写一个Diffusion-limited Aggregation模型的代码

答：以下是一个Diffusion-limited Aggregation模型的Python代码：import numpy as np
import matplotlib.pyplot as plt

# Set the number of particles
n=1000

# Set the diffusion constant
D=1.0

# Generate the initial positions of the particles
x=np.random.uniform(0,1,n)
y=np.random.uniform(0,1,n)

# Set the maximum time and the timestep
tmax=100
dt=0.01

# Set the size of the aggregation and the aggregation rate
R=0.05
k=0.3

# Set the maximum number of steps
nmax=int(tmax/dt)

# Initialize an array to store the particle positions
xsave=np.zeros((nmax,n))
ysave=np.zeros((nmax,n))

# Save the initial positions
xsave[0,:]=x
ysave[0,:]=y

# Perform the diffusion-limited aggregation
for i in range(nmax-1):
# Calculate the distance between particles
r=np.sqrt((x[:,None]-x[None,:])**2 + (y[:,None]-y[None,:])**2)
# Set the distance between particles to a large value if they are the same particle
r[np.diag_indices(n)]=np.inf
# Calculate the distance between particles and the aggregation
d=np.sqrt((x-0.5)**2 + (y-0.5)**2)
# Calculate the diffusion coefficient
Dx=D*(1-k*(r<R))
Dy=D*(1-k*(r<R))
# Calculate the rate of aggregation
kx=k*(d<R)
ky=k*(d<R)
# Calculate the movement of the particles
dx=np.sum(Dx,axis=1)-kx*(x-0.5)
dy=np.sum(Dy,axis=1)-ky*(y-0.5)
x+=dx*dt
y+=dy*dt
# Save the particle positions
xsave[i+1,:]=x
ysave[i+1,:]=y

# Plot the results
plt.scatter(xsave[-1,:],ysave[-1,:])
plt.show()