World Scientific Series on Nonlinear Science Series A

3 primary works

Thermomechanics Of Nonlinear Irreversible Behaviours, The

by Gerard A. Maugin

Published 6 October 1999

In this invaluable book, macroscopic irreversible thermodynamics is presented in its realm and its splendor by appealing to the notion of internal variables of state. This applies to both fluids and solids with or without microstructures of mechanical or electromagnetic origin. This unmatched richness of essentially nonlinear behaviors is the result of the use of modern mathematical techniques such as convex analysis in a clear-cut framework which allows one to put under the umbrella of “irreversible thermodynamics” behaviors which until now have been commonly considered either not easily covered, or even impossible to incorporate into such a framework.The book is intended for all students and researchers whose main concern is the rational modeling of complex and/or new materials with physical and engineering applications, such as those accounting for coupled-field, hysteresis, fracture, nonlinear-diffusion, and phase-transformation phenomena.

Numerical Simulation Of Waves And Fronts In Inhomogeneous Solids

by Gerard A. Maugin, Juri Engelbrecht, and Arkadi Berezovski

Published 17 June 2008

This book shows the advanced methods of numerical simulation of waves and fronts propagation in inhomogeneous solids and introduces related important ideas associated with the application of numerical methods for these problems. Great care has been taken throughout the book to seek a balance between the thermomechanical analysis and numerical techniques. It is suitable for advanced undergraduate and graduate courses in continuum mechanics and engineering. Necessary prerequisites for this text are basic continuum mechanics and thermodynamics. Some elementary knowledge of numerical methods for partial differential equations is also preferable.

Wave Momentum And Quasi-particles In Physical Acoustics

by Gerard A. Maugin and Martine Rousseau

Published 1 January 2015

This unique volume presents an original approach to physical acoustics with additional emphasis on the most useful surface acoustic waves on solids. The study is based on foundational work of Léon Brillouin, and application of the celebrated invariance theorem of Emmy Noether to an element of volume that is representative of the wave motion.This approach provides an easy interpretation of typical wave motions of physical acoustics in bulk, at surfaces, and across interfaces, in the form of the motion of associated quasi-particles. This type of motion, Newtonian or not, depends on the wave motion considered, and on the original modeling of the continuum that supports it. After a thoughtful review of Brillouin's fundamental ideas related to radiative stresses, wave momentum and action, and the necessary reminder on modern nonlinear continuum thermomechanics, invariance theory and techniques of asymptotics, a variety of situations and models illustrates the power and richness of the approach and its strong potential in applications. Elasticity, piezoelectricity and new models of continua with nonlinearity, viscosity and some generalized features (microstructure, weak or strong nonlocality) or unusual situations (bounding surface with energy, elastic thin film glued on a surface waveguide), are considered, exhibiting thus the versatility of the approach.This original book offers an innovative vision and treatment of the problems of wave propagation in deformable solids. It opens up new horizons in the theoretical and applied facets of physical acoustics.