Physics Examples

GUI Examples

1) Travelling wave packet

Models a travelling Gaussian wave packet under dispersion $\partial_t \psi = i \beta_2 \partial_{xx} \psi$.

local sim = require("libsimcore")
local dt = 0.025
local N = 768
local ctx = sim.sim_create()

sim.sim_set_timestep(ctx, dt)
sim.sim_set_visual_mode(ctx, "polar")

local field = sim.sim_add_field(ctx, {N}, {
    type = "complex_double",
    fill = {0, 0}
})

sim.sim_add_stimulus_operator(ctx, field, {
    type = "stimulus_gaussian_travel",
    amplitude = 0.25,
    center = 6.0 * math.pi,
    velocity = 1,
    sigma = 1,
    omega = 1,
    spacing = 0.1
})

sim.sim_add_dispersion_operator(ctx, field, {
    coefficient = 1.5,
    order = 2,
    spacing = 0.1
})

local integrator = sim.sim_create_context_integrator(ctx, "euler", {
    adaptive = false,
    initial_dt = dt
})

sim.sim_set_integrator(ctx, integrator)

return ctx

CLI Examples

1) Heat diffusion on a line

Models 1D diffusion $\partial_t T = \nu\,\partial_{xx} T$ with a point hot spot so the Crank–Nicolson step damps the peak over time.

local temp = sim.sim_add_field(ctx, {256}, {
    fill = 0.0
})

temp:values()[128] = 1.0 -- hot spot

sim.sim_add_linear_dissipative_operator(ctx, temp, {
    viscosity = 0.5,
    alpha = 2.0,
    spacing = 0.01
})

local integrator = sim.sim_create_context_integrator(ctx, "crank_nicolson", {
    initial_dt = 0.01
})

sim.sim_set_integrator(ctx, integrator)

3) Thermostat energy clamp

Drives the energy toward $E_{\text{target}} = 1.5$ with a soft gain, acting like a discrete feedback loop $E_{n+1} \approx E_n - \lambda(E_n - E_{\text{target}})$.

local state = sim.sim_add_field(ctx, {256}, {
    type = "complex_double"
})

sim.sim_add_thermostat_operator(ctx, state, {
    mode = "soft_lambda",
    E_target = 1.5,
    lambda_soft_gain = 0.1
})

sim.sim_add_stimulus_operator(ctx, state, {
    type = "stimulus_sine",
    amplitude = 0.5,
    wavenumber = 1.0,
    omega = 0.2
})