simpok

High level Python API for phase field simulation of phase-ordering kinetics, with all computationally intensive operations, including GPU-accelerated kernels, implemented in Mojo programming langauge.

Implemented Systems: Dimensionless CHC, TDGL, and SDSD solvers

Install

pip install simpok

The models

TDGL — nonconserved scalar order parameter (Model A).

∂ψ/∂t = ψ − ψ³ + h + ∇²ψ + θ

CHC — conserved scalar order parameter (Model B).

∂ψ/∂t = −∇²(ψ − ψ³ + ∇²ψ) + ∇·θ

SDSD — surface-directed spinodal decomposition. The same conserved dynamics in contact with a wall at z = 0 that prefers one component: the bulk phase separates while the wall is wetted.

∂ψ/∂t = −∇²(ψ − ψ³ + ½∇²ψ − V(z)) + ∇·θ                    z > 0

h₁ + gψ + γ ∂ψ/∂z = 0                                      at z = 0
∂/∂z(−ψ + ψ³ − ½∇²ψ + V) = 0                               at z = 0

with the long-ranged wall potential V(z) = −V₀/zⁿ (cut off at −V₀ for z ≤ 1).

API

TDGL(ny=256, nx=256, dx=1.0, dt=0.1, h=0.0, eps=0.0, dtype=np.float64, device="auto")
CHC (ny=256, nx=256, dx=1.0, dt=0.01, eps=0.0, dtype=np.float64, device="auto")
SDSD(nz=256, nx=256, dx=1.0, dt=0.03, h1=0.8, g=-0.4, gamma=0.4, v0=None, n=4,
     potential=None, eps=0.0, dtype=np.float64, device="auto")

The wall potential of SDSD defaults to the power law above, shaped by v0 and n. Any other shape can be passed to potential as a callable of z or as one value per row:

SDSD(potential=lambda z: -0.8 * np.exp(-z / 3.0))        # short-ranged well
SDSD(potential=lambda z: np.where(z <= 5.0, -0.8, 0.0))  # square well
SDSD(potential=np.zeros(256))                            # no potential at all

Examples

Runnable scripts for all three solvers are in examples/.

Hardware notes

• Supported Device — GPU (AMD, NVIDIA, APPLE) and CPU

License

MIT — see LICENSE.