diffusion coefficient code using random walk

Here is an example code for a diffusion simulation using random walk in Python:

import numpy as np
import matplotlib.pyplot as plt

# Set up variables
num_particles = 1000
num_steps = 100
step_size = 1

# Initialize particle positions
positions = np.zeros(num_particles)

# Initialize array to store particle positions at each step
positions_history = np.zeros((num_steps, num_particles))

# Loop through each step
for i in range(num_steps):
    # Generate random step sizes for each particle
    steps = np.random.normal(scale=step_size, size=num_particles)
    
    # Update particle positions
    positions += steps
    
    # Store positions at this step
    positions_history[i] = positions

# Calculate mean squared displacement (MSD) for each time step
msd = np.mean((positions_history - np.mean(positions_history, axis=0))**2, axis=1)

# Calculate diffusion coefficient
diff_coeff = msd / (2 * step_size * num_steps)

# Plot MSD and diffusion coefficient
fig, ax = plt.subplots(1, 2, figsize=(10, 4))
ax[0].plot(msd)
ax[0].set_xlabel('Time step')
ax[0].set_ylabel('Mean squared displacement')
ax[1].plot(diff_coeff)
ax[1].set_xlabel('Time step')
ax[1].set_ylabel('Diffusion coefficient')
plt.show()

In this code, we first set up variables such as the number of particles, number of steps, and step size. We then initialize particle positions and an array to store positions at each step.

We loop through each step and generate random step sizes for each particle using `numpy.random.normal()`. We then update particle positions and store positions at this step.

We calculate the mean squared displacement (MSD) for each time step and use this to calculate the diffusion coefficient. We then plot both the MSD and diffusion coefficient using `matplotlib.pyplot`.

Note that this code assumes a one-dimensional system. If you want to simulate diffusion in higher dimensions, you will need to modify the code accordingly.