Mechanics And Mathematics Of Crystals

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Mechanics And Mathematics Of Crystals

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Author : Jerald L. Ericksen
language : en
Publisher: World Scientific
Release Date : 2005

Mechanics And Mathematics Of Crystals written by Jerald L. Ericksen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.

This book is a unique and comprehensive collection of pioneering contributions to the mechanics of crystals by J L Ericksen, a prominent and leading contributor to the study of the mechanics and mathematics of crystalline solids over the past 35 years.It presents a splendid corpus of research papers that cover areas on crystal symmetry, constitutive equations, defects and phase transitions — all topics of current importance to a broad group of workers in the field.The volume thus provides in one place material that is frequently referenced by numerous researchers on crystals across a spectrum of activities in areas of continuum mechanics, applied mathematics, engineering and materials science.Each group of papers or chapters in the book is preceded by a summary introduction that describes how the papers on that topic fit together, and in which Ericksen sketches the context of each paper and shares with the reader his thinking and insightfulness in writing it. The volume, edited by internationally renowned scholars whose works in finite elasticity and continuum mechanics have appeared in a variety of books and prestigious journals published over the past four decades, also includes a very interesting brief autobiography by Ericksen. In it he describes his early life in Oregon, his wartime experiences, his student days and postgraduate study, his introduction to scientific work, and what motivated him in his research. An English translation and revision of the first paper in this volume, originally published in Russian, appears here for the first time.

Nonlinear Mechanics Of Crystals

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Author : John D. Clayton
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-01

Nonlinear Mechanics Of Crystals written by John D. Clayton and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-01 with Science categories.

This book describes behavior of crystalline solids primarily via methods of modern continuum mechanics. Emphasis is given to geometrically nonlinear descriptions, i.e., finite deformations. Primary topics include anisotropic crystal elasticity, plasticity, and methods for representing effects of defects in the solid on the material's mechanical response. Defects include crystal dislocations, point defects, twins, voids or pores, and micro-cracks. Thermoelastic, dielectric, and piezoelectric behaviors are addressed. Traditional and higher-order gradient theories of mechanical behavior of crystalline solids are discussed. Differential-geometric representations of kinematics of finite deformations and lattice defect distributions are presented. Multi-scale modeling concepts are described in the context of elastic and plastic material behavior. Representative substances towards which modeling techniques may be applied are single- and poly- crystalline metals and alloys, ceramics, and minerals. This book is intended for use by scientists and engineers involved in advanced constitutive modeling of nonlinear mechanical behavior of solid crystalline materials. Knowledge of fundamentals of continuum mechanics and tensor calculus is a prerequisite for accessing much of the text. This book could be used as supplemental material for graduate courses on continuum mechanics, elasticity, plasticity, micromechanics, or dislocation mechanics, for students in various disciplines of engineering, materials science, applied mathematics, and condensed matter physics.

Continuum Models For Phase Transitions And Twinning In Crystals

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Author : Mario Pitteri
language : en
Publisher: CRC Press
Release Date : 2002-06-27

Continuum Models For Phase Transitions And Twinning In Crystals written by Mario Pitteri and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-06-27 with Mathematics categories.

Continuum Models for Phase Transitions and Twinning in Crystals presents the fundamentals of a remarkably successful approach to crystal thermomechanics. Developed over the last two decades, it is based on the mathematical theory of nonlinear thermoelasticity, in which a new viewpoint on material symmetry, motivated by molecular theories, plays a c

Mechanics And Mathematics Of Crystals Selected Papers Of J L Ericksen

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Author : Jerald L Ericksen
language : en
Publisher: World Scientific
Release Date : 2005-04-13

Mechanics And Mathematics Of Crystals Selected Papers Of J L Ericksen written by Jerald L Ericksen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-04-13 with Science categories.

This book is a unique and comprehensive collection of pioneering contributions to the mechanics of crystals by J L Ericksen, a prominent and leading contributor to the study of the mechanics and mathematics of crystalline solids over the past 35 years.It presents a splendid corpus of research papers that cover areas on crystal symmetry, constitutive equations, defects and phase transitions — all topics of current importance to a broad group of workers in the field.The volume thus provides in one place material that is frequently referenced by numerous researchers on crystals across a spectrum of activities in areas of continuum mechanics, applied mathematics, engineering and materials science.Each group of papers or chapters in the book is preceded by a summary introduction that describes how the papers on that topic fit together, and in which Ericksen sketches the context of each paper and shares with the reader his thinking and insightfulness in writing it. The volume, edited by internationally renowned scholars whose works in finite elasticity and continuum mechanics have appeared in a variety of books and prestigious journals published over the past four decades, also includes a very interesting brief autobiography by Ericksen. In it he describes his early life in Oregon, his wartime experiences, his student days and postgraduate study, his introduction to scientific work, and what motivated him in his research. An English translation and revision of the first paper in this volume, originally published in Russian, appears here for the first time.

Finite Plastic Deformation Of Crystalline Solids

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Author : K. S. Havner
language : en
Publisher: Cambridge University Press
Release Date : 1992-03-27

Finite Plastic Deformation Of Crystalline Solids written by K. S. Havner and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-03-27 with Mathematics categories.

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Mathematical Modeling In Optical Science

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Author : Gang Bao
language : en
Publisher: SIAM
Release Date : 2001-01-01

Mathematical Modeling In Optical Science written by Gang Bao and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Science categories.

This volume addresses recent developments in mathematical modeling in three areas of optical science: diffractive optics, photonic band gap structures, and waveguides. Particular emphasis is on the formulation of mathematical models and the design and analysis of new computational approaches. The book contains cutting-edge discourses on emerging technology in optics that provides significant challenges and opportunities for applied mathematicians, researchers, and engineers.

Mathematical Techniques In Crystallography And Materials Science

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Author : Edward Prince
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-03-23

Mathematical Techniques In Crystallography And Materials Science written by Edward Prince and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-23 with Mathematics categories.

""Mathematical techniques in Crystallography and Materials Science" brings together common and less familiar mathematical procedures used in studies of the structures and physical properties of solids. This practical guide and reference serves as a unified source book for students and professionals, and it provides a solid basis for further studies in more specialized literature.

Physical Properties Of Crystals

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Author : J. F. Nye
language : en
Publisher: Oxford University Press
Release Date : 1985

Physical Properties Of Crystals written by J. F. Nye and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.

First published in 1957, this classic study has been reissued in a paperback version that includes an additional chapter bringing the material up to date. The author formulates the physical properties of crystals systematically in tensor notation, presenting tensor properties in terms of their common mathematical basis and the thermodynamic relations between them. The mathematical groundwork is laid in a discussion of tensors of the first and second ranks. Tensors of higher ranks and matrix methods are then introduced as natural developments of the theory. A similar pattern is followed in discussing thermodynamic and optical aspects.

Geometric Methods In The Elastic Theory Of Membranes In Liquid Crystal Phases

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Author : Zhong-Can Ou-Yang
language : en
Publisher: World Scientific
Release Date : 1999

Geometric Methods In The Elastic Theory Of Membranes In Liquid Crystal Phases written by Zhong-Can Ou-Yang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Science categories.

This book contains a comprehensive description of the mechanical equilibrium and deformation of membranes as a surface problem in differential geometry. Following the pioneering work by W Helfrich, the fluid membrane is seen as a nematic or smectic ? A liquid crystal film and its elastic energy form is deduced exactly from the curvature elastic theory of the liquid crystals. With surface variation the minimization of the energy at fixed osmotical pressure and surface tension gives a completely new surface equation in geometry that involves potential interest in mathematics. The investigations of the rigorous solution of the equation that have been carried out in recent years by the authors and their co-workers are presented here, among which the torus and the discocyte (the normal shape of the human red blood cell) may attract attention in cell biology. Within the framework of our mathematical model by analogy with cholesteric liquid crystals, an extensive investigation is made of the formation of the helical structures in a tilted chiral lipid bilayer, which has now become a hot topic in the fields of soft matter and biomembranes.