pyReSpect-freq

Extract the continuous and discrete relaxation spectra from complex modulus G*(w). Papers which describe the method are:

• Shanbhag, S., "Relaxation spectra using nonlinear Tikhonov regularization with a Bayesian criterion", Rheologica Acta, 2020, 59, 509 [doi: 10.1007/s00397-020-01212-w].
• Shanbhag, S., "pyReSpect: A Computer Program to Extract Discrete and Continuous Spectra from Stress Relaxation Experiments", Macromolecular Theory and Simulations, 2019, 1900005 [doi: 10.1002/mats.201900005].
• Takeh, A. and Shanbhag, S. "A computer program to extract the continuous and discrete relaxation spectra from dynamic viscoelastic measurements", Appl. Rheol. 2013, 23, 24628.

Files

Code Files

This repository contains two python modules contSpec.py discSpec.py. They extract the continuous and discrete relaxation spectra from a stress relaxation data. (w versus G*(w) experiment or simulation).

It containts a third module common.py which contains utilities required by both contSpec.py and discSpec.py.

In addition to the python modules, jupyter notebooks interactContSpec.ipynb. This provisionally allows the user to experiment with parameter settings interactively.

Input Files

The user is expected to supply two files:

• inp.dat is used to control parameters and settings
• Gst.dat which contains three columns of data w, G' and, G" [07/2023: optionally 2 more columns specifying weights]

Output Files

Text files containing output from the code are stored in a directory output/. These include a fit of the data, the spectra, and other files relevant to the continuous or discrete spectra calculation.

Graphical and onscreen output can be suppressed by appropriate flags in inp.dat.

Test Files

A bunch of test files are supplied in the folder tests/.

Usage

Once inp.dat and Gst.dat are furnished, running the code is simple.

To get the continuous spectrum:

python3 contSpec.py

The continuous spectrum must be extracted before the discrete spectrum is computed. The discrete spectrum can then be calculated by

python3 discSpec.py

Interactive Mode

The interactive mode offers a "GUI" for exploring parameter settings. To launch use jupyter notebook interactContSpec.ipynb.

Pre-requisites

The numbers in parenthesis show the latest versions this program has been tested on.

python3 (3.8) numpy (1.24) scipy (1.10)

For interactive mode:

jupyter-core (4.6.3) jupyter-notebook (6.0.3) ipywidgets (8.1.1)

History

The code is based on the Matlab program ReSpect, which extract the continuous and discrete relaxation spectra from frequency data, G*(w).

Major Upgrade: March-Apr 2019

• added ability to infer plateau modulus G0; modified all python routines and reorganized inp.dat
• use a Bayesian formulation to infer uncertainty in the continuous spectrum
• currently keeping old method to determine critical lambda, but using a far more efficient method (3-4x savings in compute time)
• made discSpec.py compliant with G0
• lots of bug-fixes
• organized tests/ folder better.

Major Upgrade: Jan 2019

• moved all common imports and definitions to common; made completely visible
• in discSpec(): added a NLLS routine to optimize tau; use previous optima as initial guesses for final tau; this greatly improved the quality of fits.

Major Upgrade: August 2018

• Incorporating changes from pyReSpect-time into frequency calculation
• discrete spectrum only "magic" mode from now on, since it works so well
• Major improvements in discrete spectrum (AIC/mergemodes)