#### NOTE
[Go to the end](#sphx-glr-download-auto-examples-normal-mode-analysis-plot-normal-mode-analysis-py)
to download the full example code.
# Normal Mode Analysis (NMA)
This example demonstrates how to use the NormalModeAnalyzer in pylimer-tools
to predict the loss and storage modulus of polymer networks using exact eigenvalue
solvers or the Kernel Polynomial Method (KPM).
Reference: Gusev and Bernhard [[GB24](../../acknowledgements.html.md#id7)]
```Python
import os
from pathlib import Path
import numpy as np
import pandas as pd
from pylimer_tools.io.read_lammps_output_file import read_data_file
from pylimer_tools_cpp import NormalModeAnalyzer, NormalModeSolver
# Load a LAMMPS data file (replace with your file)
def _find_fixtures_dir() -> Path:
for cur in (
[Path(__file__).resolve().parent] if "__file__" in globals() else []
) + [Path.cwd()]:
for p in [cur] + list(cur.parents):
candidate = p / "tests" / "pylimer_tools" / "fixtures"
if candidate.is_dir():
return candidate
return Path("tests/pylimer_tools/fixtures").resolve()
_fixtures_dir = _find_fixtures_dir()
filePath = str(_fixtures_dir / "structure/network_100_a_46.structure.out")
universe = read_data_file(filePath)
edges = universe.get_edges()
# Create the normal mode analyzer
nma = NormalModeAnalyzer(
edges["edge_from"],
edges["edge_to"],
)
# 1. Exact analysis with connected component decomposition and
# dense/sparse solver
nma.find_all_eigenvalues(
solver=NormalModeSolver.AUTO,
compute_eigenvectors=False,
decompose_components=True,
)
# Get the storage and loss modulus across frequencies
frequencies = np.logspace(-4, 3, num=int(1e3))
storage_modulus_exact = nma.evaluate_storage_modulus(omega=frequencies)
loss_modulus_exact = nma.evaluate_loss_modulus(omega=frequencies)
# 2. Kernel Polynomial Method (KPM) without computing full eigenvalues
# KPM calculates viscoelastic moduli in O(N) time for large networks.
storage_modulus_kpm = nma.evaluate_storage_modulus_kpm(
omega=frequencies,
num_moments=512,
num_random_vectors=20,
num_quadrature_points=1024,
)
loss_modulus_kpm = nma.evaluate_loss_modulus_kpm(
omega=frequencies,
num_moments=512,
num_random_vectors=20,
num_quadrature_points=1024,
)
```
Plot and compare the results
```Python
df = pd.DataFrame(
{
"Frequency": frequencies,
"Storage Modulus (Exact)": storage_modulus_exact,
"Loss Modulus (Exact)": loss_modulus_exact,
"Storage Modulus (KPM)": storage_modulus_kpm,
"Loss Modulus (KPM)": loss_modulus_kpm,
}
)
df.set_index("Frequency", inplace=True)
_ = df.plot(
title="Normal Mode Analysis: Exact vs KPM Moduli",
loglog=True,
style={
"Storage Modulus (Exact)": "b-",
"Loss Modulus (Exact)": "r-",
"Storage Modulus (KPM)": "b--",
"Loss Modulus (KPM)": "r--",
},
)
```
```none
/home/runner/work/pylimer-tools/pylimer-tools/examples/normal_mode_analysis/plot_normal_mode_analysis.py:87: Pandas4Warning: The inplace keyword in DataFrame.set_index is deprecated and will be removed in a future version (PDEP-8).
See https://pandas.pydata.org/docs/dev/whatsnew/v3.1.0.html#deprecation-inplace for more details.
df.set_index("Frequency", inplace=True)
```
**Total running time of the script:** (0 minutes 7.937 seconds)
[`Download Jupyter notebook: plot_normal_mode_analysis.ipynb`](_downloads/fad61465a562c82c11b547553dceb6b1/plot_normal_mode_analysis.ipynb)
[`Download Python source code: plot_normal_mode_analysis.py`](_downloads/05d5229a50b4f1c9fbea77654e66bc82/plot_normal_mode_analysis.py)
[`Download zipped: plot_normal_mode_analysis.zip`](_downloads/fc9f8d7f4f2d7f7b2b6529e1a4935dd6/plot_normal_mode_analysis.zip)
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