2D Lennard–Jones gas

The tool opens with a reproducible initial state at time zero, paused. Physics edits rebuild it paused; Play/Pause advances model time. Options contains examples, integration settings, rate, seed, averaging and One step. Reset restores all defaults. Restart in Options repeats the current inputs and seed. Only raw input text is kept, including partial or invalid drafts; particle states, averages, time and menus are not saved.

All values use reduced units: σ = ε = m = kB = 1, τ = σ√(m/ε), T* = kBT/ε, ρ* = Nσ²/A and P* = Pσ²/ε. L* = √(N/ρ*) determines the actual box size. This is 2D pressure (energy per area), not a pressure in MPa. The presets describe starting densities, not guaranteed equilibrium phases.

The pair potential is U*(r*) = 4(r*⁻¹² − r*⁻⁶) − U*LJ(2.5) below r꜀* = 2.5, and zero beyond it. Its force is 24(2r*⁻¹³ − r*⁻⁷), with zero at r* = 2^(1/6). The potential shift preserves this force. No tail correction is applied. Velocity Verlet recomputes forces between its two half kicks; periodic minimum images are used. Overlaps below 0.6 σ stop the run instead of clipping the force.

Seed fixes the small position jitter and initial Gaussian velocities. Mean velocity is removed and initial temperature is normalized using 2N − 2 thermal degrees of freedom. With K measured relative to the centre of mass, T* = K*/(N − 1) and P* = (2K* + Σpairs r*F*)/(2L*²). For example, N = 144 and ρ* = 0.3 give L* ≈ 21.91; initial T* = 1 does not stay fixed in NVE.

NVE leaves the system isolated. Optional velocity rescaling forces the target T* after every step; it does not generate a canonical ensemble. Heat Q* records the resulting kinetic-energy change, positive into the system. The displayed energy balance is (E* − E*₀ − Q*)/N. Compare with half the time step to assess numerical error: a continuous shifted potential still has a force jump at the cutoff.

Means use equally spaced post-step samples after the chosen start time. Restart averages begins a fresh measurement at the current model time. Neither a fixed discard time nor a smooth mean proves equilibration; samples are correlated and no uncertainty estimate is supplied. The colour scale stays fixed from v* = 0 to 5; higher speeds saturate only the colour.

References: Lennard–Jones potential, temperature and degrees of freedom, pressure and virial, velocity Verlet.

Restart reproduces the chosen seed; Pause/Resume and One step keep the current state.