Numerical computation of relaxation spectra from mechanical measurements in biopolymers

In the present investigation, a computational methodology to treat relaxation spectra from mechanical data is developed. To calculate the spectral function that represents the relaxation process of the material, three different regularization algorithms were tested using MATLAB. Two algorithms employ Tikhonov’s regularization whereas the third investigative tool is an implementation of the CONTIN algorithm. These efforts improved the ability to look at data hence allowing utilization of the L-curve criterion in order to locate the optimum regularization parameter for accurate data inversion. Algorithms were first evaluated with hypothetical data followed by experimental datasets of hydrated gluten as a model biopolymer system. Essentially, algorithms converge on a specific relaxation spectrum that unveils the molecular features of gluten structure. The methodology described is not limited to mechanical measurements but should be used with any type of exponential decay in studies of relaxation processes.