عنوان

Coherent structures in granular crystals :

3319778846

9783319778846

3319778838

9783319778839

Coherent structures in granular crystals :

[Book]

from experiment and modelling to computation and mathematical analysis /

Christopher Chong, Panayotis G. Kevrekidis.

Cham, Switzerland :

Springer,

2018.

1 online resource

SpringerBriefs in physics

Includes bibliographical references.

Intro; Preface; Acknowledgements; Contents; 1 Introduction and Motivation of Models; 1.1 Dynamics of Hertzian Beads; 1.2 The Linear Discrete Wave Equation; 1.3 The Nonlinear States: Dispersive Shock Waves, Traveling Solitary Waves, and Discrete Breathers; References; 2 Dispersive Shock Waves; 2.1 Overview; 2.2 Theoretical Analysis of Shock Waves; 2.3 Prototypical Numerical Computations; 2.4 Outlook; References; 3 Traveling Waves; 3.1 Overview; 3.2 Traveling Waves With Precompression: The KdV and Toda Limits; 3.3 Traveling Waves Without Precompression I: The Continuum Limit.

3.4 Traveling Waves Without Precompression II: Asymptotic and Numerically Exact ResultsReferences; 4 Discrete (Dark) Breathers; 4.1 Discrete Breathers: Overview and Theoretical Analysis; 4.2 Connection with Experimental Results; References; 5 Heterogeneous Media; 5.1 Overview; 5.2 Traveling Solitary Waves in Heterogeneous Chains; 5.3 From Isolated Defect Modes to Bright Breathers in Dimer Chains; References; 6 Media with Onsite Forces: The Newton's Cradle and Beyond; 6.1 Breathers in the Newton's Cradle; 6.2 Solitary Waves and Breathers in Locally Resonant Granular Chains; References.

7 Higher Dimensional Lattices7.1 Overview; 7.2 Conical Diffraction in the Hexagonal Packing; 7.3 Other Work in Higher Dimensional Lattices and Future Directions; References; Appendix; A.1 Numerical Computation of Traveling Solitary Waves and Their Stability; A.2 Numerical Computation of Breathers and Their Stability; A.3 Derivation of the Nonlinear Schrödinger Equation; References.

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This book summarizes a number of 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 blend 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 analyse them. While the focus is on principal one-dimensional solutions such as shock waves, traveling waves, and discrete breathers, numerous extensions of the discussed patterns, e.g., in two dimensions, chains with defects, heterogeneous settings, and other recent developments are discussed. The book appeals to researchers in the field, as well as for graduate and advanced undergraduate students. It will be of interest to mathematicians, physicists and engineers alike.

Springer Nature

com.springer.onix.9783319778846

Coherent structures in granular crystals.

9783319778839

Crystals-- Mechanical properties.

Granular materials-- Mechanical properties.

Granular materials-- Mechanical properties.

Materials science.

Materials-- States of matter.

Mathematical modelling.

Mathematical physics.

Maths for engineers.

TECHNOLOGY & ENGINEERING-- Engineering (General)

TECHNOLOGY & ENGINEERING-- Reference.

PHF

TEC-- 009000

TEC-- 035000

Chong, Christopher

Kevrekidis, Panayotis G.

20200823112655.0

pn

[Book]

Y