Voronoi

This script shows how to use mumax⁺’s Voronoi Tesselator. This is inspired by figure 19 of the paper The design and verification of MuMax3.

import matplotlib.pyplot as plt
import numpy as np

from mumaxplus import Ferromagnet, Grid, World
from mumaxplus.util import Circle, VoronoiTessellator
from mumaxplus.util import show_field, vortex

# Set up simulation parameters
N = 256
c = 4e-9
d = 40e-9

world = World(cellsize=(c, c, d))
grid = Grid((N, N, 1))

# Create a circle
diam = N*c
geo = Circle(diam).translate(diam/2, diam/2, 0)

# Initialize a Voronoi Tesselator using a grainsize of 40e-9 m
tessellator = VoronoiTessellator(40e-9)
regions = tessellator.generate(world, grid)

# Create Ferromagnet
magnet = Ferromagnet(world, grid, geometry=geo, regions=regions)
magnet.alpha = 3
magnet.aex = 13e-12
magnet.msat = 860e3

# Set vortex magnetization
magnet.magnetization = vortex(magnet.center, 2*c, 1, 1)
show_field(magnet.magnetization)

for i in tessellator.indices:
    # Set random anisotropy axes in each region
    anisC1 = tuple(np.random.normal(size=3))
    anisC2 = tuple(np.random.normal(size=3))
    magnet.anisC1.set_in_region(i, anisC1)
    magnet.anisC2.set_in_region(i, anisC2)

    # Create a random 10% anisotropy variation
    K = 1e5
    magnet.kc1.set_in_region(i, K + np.random.normal() * 0.1 * K)

# Vary interregion aex
magnet.scale_exchange = 0.9

# Evolve the world in time
world.timesolver.run(0.1e-9)

show_field(magnet.magnetization)

fig = plt.figure()
plt.imshow(magnet.kc1()[0][0], vmin=np.unique(magnet.kc1().flatten())[1],
            vmax=np.max(magnet.kc1()), cmap="Greys")
plt.title(r"First cubic anisotropy constant $K_{c1}$ (J / m³)")
plt.xlabel(r"$x$ (m)")
plt.ylabel(r"$y$ (m)")
plt.colorbar()
plt.show()