheometry — explore how frequency, strain amplitude, and material viscoelasticity determine storage modulus G' and loss modulus G''
- [Thixotropy & Time-Dependent Flow](/lab/rheology/thixotropy): Simulate thixotropic behavior — explore how viscosity evolves over time during shearing and recovery as microstructure breaks down and rebuilds
- [Viscosity Models & Shear Response](/lab/rheology/viscosity-models): Simulate non-Newtonian viscosity models — explore how shear rate, consistency index, and power-law exponent govern shear-thinning and shear-thickening behavior
- [Yield Stress & Plastic Flow](/lab/rheology/yield-stress): Simulate yield stress phenomena — explore how Bingham plastics and soft solids transition from solid-like to flowing behavior under applied stress

### Semiconductor Physics (5 simulations)
- [LED Emission Spectrum & Efficiency Simulator](/lab/semiconductor/led-emission): Simulate how band gap energy, temperature, and current density determine an LED's emission wavelength, spectral width, and luminous efficiency
- [MOSFET Operation & Switching Simulator](/lab/semiconductor/mosfet-operation): Simulate MOSFET output characteristics, transfer curves, and switching behavior with adjustable gate voltage, threshold, and channel parameters
- [PN Junction Diode Characteristics Simulator](/lab/semiconductor/pn-junction): Simulate the IV curve, depletion region, and built-in potential of a PN junction diode with adjustable doping concentrations, temperature, and applied voltage
- [Semiconductor Band Gap & Doping Simulator](/lab/semiconductor/band-gap): Explore how temperature, doping concentration, and material type affect the band gap, Fermi level, and carrier concentrations in semiconductors
- [Solar Cell IV Curve & Efficiency Simulator](/lab/semiconductor/solar-cell): Simulate the current-voltage characteristics, maximum power point, and efficiency of a solar cell with adjustable irradiance, temperature, and cell parameters

### Sound & Music (5 simulations)
- [Chladni Patterns (Vibrating Plates)](/lab/sound-music/chladni-patterns): Visualize the beautiful geometric patterns that form on vibrating plates — sand settles along nodal lines revealing the mathematics of standing waves in 2D.
- [Harmonic Series & Timbre](/lab/sound-music/harmonic-series): Visualize how harmonics combine to create timbre — watch individual overtones stack into complex waveforms that define every instrument's unique sound.
- [Musical Intervals & Consonance](/lab/sound-music/musical-intervals): Explore why some note combinations sound harmonious and others clash — visualize the waveform interference that creates consonance and dissonance.
- [Resonance & Natural Frequency](/lab/sound-music/resonance): Drive an oscillator at different frequencies and watch amplitude explode at resonance — explore how damping controls the sharpness of the resonance peak.
- [Waveform Synthesis](/lab/sound-music/waveform-synthesis): Generate and visualize classic waveforms — sine, square, sawtooth, triangle — with amplitude modulation and real-time spectral analysis.

### Special & General Relativity (4 simulations)
- [Length Contraction Visualizer](/lab/relativity/length-contraction): See how objects physically shorten along the direction of motion at relativistic speeds
- [Mass-Energy Equivalence Calculator](/lab/relativity/mass-energy): Explore E=mc² and relativistic energy with real-world comparisons from grams to megatons
- [Time Dilation Calculator](/lab/relativity/time-dilation): Visualize how time slows down for objects moving at relativistic speeds with the Lorentz factor
- [Twin Paradox Simulator](/lab/relativity/twin-paradox): Simulate the twin paradox with a Minkowski spacetime diagram showing how the traveling twin ages less

### Spectroscopy & Spectral Analysis (5 simulations)
- [Absorption Line Profiles & Beer-Lambert Law](/lab/spectroscopy/absorption-lines): Simulate absorption spectroscopy — explore concentration, path length, molar absorptivity, and line width to visualize Beer-Lambert transmission and absorption line shapes
- [Atomic Emission Spectrum Generator](/lab/spectroscopy/emission-spectrum): Simulate atomic emission spectra — explore atomic number, excitation energy, temperature, and line broadening to visualize characteristic spectral lines from quantum transitions
- [Mass Spectrometry & Fragmentation](/lab/spectroscopy/mass-spectrometry): Simulate mass spectrometry — explore molecular mass, ionization energy, acceleration voltage, and magnetic field to visualize ion trajectories and mass spectra
- [Raman Scattering & Vibrational Modes](/lab/spectroscopy/raman-scattering): Simulate Raman spectroscopy — explore laser wavelength, molecular bond strength, reduced mass, and temperature to visualize Stokes and anti-Stokes shifts
- [X-Ray Diffraction & Crystal Structure](/lab/spectroscopy/xray-diffraction): Simulate X-ray diffraction from crystal lattices — explore lattice spacing, X-ray wavelength, crystal type, and beam angle to visualize Bragg peaks and diffraction patterns

### Stellar Evolution & Astrophysics (5 simulations)
- [Chandrasekhar Mass Limit](/lab/stellar-evolution/chandrasekhar-limit): Explore the Chandrasekhar limit — simulate how electron degeneracy pressure supports white dwarfs up to 1.44 M☉ and what happens when mass exceeds this critical threshold
- [Hertzsprung-Russell Diagram Explorer](/lab/stellar-evolution/hr-diagram): Plot stars on the HR diagram — explore how mass determines luminosity, temperature, and evolutionary stage across the main sequence, giant branch, and white dwarf cooling track
- [Main-Sequence Hydrogen Burning](/lab/stellar-evolution/main-sequence): Model hydrogen fusion on the main sequence — explore how stellar mass controls core temperature, fusion rate, luminosity, and lifetime through the pp-chain and CNO cycle
- [Stellar Nucleosynthesis Pathways](/lab/stellar-evolution/stellar-nucleosynthesis): Trace element production in stars — explore how mass and core temperature control fusion stages from hydrogen through silicon, building the periodic table layer by layer
- [White Dwarf Cooling Curves](/lab/stellar-evolution/white-dwarf-cooling): Simulate white dwarf thermal evolution — explore how mass, composition, and crystallization control cooling rates over billions of years

### String Theory & Extra Dimensions (5 simulations)
- [AdS/CFT Correspondence & Holographic Duality](/lab/string-theory/ads-cft): Experience the holographic principle — watch how a gravitational theory in anti-de Sitter space maps to a conformal field theory on its boundary
- [Brane Worlds & Bulk Space](/lab/string-theory/brane-worlds): Navigate through higher-dimensional bulk space and observe how our universe may exist as a 3-brane floating in a larger dimensional reality
- [Extra Dimensions & Calabi-Yau Manifolds](/lab/string-theory/extra-dimensions): Visualize the hidden dimensions of string theory — watch Calabi-Yau manifolds unfold and explore how extra dimensions shape the physics we observe
- [String Vibration Modes & Particle Spectrum](/lab/string-theory/string-vibrations): Watch fundamental strings vibrate in different modes and see how each vibration pattern corresponds to a different elementary particle in the Standard Model
- [Supersymmetry & Partner Particles](/lab/string-theory/supersymmetry): Explore supersymmetry by visualizing the boson-fermion partner spectrum — every known particle has a superpartner with different spin statistics

### Superconductivity & Zero Resistance (5 simulations)
- [BCS Theory: Cooper Pair Formation & Energy Gap](/lab/superconductivity/bcs-theory): Simulate Cooper pair condensation and the superconducting energy gap as a function of temperature and coupling strength
- [Critical Field: Hc vs Temperature Phase Diagram](/lab/superconductivity/critical-field): Explore the superconducting phase diagram — critical magnetic field as a function of temperature for type-I superconductors
- [Josephson Junction & SQUID](/lab/superconductivity/josephson-junction): Simulate the DC and AC Josephson effects — supercurrent tunneling across a weak link and SQUID flux sensitivity
- [Meissner Effect: Magnetic Flux Expulsion](/lab/superconductivity/meissner-effect): Visualize how a superconductor expels magnetic flux below Tc — the Meissner effect with London penetration depth
- [Type-II Vortex: Abrikosov Vortex Lattice](/lab/superconductivity/type-ii-vortex): Visualize the Abrikosov vortex lattice in type-II superconductors — flux quantization, vortex interactions, and lattice melting

### Thermodynamics & Statistical Mechanics (4 simulations)
- [Boltzmann Brain Timescale Calculator](/lab/thermodynamics/boltzmann-brain): Explore the mind-bending timescales of thermal fluctuations — how long until random chance assembles a conscious brain from the void
- [Carnot Cycle Efficiency Calculator](/lab/thermodynamics/carnot-efficiency): Visualize the Carnot cycle on a PV diagram and calculate the theoretical maximum efficiency of any heat engine operating between two temperatures
- [Entropy & Particle Diffusion Simulator](/lab/thermodynamics/entropy-simulator): Watch particles diffuse from order to disorder and observe entropy increase in real time — a visual demonstration of the Second Law of Thermodynamics
- [Maxwell–Boltzmann Speed Distribution](/lab/thermodynamics/maxwell-boltzmann): Explore how temperature and molecular mass shape the distribution of particle speeds in a gas — and why some molecules escape Earth's gravity

### Vacuum Science & Technology (5 simulations)
- [Helium Leak Detection & Sensitivity](/lab/vacuum-science/leak-detection): Simulate helium leak rate measurements, minimum detectable leak size, and response time for mass-spectrometer leak detectors
- [Mean Free Path & Knudsen Number](/lab/vacuum-science/mean-free-path): Visualize molecular collisions, mean free path length, and Knudsen number across vacuum pressure regimes
- [Outgassing & Bakeout Kinetics](/lab/vacuum-science/outgassing): Model surface desorption rates, outgassing decay curves, and bakeout temperature optimization for UHV systems
- [Pumping Speed & Throughput](/lab/vacuum-science/pump-speed): Calculate effective pumping speed, throughput, and pumpdown time for vacuum chambers with conductance-limited connections
- [Sputtering Rate & Thin Film Growth](/lab/vacuum-science/thin-film-deposition): Model magnetron sputtering deposition rate, film thickness, and mean free path of sputtered atoms as a function of power, pressure, and target material

### Waves & Optics (6 simulations)
- [Doppler Effect Simulator](/lab/waves-optics/doppler-effect): Watch wavefronts compress and stretch as a source moves, demonstrating the Doppler shift that changes the pitch of sirens and the color of stars.
- [Electromagnetic Spectrum Explorer](/lab/waves-optics/electromagnetic-spectrum): Navigate the full electromagnetic spectrum from radio waves to gamma rays, exploring wavelength, frequency, energy, and real-world applications of each band.
- [Single-Slit Diffraction](/lab/waves-optics/diffraction-single-slit): Watch light spread and form diffraction patterns through a single slit, revealing the wave nature of light and the counter-intuitive relationship between slit width and pattern width.
- [Snell's Law & Refraction](/lab/waves-optics/snells-law): Watch light bend as it passes between materials of different refractive indices, and discover the critical angle for total internal reflection.
- [Standing Waves & Harmonics](/lab/waves-optics/standing-waves): Watch a vibrating string form standing wave patterns with nodes and antinodes, exploring how tension, density, and harmonic number determine pitch.
- [Wave Interference & Superposition](/lab/waves-optics/wave-interference): Visualize how two waves combine through superposition, producing constructive and destructive interference patterns including beats.

## psychology (2 topics, 9 simulations)

### Cognitive Biases & Decision Science (4 simulations)
- [Anchoring Effect Simulator](/lab/cognitive-biases/anchoring-effect): Simulate how an initial anchor biases a population of estimates through insufficient adjustment, visualized as histogram and scatter plot
- [Bayes' Theorem Visualizer](/lab/cognitive-biases/bayes-theorem): Explore how prior beliefs update with evidence using Bayes' theorem, with probability trees and natural frequency displays
- [Prospect Theory Value Function](/lab/cognitive-biases/prospect-theory): Visualize Kahneman-Tversky's S-shaped value function and probability weighting — the foundation of behavioral economics
- [Survivorship Bias Simulator](/lab/cognitive-biases/survivorship-bias): Simulate selection bias in company returns — see how looking only at survivors inflates perceived performance

### Psychoacoustics & Hearing Science (5 simulations)
- [Auditory Masking & Critical Bands](/lab/psychoacoustics/masking-effect): Simulate auditory masking — explore how a louder masker tone renders nearby frequencies inaudible and how critical bandwidth shapes perceptual audio coding
- [Binaural Sound Localization](/lab/psychoacoustics/binaural-localization): Simulate binaural sound localization — explore how interaural time difference (ITD) and interaural level difference (ILD) enable the brain to determine sound source direction
- [Equal-Loudness Contours (Fletcher-Munson)](/lab/psychoacoustics/equal-loudness): Simulate equal-loudness contours — explore how the human ear perceives loudness differently across frequency and how phon curves shape audio engineering
- [Hearing Threshold & Audiogram](/lab/psychoacoustics/hearing-threshold): Simulate absolute hearing thresholds — explore how the ear's sensitivity varies with frequency and how age, noise exposure, and hearing conditions affect the audiogram
- [Pitch Perception & Basilar Membrane](/lab/psychoacoustics/pitch-perception): Simulate pitch perception — explore how frequency maps to perceived pitch through the basilar membrane's tonotopic organization, mel scale, and place-rate theory

## science (6 topics, 30 simulations)

### Archaeology & Dating Methods (5 simulations)
- [Archaeological Site Survey Grid Simulator](/lab/archaeology/site-survey): Plan and execute a systematic archaeological survey using grid squares — visualize artifact density heatmaps and optimize sampling strategies for site discovery
- [Artifact Typology & Seriation Simulator](/lab/archaeology/artifact-classification): Classify artifacts into typological groups and arrange assemblages chronologically using frequency seriation — the statistical backbone of relative dating
- [Radiocarbon C-14 Decay Dating Simulator](/lab/archaeology/radiocarbon-dating): Watch Carbon-14 atoms decay exponentially and see how archaeologists convert remaining C-14 ratios into calendar ages for organic samples up to 50,000 years old
- [Stratigraphic Layer Analysis Simulator](/lab/archaeology/stratigraphy): Build and analyze sediment layers to understand the law of superposition — how archaeologists read time from the vertical sequence of deposits at an excavation site
- [Tree Ring Dating & Climate Proxy Simulator](/lab/archaeology/dendrochronology): Analyze tree ring patterns to date wooden artifacts and reconstruct past climate — cross-matching ring width sequences that extend calendars back thousands of years

### Astrophysics & Cosmology (5 simulations)
- [Cosmic Inflation & Early Universe](/lab/astrophysics/cosmic-inflation): Simulate the first fraction of a second after the Big Bang — watch the universe inflate exponentially and seed the structure of everything
- [Dark Energy & Accelerating Expansion](/lab/astrophysics/dark-energy): Simulate the accelerating expansion of the universe — explore how dark energy density, matter content, and the cosmological constant shape cosmic fate
- [Gravitational Wave Detection & Mergers](/lab/astrophysics/gravitational-waves): Simulate gravitational waves from merging compact objects — visualize spacetime ripples and the chirp signal detected by LIGO
- [Neutron Star Density & Structure](/lab/astrophysics/neutron-star): Explore the extreme physics of neutron stars — compress solar masses into city-sized spheres and observe how density, gravity, and rotation behave
- [Supernova Explosion Lifecycle](/lab/astrophysics/supernova-lifecycle): Watch a massive star collapse and explode as a supernova — simulate the shockwave, nucleosynthesis, and remnant formation in real time

### Cartography & Navigation (5 simulations)
- [Geographic Coordinate System Transforms](/lab/cartography/coordinate-systems): Convert between geographic coordinate systems — visualize how latitude/longitude, UTM, and MGRS grids map to positions on the globe
- [GPS Trilateration Positioning](/lab/cartography/gps-trilateration): Visualize how GPS receivers calculate position from satellite signals — see trilateration circles intersect and understand dilution of precision
- [Great Circle Distance & Navigation Routes](/lab/cartography/great-circle): Calculate and visualize great circle routes between any two points on Earth — see why airplanes fly curved paths on flat maps and compare to rhumb lines
- [Map Projections & Distortion Comparison](/lab/cartography/map-projections): Compare how Mercator, Mollweide, and other map projections distort area, shape, and distance — see Tissot indicatrices reveal the hidden warping
- [Topographic Contour Line Generation](/lab/cartography/contour-mapping): Generate topographic contour maps from elevation data — watch contour lines trace terrain features like peaks, valleys, saddles, and ridgelines

### Food Science & Chemistry (5 simulations)
- [Emulsion Stability Simulator](/lab/food-science/emulsification): Simulate oil-in-water emulsion stability — adjust droplet size, emulsifier concentration, and viscosity to see how quickly an emulsion separates
- [Fermentation Kinetics Simulator](/lab/food-science/fermentation): Model ethanol fermentation kinetics — adjust temperature, sugar concentration, and yeast density to watch how ethanol yield evolves over time
- [Maillard Reaction Simulator](/lab/food-science/maillard-reaction): Explore how temperature, time, pH, and moisture affect Maillard browning intensity — the chemistry behind golden crusts, roasted coffee, and seared steaks
- [Pasteurization Time-Temperature Simulator](/lab/food-science/pasteurization): Visualize pasteurization thermal kill curves — adjust temperature, hold time, and target pathogen to calculate log-reduction and safety margins
- [Sugar Crystallization Simulator](/lab/food-science/crystallization): Model sugar crystallization from supersaturated solutions — control temperature, supersaturation, and agitation to grow or prevent crystals

### Forensic Analysis & Crime Science (5 simulations)
- [Blood Spatter Pattern Analysis](/lab/forensic-analysis/blood-spatter): Analyze blood spatter patterns — compute impact angles, origin points, and velocity categories from stain geometry
- [DNA Profiling & STR Match Probability](/lab/forensic-analysis/dna-profiling): Simulate DNA profiling — explore how STR loci count, allele frequencies, and population genetics determine match probability
- [Fingerprint Minutiae Matching Simulator](/lab/forensic-analysis/fingerprint-matching): Simulate fingerprint matching — explore how minutiae count, false acceptance rate, and match threshold affect identification reliability
- [Forensic Ballistics Trajectory Reconstructor](/lab/forensic-analysis/ballistics-trajectory): Reconstruct bullet trajectories — compute muzzle velocity, drop, drift, and impact angle for forensic ballistics analysis
- [Forensic Toxicology Screening Model](/lab/forensic-analysis/toxicology-screening): Model toxicology pharmacokinetics — simulate drug absorption, distribution, and elimination to estimate blood concentration over time

### Sports Science & Athletics (5 simulations)
- [Athletic Reaction Time Distribution](/lab/sports-science/reaction-time): Model the statistical distribution of reaction times in competitive sports — from sprint starts to goalkeeper saves and false start thresholds
- [Cycling Drafting & Aerodynamic Advantage](/lab/sports-science/drafting-aerodynamics): Simulate the aerodynamic drag reduction of drafting in cycling — see how gap distance, speed, and group size affect power savings
- [Elo Rating System & Tournament Simulation](/lab/sports-science/elo-rating): Simulate round-robin tournaments with the Elo rating system — watch ratings converge to true skill levels through matchplay dynamics
- [Sprint Biomechanics & Force Curves](/lab/sports-science/sprint-biomechanics): Visualize ground reaction forces during a 100m sprint — see how stance time, peak force, and stride frequency evolve from start to maximum velocity
- [Training Load Periodization Model](/lab/sports-science/training-periodization): Model the fitness-fatigue relationship in athletic training — visualize how training load, recovery, and tapering affect performance readiness over time

## social-science (3 topics, 15 simulations)

### Economics & Finance (5 simulations)
- [Compound Interest & Wealth Growth Simulator](/lab/economics/compound-interest): Visualize how compound interest transforms savings over time, comparing contributions vs interest earned with the Rule of 72 and milestone tracking
- [Gini Coefficient & Income Inequality Simulator](/lab/economics/gini-inequality): Explore income inequality through the Lorenz curve and Gini coefficient, with Pareto-distributed incomes, redistribution effects, and real-world country comparisons
- [Inflation & Money Supply Simulator](/lab/economics/inflation-money-supply): Model the Quantity Theory of Money (MV=PY) to visualize how money supply growth, velocity changes, and real GDP growth determine inflation and purchasing power erosion
- [Market Bubble Dynamics Simulator](/lab/economics/market-bubbles): Model speculative market bubbles with positive feedback loops, herd behavior, and sudden crashes — visualizing the divergence between fundamental value and market price
- [Supply & Demand Equilibrium Simulator](/lab/economics/supply-demand): Visualize how supply and demand curves determine market equilibrium price and quantity, with consumer/producer surplus and deadweight loss from taxation

### Sociology & Social Dynamics (5 simulations)
- [Condorcet Voting Paradox](/lab/sociology/voting-paradox): Discover why there is no perfect voting system — compare plurality, runoff, Borda, and Condorcet methods and watch them produce different winners from identical ballots
- [Information Cascade in Networks](/lab/sociology/social-network-cascade): Watch ideas spread through social networks — seed nodes trigger adoption cascades whose success depends on network structure, connection density, and individual thresholds
- [Schelling Segregation Model](/lab/sociology/schelling-segregation): Watch neighborhoods self-segregate from mild individual preferences — Schelling's Nobel Prize-winning model reveals how tolerance at the micro level produces segregation at the macro level
- [Social Opinion Dynamics](/lab/sociology/opinion-dynamics): Watch opinions cluster, polarize, and fragment — a bounded confidence model showing how social influence, extremism, and noise shape public opinion landscapes
- [Wealth Distribution Dynamics](/lab/sociology/wealth-distribution): Watch inequality emerge from fair rules — random wealth exchanges between equal agents naturally produce exponential distributions, Pareto principles, and Gini coefficients matching real economies

### Voting & Democracy (5 simulations)
- [Arrow's Impossibility Theorem](/lab/voting-democracy/arrows-impossibility): See how the same voters produce different winners under plurality, Borda, Condorcet, ranked-choice, and approval voting — proving Arrow's impossibility theorem visually
- [Electoral College vs Popular Vote](/lab/voting-democracy/electoral-college): Simulate how a candidate can win the presidency while losing the popular vote — explore the mathematics of the Electoral College
- [Gerrymandering Geometry](/lab/voting-democracy/gerrymandering): Visualize how drawing district boundaries on the same electorate can manufacture wildly different election outcomes — the dark geometry of gerrymandering
- [Political Polarization Model](/lab/voting-democracy/political-polarization): Watch a moderate population split into extremes as echo chambers, media bias, and radicalization drive opinions apart over generations
- [Proportional vs Winner-Take-All](/lab/voting-democracy/proportional-representation): Compare D'Hondt, Sainte-Lague, and largest-remainder seat allocation methods — see how electoral thresholds and rounding rules reshape legislatures

## social-sciences (2 topics, 10 simulations)

### Demography & Population Studies (5 simulations)
- [Demographic Transition Model](/lab/demography/demographic-transition): Simulate the demographic transition — explore how development stage, healthcare access, industrialization, and urbanization drive the shift from high to low birth and death rates
- [Fertility Rate & Replacement Level](/lab/demography/fertility-rate): Simulate total fertility rate dynamics — explore how desired family size, contraception prevalence, female education, and child mortality affect TFR and replacement thresholds
- [Life Table & Survival Analysis](/lab/demography/life-table): Simulate actuarial life tables — explore how infant mortality, adult mortality hazard, maximum lifespan, and initial cohort size shape survival curves and life expectancy
- [Migration Flow & Push-Pull Model](/lab/demography/migration-model): Simulate migration flows between regions — explore how wage differential, distance, origin population, and border friction govern migration rates using the gravity model
- [Population Pyramid & Age-Sex Distribution](/lab/demography/population-pyramid): Simulate population pyramids — explore how birth rate, death rate, growth rate, and migration shape the age-sex structure of a population over time

### Urban Planning & City Design (5 simulations)
- [Green Space Distribution & Urban Ecology](/lab/urban-planning/green-space): Model how parks, urban forests, and green corridors affect biodiversity, air quality, heat island reduction, and resident well-being across a city grid.
- [Population Density & Infrastructure Costs](/lab/urban-planning/population-density): Explore how population density affects infrastructure costs per capita, service delivery efficiency, and the economic viability of public transit — the core trade-off in urban form.
- [Traffic Network & Congestion Flow](/lab/urban-planning/traffic-network): Simulate vehicular traffic flow through a city road network — observe congestion patterns, Braess's paradox, and how signal timing affects throughput.
- [Walkability Score & Pedestrian Access](/lab/urban-planning/walkability): Calculate neighborhood walkability scores based on intersection density, land-use mix, block length, and amenity proximity — the metrics that predict whether people walk or drive.
- [Zoning & Land Use Model](/lab/urban-planning/zoning-model): Interactive zoning simulator that models how residential, commercial, and industrial zone allocations shape city structure, property values, and livability.