Platform Stats
Wave 24 Blog Posts
- Spotlight #45 — Fluid Dynamics & Turbulence: Navier-Stokes equations, Reynolds number and the laminar-turbulent transition, Bernoulli’s principle and lift, boundary layers and skin friction, von Kármán vortex street and Tacoma Narrows, Kolmogorov energy cascade and the −5/3 law, compressible flow and Mach number, superfluids and quantum turbulence.
- Learning #34 — Thermodynamics & Statistical Mechanics: The four laws; entropy S = kB ln W and the arrow of time; Carnot cycle η = 1 − TC/TH; thermodynamic potentials (U, H, A, G); Boltzmann distribution and partition function Z; canonical, microcanonical, and grand canonical ensembles; phase transitions and Ising universality; quantum statistics (Bose-Einstein, Fermi-Dirac); Landauer’s principle and Maxwell’s demon.
New Simulation: Gravitational Wave Chirp
🌌 Gravitational Wave Chirp Visualiser
An interactive LIGO-style gravitational wave explorer. Two compact objects (neutron stars or black holes) spiral inward under radiation reaction, emitting a chirp waveform h(t) whose frequency and amplitude both rise as the binary loses energy to gravitational radiation, until the objects merge and the signal ends.
Physics & maths
The strain in general relativity (post-Newtonian quadrupole approximation):
f(t) = (1/π) (5/256)³⁄&sup8; (G𝓅/c³)&sup5;⁄&sup8; (tc−t)−3/8
𝓅 = (m1m2)³⁄&sup5; / (m1+m2)¹⁄&sup5; (chirp mass)
h+(t) = (4/r)(G𝓅/c²)&sup5;⁄³ (πf)2/3 cos(2πφ(t))
The simulation lets you set individual masses m1, m2, and the luminosity distance r. The waveform canvas shows real-time strain h(t) vs time, an animated frequency spectrogram, and the inspiral trajectory of each body in the source plane. An optional LIGO detector response overlays instrumental noise (aLIGO design sensitivity Sn(f)) on the signal, illustrating matched filtering.
Engineering notes
The inspiral waveform uses the 0PN (leading-order post-Newtonian) chirp formula plus a 1PN amplitude correction. Time is measured backward from the coalescence time tc, computed from the initial separation. The frequency sweep is numerically integrated at Δt = 0.5 ms with a 4th-order Runge-Kutta step on the orbital phase. The spectrogram is a running STFT (short-time Fourier transform with a Hann window, 128 samples) rendered as an image strip on a second canvas. Detector noise is pre-tabulated from the analytical aLIGO fit (L. Martynov et al. 2016) and overlaid as a semi-transparent shaded region on the strain plot.
New Simulation: Phase Equilibrium
⚛️ Thermodynamic Phase Equilibrium
A reaction-coordinate tool for chemical equilibrium. Given the generic reversible reaction aA + bB ⇌ cC + dD, the simulator shows the Gibbs energy landscape G(Q) where Q is the reaction quotient, equilibrium at Q = K (minimum G), and the Le Chatelier response to perturbations in concentration, temperature, and pressure.
Physics & maths
Equilibrium: Q = K ⟺ ΔrG = 0
ΔrG° = −RT ln K
van’t Hoff: d ln K/dT = ΔrH°/(RT²)
Kp = Kc(RT)Δn (Δn = moles gas products − reactants)
Sliders control ΔH°, ΔS°, temperature T, and whether each species is gaseous or aqueous (for pressure effects via Kp). Animated concentration bars show the approach to equilibrium from a chosen initial composition using the ICE (Initial-Change-Equilibrium) method. The G(Q) curve is rendered on Canvas 2D with a draggable “Q marker” that shows ΔrG in real time.
Engineering notes
The Gibbs landscape G(Q) = ΔG° + RT(a ln a + b ln b − c ln c − d ln d) is sampled at N = 400 points on a log scale from Q = 10−&sup6; to 10&sup6;. A Newton-Raphson solver finds K from the closed-form van’t Hoff equation. ICE concentrations are solved with a bisection method (10 iterations) to locate equilibrium extent ξ. The van’t Hoff plot (ln K vs 1/T) is rendered as a second canvas, showing the slope −ΔH°/R.
What’s Next: Wave 25
Wave 25 will push into plasma physics, quantum computing, and ecology. Planned simulations include:
- Tokamak magnetic confinement — toroidal/poloidal field, drift trajectories, MHD stability.
- Quantum circuit simulator — single-qubit gates on Bloch sphere, CNOT, Bell states, measurement collapse.
- Lotka-Volterra ecosystem — predator-prey oscillations, Jacobian stability, multiple species interactions.
- Debye shielding — plasma screening length, Yukawa potential, plasma oscillations.
Blog posts: Spotlight #46 on Plasma Physics & MHD; Learning #35 on Quantum Computing & Quantum Information.