0
$\begingroup$

Cross-posted on MMSE (Matter Modeling Stack Exchange).

The following are the movements of the center of mass of a polymer chain over time in a monte carlo simulation.

#   cm-X     cm-Y    cm-Z
9.507 21.232 9.910
9.092 18.427 7.308
7.994 14.856 4.675
0.533 12.138 -1.163
-0.056 6.735 -5.470
-2.138 4.950 -7.280
0.736 13.076 -10.012
9.516 14.611 -12.470
0.886 17.235 -10.714
-8.954 21.381 -11.735
-7.457 16.042 -16.710
-0.842 13.984 -17.874
-2.799 13.195 -14.247
0.738 14.792 -11.774
5.760 9.218 -10.846
8.406 13.735 -15.946
6.848 12.679 -9.621
13.569 14.036 -6.348
8.665 12.724 -8.238
... ... ... ... ...

I want to draw a log-log plot of MSD (mean square displacement) versus t of a movement of the polymer chain to examine the diffusion behavior.

The problem I am facing is that the plot should be a near-straight line, whereas my plot is not.

What am I doing incorrectly?

Without smoothing:

enter image description here

With smooting:

enter image description here

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

# Function to compute moving average
def moving_average(x, w):
    return np.convolve(x, np.ones(w), 'valid') / w

# Read data from file, skipping the first row (header)
data = np.loadtxt('cm.dat', skiprows=1)

# Wrap CM values if they exceed -1000 or +1000
data = np.mod(data + 1000, 2000) - 1000  # performs the wrap operation

# Initialize reference point
x0, y0, z0 = data[0]

# Compute squared displacement for each time step
SD = [(x - x0)**2 + (y - y0)**2 + (z - z0)**2 for x, y, z in data]

# Compute the cumulative average of SD to get MSD at each time step
MSD = np.cumsum(SD) / np.arange(1, len(SD) + 1)

# Size of the moving window for smoothing
window_size = 100

# Apply moving average smoothing to MSD
MSD_smoothed = moving_average(MSD, window_size)

# Generate time steps for smoothed MSD
t_smoothed = np.arange(window_size, len(MSD) + 1)

# Create a log-log plot of smoothed MSD versus t
plt.figure(figsize=(8, 6))
plt.loglog(t_smoothed, MSD_smoothed, marker='o')
plt.title('Smoothed Mean Squared Displacement vs Time')
plt.xlabel('Time step')
plt.ylabel('Smoothed MSD')
plt.grid(True, which="both", ls="--")
plt.savefig('msd_plot_smoothed.png')
$\endgroup$
0

1 Answer 1

2
$\begingroup$

Why should it be a straight line? That is perhaps true if you had infinitely many samples, but you don't. So the question is: How does the curve change if you add more and more samples?

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.