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Crystals and polycrystals, composites and polymers, grids and multibar systems can be considered as examples of media with microstructure. A characteristic feature of all such models is the existence of scale parameters which are con nected with microgeometry or long-range interacting forces. As a result the cor responding theory must essentially be a nonlocal one. This treatment provides a systematic investigation of the effects of micro structure, inner degrees of freedom and non locality in elastic media. The prop agation of linear and nonlinear waves in dispersive media, static, deterministic and stochastic problems, and the theory of local defects and dislocations are considered in detail. Especial attention is paid to approximate models and lim iting transitions to classical elasticity. The book forms the second part of a revised and updated edition of the author's monograph published under the same title in Russian in 1975. The first part (Vol. 26 of Springer Series in Solid-State Sciences) presents a self contained theory of one-dimensional models. The theory of three-dimensional models is considered in this volume. I would like to thank E. Kroner and A. Seeger for supporting the idea of an English edition of my original Russian book. I am also grateful to E. Borie, H. Lotsch and H. Zorski who read the manuscript and offered many sugges tions. Houston, Texas Isaak A. Kunin January, 1983 Contents 1. Introduction ...
Crystals and polycrystals,composites and polymers, grids and multibar systems can be considered as examples of media with microstructure. A characteristic feature of all such models is the existence of scale parameters which are connected with micro geometry or long-range interacting forces. As a result the corresponding theory must essentially be a nonlocal one. The book is devoted to a systematic investigation of effects of microstructure, inner degrees of freedom and nonlocality in elastic media. The propagation of linear and nonlinear waves in dispersive media, static problems, and the theory of defects are considered in detail. Much attention is paid to approximate models and limiting tran sitions to classical elasticity. The book can be considered as a revised and updated edition of the author's book under the same title published in Russian in 1975. The frrst volume presents a self-con tained theory of one-dimensional models. The theory of three-dimensional models will be considered in a forthcoming volume. The author would like to thank H. Lotsch and H. Zorsky who read the manuscript and offered many suggestions.
Reflecting new developments in the study of Saint-Venant's problem, Classical and Generalized Models of Elastic Rods focuses on the deformation of elastic cylinders for three models of continuum: classical elastic continuum, Cosserat elastic body, and porous elastic material. The author presents a method to construct Saint-Venant's solutions, minim
Problems concerning non-classical elastic solids continue to attract the attention of mathematicians, scientists and engineers. Research in this area addresses problems concerning many substances, such as crystals, polymers, composites, ceramics and blood. This comprehensive, accessible work brings together recent research in this field, and will be of great interest to mathematicians, physicists and other specialists working in this area.
Statistical Physics II introduces nonequilibrium theories of statistical mechanics from the viewpoint of the fluctuation-disipation theorem. Emphasis is placed on the relaxation from nonequilibrium to equilibrium states, the response of a system to an external disturbance, and general problems involved in deriving a macroscopic physical process from more basic underlying processes. Fundamental concepts and methods are stressed, rather than the numerous individual applications.
Strutural Analysis of Point Defects in Solids introduces the principles and techniques of modern electron paramagnetic resonance (EPR) spectroscopy essentialfor applications to the determination of microscopic defect structures. Investigations of the microscopic and electronic structure, and also correlations with the magnetic propertiesof solids, require various multiple magnetic resonance methods, such as ENDOR and optically detected EPR or ENDOR. This book discusses experimental, technological and theoretical aspects of these techniques comprehensively, from a practical viewpoint, with many illustrative examples taken from semiconductors and other solids. The nonspecialist is informed about the potential of the different methods, while the researcher faced with the task of determining defect structures isprovided with the necessary tools, together with much information on computer-aided methods of data analysis and the principles of modern spectrometer design.
The history of applications of space group theory to solid state physics goes back more than five decades. The periodicity of the lattice and the definition of a k-space were the corner-stones of this application. Prof. Volker Heine in Vol. 35 of Solid State Physics (1980) noted that, even in perfect crystals, where k-space methods are appropriate, the local properties (such as the charge densi ty, bond order, etc.) are defined by the local environment of one atom. Natural ly, "k-space methods" are not appropriate for crystals with point defects, sur faces and interfaces, or for amorphous materials. In such cases the real-space approach favored by chemists to describe molecules has turned out to be very useful. To span the gulf between the k-space and real space methods it is helpful to recall that atoms in crystalline solids possess a site symmetry defined by the symmetry of the local environment of the atom occupying the site. The site symmetry concept is familiar to crystallographers and commonly used by them in the description of crystalline structures. However, in the application of group theory to solid state physics problems, the site symmetry approach has been used only for the last ten to fifteen years. In our book Methods oj Group Theory in the Quantum Chemistry oj Solids published in Russian in 1987 by Leningrad University Press we gave the first results of this application to the theory of electronic structure of crystals.