## Saturday, March 19, 2016

### ReSpect: Program to extract Relaxation Time Spectra

During the last Society of Rheology meeting, I presented our work on extracting relaxation spectra from complex moduli. The goal is to extract the continuous relaxation spectrum $h(\tau)$, which is given by :
\begin{align}G^{\prime}(\omega) & = \int\limits_{-\infty}^{\infty} \frac{\omega^2 \tau^2}{1 + \omega^2 \tau^2} \color{blue}{h(\tau)} d \ln \tau, \nonumber \\ G^{\prime\prime}(\omega) & = \int\limits_{-\infty}^{\infty} \frac{\omega \tau}{1 + \omega^2 \tau^2} \color{blue}{h(\tau)} d \ln \tau. \label{eqn:gstcont} \end{align}Here are the slides from the presentation. The original version of this work appeared in the journal Applied Rheology, nearly two years ago.

Takeh A, Shanbhag S: A Computer Program to Extract the Continuous and Discrete Relaxation Spectra from Dynamic Viscoelastic Measurements, Appl. Rheol. 23 (2013) 24628.

The goal was to create a program to infer spectra with the design following attributes:
• platform independence
• ease-of-use "for an experimentalist"
• transparent algorithm and implementation
• free availability
• continuous and discrete relaxation spectra
• efficiency (~10 seconds to compute)
• readability and extensibility of the code(*)
• integrated graphics(*)
• extension to modern multicore machines(*)
where * = optional.

Based on feedback I received in the months leading up to, and after the presentation, I put in a fair amount of work to improve the program, including bug-fixes, and better default parameter choices. I also added the capability of inferring the spectra from $G(t)$ data as well. The program is hosted here.

My hope is to demonstrate a few cases here on the blog.