Field · 5 models
Physics Simulations
Classical mechanics and statistical physics, simulated from their governing equations. Each model reports an accuracy check — energy drift, a conserved quantity, or agreement with an exact result — so the numbers on screen can be trusted as far as the method allows.
Models in this field
- OS-034Projectile motionThe vacuum parabola against a trajectory with quadratic air drag, and why 45° stops being the best angle.
- OS-035Harmonic oscillatorA mass on a spring with friction and a periodic push: damping regimes, phase portraits and resonance.
- OS-036Double pendulumTwo nearly identical double pendulums that part ways: sensitive dependence on initial conditions.
- OS-037DiffusionThe heat equation solved two ways, by finite differences and by random walkers, against the exact Gaussian.
- OS-038Ising modelSpins on a grid that like to align: a phase transition at T_c ≈ 2.269, simulated with Metropolis flips.
Deterministic mechanics
- Projectile motion: the exact parabola in vacuum against a numerically integrated trajectory with air drag.
- Harmonic oscillator: springs, damping regimes and resonance under a periodic force.
- Double pendulum: two linked pendulums and sensitive dependence on initial conditions — two runs that start a billionth of a radian apart soon look nothing alike.
Statistical physics
- Diffusion: the diffusion equation solved on a grid next to thousands of random walkers — two descriptions of the same spreading.
- Ising model: spins on a lattice sampled with the Metropolis algorithm, and the phase transition at the critical temperature Onsager computed exactly.
Integrators matter
Every trajectory here is computed by stepping differential equations forward in time. The step size and method decide whether energy is conserved, whether an orbit closes and whether a chaotic trajectory is meaningful for more than a few seconds. Euler vs Runge–Kutta compares the two most common methods on a problem with a known answer.