Diffusion Operators

📉 Linear Dissipative

sim_add_linear_dissipative_operator(ctx, field, opts)

Spectral fractional Laplacian. Parameters:

• viscosity (required, ≥0): diffusion coefficient.
• alpha (0..2, default 2): fractional Laplacian power.
• spacing (>0, default 1.0): grid spacing used to scale |k|.

Example:

sim.sim_add_linear_dissipative_operator(ctx, field, {
    viscosity = 0.5,
    alpha = 1.3,
    spacing = 0.05
})

sim.sim_add_linear_dissipative_operator(ctx, field, {
    viscosity = 0.0
}) -- no-op/pass-through

🔮 Linear Spectral Fusion

sim_add_linear_spectral_fusion_operator(ctx, field, opts)

Fuses dissipation, dispersion, and phase shift in one FFT pair. Parameters:

• viscosity (≥0): dissipation strength.
• alpha (0..2, default 2): dissipation order.
• dissipation_spacing (>0, default 1): scales |k| for dissipation.
• dispersion_coefficient (default 0): dispersion gain.
• dispersion_order (default 1): power on |k|.
• dispersion_reference_k (≥0, default 0): carrier offset.
• dispersion_spacing (>0, default 1): spacing for dispersion term.
• phase_rate (default 0): global phase rotation (rad/s).

Example:

sim.sim_add_linear_spectral_fusion_operator(ctx, field, {
    viscosity = 0.2,
    alpha = 2.0,
    dispersion_coefficient = 1.0,
    dispersion_order = 2.0,
    phase_rate = 0.0
})

sim.sim_add_linear_spectral_fusion_operator(ctx, field, {
    dispersion_coefficient = 0.5,
    dispersion_order = 1.0
})

🌈 Dispersion

sim_add_dispersion_operator(ctx, field, opts)

Pure spectral phase operator. Parameters:

• coefficient (required, -10..10): phase gain.
• order (0..4, default 2): |k| power.
• spacing (>0, default 1): grid spacing scaling.
• reference_k (≥0, default 0): carrier wavenumber offset.

Example:

sim.sim_add_dispersion_operator(ctx, field, {
    coefficient = 1.0,
    order = 2.0
})

sim.sim_add_dispersion_operator(ctx, field, {
    coefficient = -0.5,
    order = 1.0,
    reference_k = 0.25
})

🧠 Fractional Memory

sim_add_fractional_memory_operator(ctx, field, opts)

Long-range fractional derivative accumulator.

• order (required, 0<order≤1): fractional power.
• gain (default 0.5): scale applied to response.
• memory_steps (integer≥1): history length.

Example:

sim.sim_add_fractional_memory_operator(ctx, field, {
    order = 0.6,
    gain = 0.25,
    memory_steps = 128
})

sim.sim_add_fractional_memory_operator(ctx, field, {
    order = 1.0
}) -- first-order lag

Read/modify an existing fractional-memory operator

• sim_fractional_memory_config(ctx, op_index) -> table|nil returns { field_index, order, gain, memory_steps }.
• sim_fractional_memory_update(ctx, op_index, opts) -> true updates the live operator; only provided fields are touched.

local cfg = sim.sim_fractional_memory_config(ctx, op_index)
if cfg then
    sim.log("fracmem: field=%d order=%.2f gain=%.3f steps=%d",
        cfg.field_index, cfg.order, cfg.gain, cfg.memory_steps)
end

-- Increase memory and gain
sim.sim_fractional_memory_update(ctx, op_index, {
    memory_steps = 256,
    gain = 0.35,
})