Release Stats
New Simulations
Shape Memory Alloy
Dual canvas showing austenite↔martensite lattice transformation alongside the superelastic stress-strain hysteresis loop. Four material presets (Nitinol, Cu-Al-Ni, Fe-Mn-Si, Cu-Zn-Al), temperature and stress sliders, and an animated transformation cycle button.
Open simulation →Adsorption Isotherm
Animated surface with 28 adsorption sites and gas molecules, paired with an isotherm plot comparing Langmuir (monolayer), BET (multilayer), and Freundlich (heterogeneous) models simultaneously. Controls for P/P₀, affinity K, and BET constant C.
Open simulation →Groundwater Flow
Wide cross-section canvas with 60 animated flow particles, equipotential lines, and flow arrows. Three aquifer modes: unconfined (water table), confined (piezometric surface), and regional Tóth flow. Click the aquifer to add a pumping well and watch the drawdown cone develop.
Open simulation →Technical Highlights
🔩 Shape Memory Alloy: Phase Fraction & Clausius-Clapeyron
The SMA simulator models the martensitic transformation using a
continuous phase fraction f_aus (fraction of austenite, 0
to 1). Below the martensite finish temperature Mf, the alloy is fully
martensitic; above the austenite finish temperature Af, it is fully
austenitic. Between those temperatures, the phase fraction follows a
smooth sigmoid transition.
The Clausius-Clapeyron relation extends this to stress-induced
transformation: dσ/dT = −ΔH/(ε₀·T₀), so applying
mechanical stress at temperatures above Af shifts the transformation
window upward. This is what produces superelasticity — the
rubber-like springback when stress is removed. The stress-strain plot
traces the full loading/unloading hysteresis loop with a forward
plateau at σ_s (transformation start) and a back plateau
at σ_f (transformation finish on unloading), enclosing
the energy dissipated as latent heat.
The lattice canvas uses a 10×8 atom grid. Each atom's position is
perturbed by a shear displacement proportional to
1 − f_aus, creating a visible monoclinic distortion in
the martensitic state and recovering to the cubic layout in austenite.
A bond network drawn between nearest neighbours makes the twin
boundary between phases visually apparent.
🧪 Adsorption Isotherm: Three Models on One Plot
One of the design goals for this simulation was to show all three isotherm models side by side at all times, rather than switching between views. The right canvas always draws Langmuir (teal), BET (orange), and Freundlich (purple) curves simultaneously, with a moving dot on each curve tracking the current P/P₀ value. This makes it instantly clear how the models diverge at high pressure ratios.
The Langmuir model assumes a monolayer on identical,
independent sites: θ = KP/(1+KP). Its curve saturates
sharply and is the correct limit for clean chemisorption. The
BET (Brunauer-Emmett-Teller) model extends Langmuir
to multilayer physisorption:
q/q_m = Cx/[(1−x)(1−x+Cx)] where
x = P/P₀ and C is the BET constant encoding the ratio of
condensation enthalpy. The BET curve rises steeply near P/P₀ = 1 as
many layers condense, which is the signature behaviour for nitrogen
adsorption isotherms used in BET surface area measurements. The
Freundlich model q = K·P^(1/n) is
empirical and captures heterogeneous surfaces; it never saturates,
making it visually distinct from the other two.
The surface animation uses 28 adsorption sites arranged in a 7×4 grid
on a dark substrate rectangle. Every 8 animation ticks, the occupancy
of each site is probabilistically resampled from the current Langmuir
θ, giving a realistic flickering of adsorption-desorption
equilibrium. Gas molecules (small circles) float above the surface
with random velocities, occasionally "sticking" when they collide with
an empty site.
💧 Groundwater Flow: Darcy, Dupuit and Tóth
The groundwater simulation renders a 860×360 pixel aquifer cross-section that must communicate three distinct conceptual models within the same visual frame. The single-canvas approach (rather than the dual-canvas layout used in SMA and adsorption) was chosen because the spatial extent of the aquifer itself is the key variable — width represents lateral distance, height represents depth.
In unconfined mode, the water table profile is
computed analytically at every horizontal pixel using the Dupuit
parabolic approximation including recharge: h(x)
results from solving the 1D steady-state groundwater flow equation
d/dx[K·h·dh/dx] + R = 0. The gradient slider tilts the
water table left-to-right, while the recharge slider superimposes the
parabolic mound. When a pumping well is placed (click anywhere on the
aquifer), the Dupuit-Thiem drawdown cone
h²−h_w² = (Q/πK)·ln(r/r_w) is added as an overlay using a
dashed contour.
In confined mode, a hatched aquitard band is drawn
above the saturated zone, and the piezometric surface (hydraulic head
potential surface) is shown as a dashed line that can rise above the
aquitard — representing artesian conditions. The Theis drawdown
equation for confined aquifers h−h₀ = Q/(2πKb)·ln(r₀/r)
governs the well cone shape.
The regional flow mode depicts a two-layer Tóth system: a shallow unconfined aquifer and a deeper confined aquifer, with upward and downward vertical leakage arrows at appropriate positions. This illustrates how local flow cells (recharge at topographic highs, discharge in valleys) coexist with deeper regional flow systems.
Sixty particles are advected each frame using the local Darcy velocity
v = K·i/n plus an additional radial component toward any
active pumping well inversely proportional to distance squared.
Particles that exit the right edge or cross the water table are
reinjected on the left side, creating a steady visual flow field.
Category Coverage Update
Wave 46 targets three of the most underrepresented simulation categories on the platform:
- materials: 1 → 2 simulations (added Shape Memory Alloy)
- physical-chemistry: 1 → 2 simulations (added Adsorption Isotherm)
- earth: 2 → 3 simulations (added Groundwater Flow)
These categories remain small but are growing. The next priority targets are geophysics (seismology, gravity anomalies) and electrochemistry (Butler-Volmer kinetics, cyclic voltammetry) — both at 1–2 simulations currently.
What's Next
Wave 47 will continue filling category gaps with simulations in geophysics (seismic wave propagation), electrochemistry (electrode kinetics), and tribology (friction and wear). The blog is also due for a new Spotlight entry and a Learning explainer article — covering the physics of phase transitions across materials, biology, and climate systems.