Coherent Structures in Granular Crystals: From Experiment and Modelling to Computation and Mathematical Analysis – eBook PDF
Coherent Structures in Granular Crystals: From Experiment and Modelling to Computation and Mathematical Analysis (PDF) summarizes many fundamental developments at the interface of granular crystals and the mathematical and computational analysis of some of their key localized nonlinear wave solutions. The subject presents a combination of the appeal of granular crystals as a prototypical engineering tested for a variety of diverse applications, the novelty in the nonlinear physics of its coherent structures, and the tractability of a series of mathematical and computational techniques to evaluate them. While the emphsis is on principal one-dimensional solutions such as traveling waves, shock waves, and discrete breathers, numerous extensions of the discussed patterns, e.g., in two dimensions, heterogeneous settings, chains with defects, and other recent developments are discussed. The focus on the subject was motivated by models in condensed matter physics, ferroelectrics, high energy physics, and statistical mechanics, leading to developments in mathematical analysis, numerical computation and insights on the physical aspects of the model. The ebook appeals to researchers in the field, and also for graduate and advanced undergraduate students. It will be of interest to physicists, mathematicians and engineers alike.
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