def charged_nucleation_in_2D(writer,
args,
R=30,
D=25,
weights=(0, -10, -8, 8)):
dx = 2 * R / args.height
x = (np.arange(args.width) - args.width // 2) * dx
y = (np.arange(args.height) - args.height // 2) * dx
x, y = np.meshgrid(x, y, indexing='ij')
def source_G(t):
amount = np.exp(-0.5 * (t - 5)**2)
return (np.exp(-0.5 *
((x - D)**2 + y * y)) * weights[0] + np.exp(-0.5 * (
(x + D)**2 + y * y)) * weights[1]) * amount
def source_X(t):
amount = np.exp(-0.5 * (t - 5)**2)
return (np.exp(-0.5 *
((x - D)**2 + y * y)) * weights[2] + np.exp(-0.5 * (
(x + D)**2 + y * y)) * weights[3]) * amount
source_functions = {
'G': source_G,
'X': source_X,
}
noise_scale = 1e-4
model_g = ModelG(
bl_noise(x.shape) * noise_scale,
bl_noise(x.shape) * noise_scale,
bl_noise(x.shape) * noise_scale,
dx,
dt=args.dt,
params=args.model_params,
source_functions=source_functions,
)
print("Rendering 'Charged nucleation in 2D'")
print("Lattice constant dx = {}, time step dt = {}".format(
model_g.dx, model_g.dt))
min_G = -4.672736908320116
max_G = 0.028719261862332906
min_X = -3.8935243721220334
max_X = 1.2854028081816122
min_Y = -0.7454193158963579
max_Y = 4.20524950766914
for n in progressbar.progressbar(range(args.num_frames)):
model_g.step()
if n % args.oversampling == 0:
rgb = [
6 * (-model_g.G + max_G) / (max_G - min_G),
5 * (model_g.Y - min_Y) / (max_Y - min_Y),
0.7 * (model_g.X - min_X) / (max_X - min_X),
]
zero_line = 1 - tf.exp(-600 * model_g.Y**2)
frame = make_video_frame([c * zero_line for c in rgb])
writer.append_data(frame)
def soliton_in_g_well_2D(writer, args, R=25, D=15):
dx = 2 * R / args.height
x = (np.arange(args.width) - args.width // 2) * dx
y = (np.arange(args.height) - args.height // 2) * dx
x, y = np.meshgrid(x, y, indexing='ij')
def source_G(t):
nucleator = -np.exp(-0.5 * (t - 5)**2)
#potential = 0.015 * (np.tanh(t-25) + 1)
#potential = 0.0003 * (np.tanh(t-25) + 1) # gradient = (1+np.tanh(t-30)) * 0.0003 # see above
#u = x / R
#u = x/10 - 5 # see: "soliton_in_g_well_2D___1_seed__gradient_1__2a.mp4"
#u = x/15 # see: "soliton_in_g_well_2D___1_seed__gradient_2__2b.mp4"
#u = x/25
return (
#np.exp(-0.5*((x-D)**2+y*y)) * nucleator +
#(u*u - 1) * potential
np.exp(-0.5 * ((x)**2 + y * y)) * nucleator #+ (x+8) * potential
#(u*u - 1) * potential #+ (x+8) * gradient
)
source_functions = {
'G': source_G,
}
noise_scale = 1e-4
model_g = ModelG(
bl_noise(x.shape) * noise_scale,
bl_noise(x.shape) * noise_scale,
bl_noise(x.shape) * noise_scale,
dx,
dt=args.dt,
params=args.model_params,
source_functions=source_functions,
)
print("Rendering 'Soliton in G-well in 2D'")
print("Lattice constant dx = {}, time step dt = {}".format(
model_g.dx, model_g.dt))
G_scale = 0.02
X_scale = 0.25
Y_scale = 0.5
for n in progressbar.progressbar(range(args.num_frames)):
model_g.step()
if n % args.oversampling == 0:
rgb = [
(G_scale * 0.5 - model_g.G) / G_scale,
(model_g.Y - Y_scale * 0.5) / Y_scale,
(model_g.X - X_scale * 0.5) / X_scale,
]
zero_line = 1 - tf.exp(-600 * model_g.Y**2)
frame = make_video_frame([c * zero_line for c in rgb])
writer.append_data(frame)
def random_1D_fields():
x = linspace(-20, 20, 512)
dx = x[1] - x[0]
noise_scale = 1.0
fig, axs = subplots(2, 3)
for ax_ in axs:
for ax in ax_:
while True:
params = {
"A": rand() * 20,
"B": rand() * 20,
"k2": rand() * 2,
"k-2": rand() * 2,
"k5": rand() * 2,
"Dx": rand() * 4,
"Dy": rand() * 4,
}
model_g = ModelG(bl_noise(x.shape) * noise_scale,
bl_noise(x.shape) * noise_scale,
bl_noise(x.shape) * noise_scale,
dx,
params=params)
while model_g.t < 20:
model_g.step()
if rand() < 0.05:
G, X, Y = model_g.numpy()
if abs(X).max() >= 100:
break
G, X, Y = model_g.numpy()
if abs(X).max() < 100:
break
print("Rejected", params)
print("Done", params)
G /= abs(G).max()
X /= abs(X).max()
Y /= abs(Y).max()
ax.plot(x, G)
ax.plot(x, X)
ax.plot(x, Y)
show()
