A Critical Evaluation and Modification of the Padé–Laplace Method for Deconvolution of Viscoelastic Spectra

This paper shows that using the Padé–Laplace (PL) method for deconvolution of multi-exponential functions (stress relaxation of polymers) can produce ill-conditioned systems of equations. Analysis of different sets of generated data points from known multi-exponential functions indicates that by increasing the level of Padé approximants, the condition number of a matrix whose entries are coefficients of a Taylor series in the Laplace space grows rapidly. When higher levels of Padé approximants need to be computed to achieve stable modes for separation of exponentials, the problem of generating matrices with large condition numbers becomes more pronounced. The analysis in this paper discusses the origin of ill-posedness of the PL method and it was shown that ill-posedness may be regularized by reconstructing the system of equations and using singular value decomposition (SVD) for computation of the Padé table. Moreover, it is shown that after regularization, the PL method can deconvolute the exponential decays even when the input parameter of the method is out of its optimal range

Review on Hybrid Reinforced Polymer Matrix Composites with Nanocellulose, Nanomaterials, and Other Fibers

The use of composite materials has seen many new innovations for a large variety of applications. The area of reinforcement in composites is also rapidly evolving with many new discoveries, including the use of hybrid fibers, sustainable materials, and nanocellulose. In this review, studies on hybrid fiber reinforcement, the use of nanocellulose, the use of nanocellulose in hybrid forms, the use of nanocellulose with other nanomaterials, the applications of these materials, and finally, the challenges and opportunities (including safety issues) of their use are thoroughly discussed. This review will point out new prospects for the composite materials world, enabling the use of nano- and micron-sized materials together and creating value-added products at the industrial scale. Furthermore, the use of hybrid structures consisting of two different nano-materials creates many novel solutions for applications in electronics and sensors