Extract continuous and discrete relaxation spectra from stress relaxation modulus G(t). The papers which describe the method and test cases are:

• 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.

This repository contains two python modules contSpec.py discSpec.py. They extract the continuous and discrete relaxation spectra from a stress relaxation data. (t versus G(t) 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, a jupyter notebook interactContSpec.ipynb is also provisionally included. This allows the user to experiment with parameter settings interactively.

The user is expected to supply two files:

• inp.dat is used to control parameters and settings
• Gt.dat which contains two columns of data t and G(t) [July 2023: optional third column specifying weight of datapoints]

Text files containting 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.

A bunch of test files are supplied in the folder tests/. These data are described in the paper: Shanbhag, S., "pyReSpect: A Computer Program to Extract Discrete and Continuous Spectra from Stress Relaxation Experiments" which will appear in Macromolecular Theory and Simulations in 2019.

Once inp.dat and Gt.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

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

The numbers in parenthesis show the version this has been tested on.

python3 (3.8) numpy (1.23) scipy (1.3)

For interactive mode:

jupyter (4.3) ipywidgets (6.0.0)

The code is based on the Matlab program ReSpect, which extract the continuous and discrete relaxation spectra from frequency data, G*(w). Work was supported by National Science Foundation DMR grants number 0953002 and 1727870.

• 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

• 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.

• original program with n = 100 and lambda = 20 pts with clean 1 mode data took ~33s.
• prestore kernMat: evaluation of kernel (meshgrid S, T, and hs) by prestoring kernMat ~12.5s (~3x speed gain)
• improved least_squares setting by incorporating jacobianLM; ~6s (2x gain)
• lcurve coarser (auto) mesh, robust criterion, and interpolation ~3.5s (~1.75x gain)
• Total gain in speed as a consequence of these improvements is 33s -> 3.5s a nearly 10x gain!
• making jupyter interact compliant

• AutoMagic Mode: need only par verbose and plotting flags; auto Nopt
• switching to nnls as default fitting engine
• changed older MaxwellModes and LLS -> nnls
• some printing modifications
• hardcoding prune = True everywhere; doesn't seem to be use case otherwise
• making jupyter interact compliant