An Introduction to the Mathematical Theory of Dynamic Materials
Title | An Introduction to the Mathematical Theory of Dynamic Materials PDF eBook |
Author | Konstantin A. Lurie |
Publisher | Springer |
Pages | 287 |
Release | 2017-10-17 |
Genre | Mathematics |
ISBN | 3319653466 |
This fascinating book is a treatise on real space-age materials. It is a mathematical treatment of a novel concept in material science that characterizes the properties of dynamic materials—that is, material substances whose properties are variable in space and time. Unlike conventional composites that are often found in nature, dynamic materials are mostly the products of modern technology developed to maintain the most effective control over dynamic processes.
An Introduction to the Mathematical Theory of Dynamic Materials
Title | An Introduction to the Mathematical Theory of Dynamic Materials PDF eBook |
Author | Konstantin A. Lurie |
Publisher | Springer |
Pages | 0 |
Release | 2010-11-24 |
Genre | Mathematics |
ISBN | 9781441942593 |
This fascinating book is a treatise on real space-age materials. It is a mathematical treatment of a novel concept in material science that characterizes the properties of dynamic materials—that is, material substances whose properties are variable in space and time. Unlike conventional composites that are often found in nature, dynamic materials are mostly the products of modern technology developed to maintain the most effective control over dynamic processes.
An Introduction to the Mathematical Theory of Dynamic Materials
Title | An Introduction to the Mathematical Theory of Dynamic Materials PDF eBook |
Author | Konstantin A. Lurie |
Publisher | Springer Science & Business Media |
Pages | 188 |
Release | 2007-05-15 |
Genre | Mathematics |
ISBN | 0387382801 |
This fascinating book is a treatise on real space-age materials. It is a mathematical treatment of a novel concept in material science that characterizes the properties of dynamic materials—that is, material substances whose properties are variable in space and time. Unlike conventional composites that are often found in nature, dynamic materials are mostly the products of modern technology developed to maintain the most effective control over dynamic processes.
An Introduction to the Mathematical Theory of Vibrations of Elastic Plates
Title | An Introduction to the Mathematical Theory of Vibrations of Elastic Plates PDF eBook |
Author | Raymond David Mindlin |
Publisher | World Scientific |
Pages | 211 |
Release | 2006 |
Genre | Technology & Engineering |
ISBN | 9812772499 |
This book by the late R D Mindlin is destined to become a classic introduction to the mathematical aspects of two-dimensional theories of elastic plates. It systematically derives the two-dimensional theories of anisotropic elastic plates from the variational formulation of the three-dimensional theory of elasticity by power series expansions. The uniqueness of two-dimensional problems is also examined from the variational viewpoint. The accuracy of the two-dimensional equations is judged by comparing the dispersion relations of the waves that the two-dimensional theories can describe with prediction from the three-dimensional theory. Discussing mainly high-frequency dynamic problems, it is also useful in traditional applications in structural engineering as well as provides the theoretical foundation for acoustic wave devices. Sample Chapter(s). Chapter 1: Elements of the Linear Theory of Elasticity (416 KB). Contents: Elements of the Linear Theory of Elasticity; Solutions of the Three-Dimensional Equations; Infinite Power Series of Two-Dimensional Equations; Zero-Order Approximation; First-Order Approximation; Intermediate Approximations. Readership: Researchers in mechanics, civil and mechanical engineering and applied mathematics.
Mathematical Theory of Elasticity of Quasicrystals and Its Applications
Title | Mathematical Theory of Elasticity of Quasicrystals and Its Applications PDF eBook |
Author | Tian-You Fan |
Publisher | Springer |
Pages | 462 |
Release | 2016-09-20 |
Genre | Science |
ISBN | 9811019843 |
This interdisciplinary work on condensed matter physics, the continuum mechanics of novel materials, and partial differential equations, discusses the mathematical theory of elasticity and hydrodynamics of quasicrystals, as well as its applications. By establishing new partial differential equations of higher order and their solutions under complicated boundary value and initial value conditions, the theories developed here dramatically simplify the solution of complex elasticity problems. Comprehensive and detailed mathematical derivations guide readers through the work. By combining theoretical analysis and experimental data, mathematical studies and practical applications, readers will gain a systematic, comprehensive and in-depth understanding of condensed matter physics, new continuum mechanics and applied mathematics. This new edition covers the latest developments in quasicrystal studies. In particular, it pays special attention to the hydrodynamics, soft-matter quasicrystals, and the Poisson bracket method and its application in deriving hydrodynamic equations. These new sections make the book an even more useful and comprehensive reference guide for researchers working in Condensed Matter Physics, Chemistry and Materials Science.
Introduction to the Modern Theory of Dynamical Systems
Title | Introduction to the Modern Theory of Dynamical Systems PDF eBook |
Author | Anatole Katok |
Publisher | Cambridge University Press |
Pages | 828 |
Release | 1995 |
Genre | Mathematics |
ISBN | 9780521575577 |
This book provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up.
The Static and Dynamic Continuum Theory of Liquid Crystals
Title | The Static and Dynamic Continuum Theory of Liquid Crystals PDF eBook |
Author | Iain W. Stewart |
Publisher | CRC Press |
Pages | 351 |
Release | 2004-06-29 |
Genre | Science |
ISBN | 0203646339 |
Given the widespread interest in macroscopic phenomena in liquid crystals, stemming from their applications in displays and devices. The need has arisen for a rigorous yet accessible text suitable for graduate students, whatever their scientific background. This book satisfies that need. The approach taken in this text, is to introduce the basic continuum theory for nematic liquid crystals in equilibria, then it proceeds to simple application of this theory- in particular, there is a discussion of electrical and magnetic field effects which give rise to Freedericksz transitions, which are important in devices. This is followed by an account of dynamic theory and elementary viscometry of nemantics Discussions of backflow and flow-induced instabilities are also included. Smetic theory is also briefly introduced and summarised with some examples of equilibrium solutions as well as those with dynamic effects. A number of mathematical techniques, such as Cartesian tensors and some variational calculus, are presented in the appendices.