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Mathematical Theory Of Elasticity Of Quasicrystals And Its Applications
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Book Synopsis Mathematical Theory of Elasticity of Quasicrystals and Its Applications by : Tianyou Fan
Download or read book Mathematical Theory of Elasticity of Quasicrystals and Its Applications written by Tianyou Fan and published by Springer Science & Business Media. This book was released on 2011-05-25 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This inter-disciplinary work covering the continuum mechanics of novel materials, condensed matter physics and partial differential equations discusses the mathematical theory of elasticity of quasicrystals (a new condensed matter) and its applications by setting up new partial differential equations of higher order and their solutions under complicated boundary value and initial value conditions. The new theories developed here dramatically simplify the solving of complicated elasticity equation systems. Large numbers of complicated equations involving elasticity are reduced to a single or a few partial differential equations of higher order. Systematical and direct methods of mathematical physics and complex variable functions are developed to solve the equations under appropriate boundary value and initial value conditions, and many exact analytical solutions are constructed. The dynamic and non-linear analysis of deformation and fracture of quasicrystals in this volume presents an innovative approach. It gives a clear-cut, strict and systematic mathematical overview of the field. Comprehensive and detailed mathematical derivations guide readers through the work. By combining mathematical calculations and experimental data, theoretical analysis and practical applications, and analytical and numerical studies, readers will gain systematic, comprehensive and in-depth knowledge on continuum mechanics, condensed matter physics and applied mathematics.
Book Synopsis Mathematical Theory of Elasticity of Quasicrystals and Its Applications by : Tian-You Fan
Download or read book Mathematical Theory of Elasticity of Quasicrystals and Its Applications written by Tian-You Fan and published by Springer. This book was released on 2016-09-20 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Theory Of Elasticity And Generalized Dynamics Of Quasicrystals And Its Applications by : Tian-you Fan
Download or read book Mathematical Theory Of Elasticity And Generalized Dynamics Of Quasicrystals And Its Applications written by Tian-you Fan and published by World Scientific. This book was released on 2023-12-27 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a detailed description on mathematical theory of elasticity and generalized dynamics of solid quasicrystals and its applications.The Chinese edition of the book Mathematical Theory of Elasticity of Quasicrystals and Its Applications was published by the Beijing Institute of Technology Press in 1999, written by Prof Tian-You Fan. In this English edition of the book, the phonon-phason dynamics, defect dynamics and hydrodynamics of solid quasicrystals are included, so the scope of the book is beyond elasticity. Hence, the title in this edition is changed to Mathematical Theory of Elasticity and Generalized Dynamics of Quasicrystals and Its Applications. This book is the first and only monograph in the scope of quasicrystals since first published in 1999 in China and worldwide. In this edition, the two-dimensional quasicrystals of second kind, soft-matter quasicrystals and photonic bade-gap and application of photonic quasicrystals are added.This book combines the mechanical and physical behavior of quasicrystals and mathematical physics, which may help graduate students and researchers in the fields of new materials, condensed matter physics, applied mathematics and engineering science.
Book Synopsis Mathematical Theory of Elasticity and Generalized Dynamics of Quasicrystals and Its Applications by : Tian-You Fan
Download or read book Mathematical Theory of Elasticity and Generalized Dynamics of Quasicrystals and Its Applications written by Tian-You Fan and published by World Scientific Publishing Company. This book was released on 2023-12-29 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a detailed description on mathematical theory of elasticity and generalized dynamics of solid quasicrystals and its applications.The Chinese edition of the book Mathematical Theory of Elasticity of Quasicrystals and Its Applications was published by the Beijing Institute of Technology Press in 1999, written by Prof Tian-You Fan. In this English edition of the book, the phonon-phason dynamics, defect dynamics and hydrodynamics of solid quasicrystals are included, so the scope of the book is beyond elasticity. Hence, the title in this edition is changed to Mathematical Theory of Elasticity and Generalized Dynamics of Quasicrystals and Its Applications. This book is the first and only monograph in the scope of quasicrystals since first published in 1999 in China and worldwide. In this edition, the two-dimensional quasicrystals of second kind, soft-matter quasicrystals and photonic bade-gap and application of photonic quasicrystals are added.This book combines the mechanical and physical behavior of quasicrystals and mathematical physics, which may help graduate students and researchers in the fields of new materials, condensed matter physics, applied mathematics and engineering science.
Book Synopsis Generalized Dynamics of Soft-Matter Quasicrystals by : Tian-You Fan
Download or read book Generalized Dynamics of Soft-Matter Quasicrystals written by Tian-You Fan and published by Springer. This book was released on 2017-10-14 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book systematically introduces the mathematical models and solutions of generalized hydrodynamics of soft-matter quasicrystals (SMQ). It provides methods for solving the initial-boundary value problems in these systems. The solutions obtained demonstrate the distribution, deformation and motion of the soft-matter quasicrystals, and determine the stress, velocity and displacement fields. The interactions between phonons, phasons and fluid phonons are discussed in some fundamental materials samples. Mathematical solutions for solid and soft-matter quasicrystals are compared, to help readers to better understand the featured properties of SMQ.
Book Synopsis Generalized Dynamics of Soft-Matter Quasicrystals by : Tian-You Fan
Download or read book Generalized Dynamics of Soft-Matter Quasicrystals written by Tian-You Fan and published by Springer Nature. This book was released on 2022-01-17 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights the mathematical models and solutions of the generalized dynamics of soft-matter quasicrystals (SMQ) and introduces possible applications of the theory and methods. Based on the theory of quasiperiodic symmetry and symmetry breaking, the book treats the dynamics of individual quasicrystal systems by reducing them to nonlinear partial differential equations and then provides methods for solving the initial-boundary value problems in these equations. The solutions obtained demonstrate the distribution, deformation and motion of SMQ and determine the stress, velocity and displacement fields. The interactions between phonons, phasons and fluid phonons are discussed in some fundamental materials samples. The reader benefits from a detailed comparison of the mathematical solutions for both solid and soft-matter quasicrystals, gaining a deeper understanding of the universal properties of SMQ. The second edition covers the latest research progress on quasicrystals in topics such as thermodynamic stability, three-dimensional problems and solutions, rupture theory, and the photonic band-gap and its applications. These novel chapters make the book an even more useful and comprehensive reference guide for researchers in condensed matter physics, chemistry and materials sciences.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 2004 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Integral Equations, Boundary Value Problems and Related Problems by : Xing Li
Download or read book Integral Equations, Boundary Value Problems and Related Problems written by Xing Li and published by World Scientific. This book was released on 2013 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, we report new results about various theories and methods of integral equation, boundary value problems for partial differential equations and functional equations, and integral operators including singular integral equations, applications of boundary value problems and integral equations to mechanics and physics, numerical methods of integral equations and boundary value problems, theories and methods for inverse problems of mathematical physics, Clifford analysis and related problems.
Download or read book Hydrodynamics written by Harry Schulz and published by BoD – Books on Demand. This book was released on 2011-12-22 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: The phenomena related to the flow of fluids are generally complex, and difficult to quantify. New approaches - considering points of view still not explored - may introduce useful tools in the study of Hydrodynamics and the related transport phenomena. The details of the flows and the properties of the fluids must be considered on a very small scale perspective. Consequently, new concepts and tools are generated to better describe the fluids and their properties. This volume presents conclusions about advanced topics of calculated and observed flows. It contains eighteen chapters, organized in five sections: 1) Mathematical Models in Fluid Mechanics, 2) Biological Applications and Biohydrodynamics, 3) Detailed Experimental Analyses of Fluids and Flows, 4) Radiation-, Electro-, Magnetohydrodynamics, and Magnetorheology, 5) Special Topics on Simulations and Experimental Data. These chapters present new points of view about methods and tools used in Hydrodynamics.
Book Synopsis Proceedings of the Third International Conference on Sustainable Civil Engineering and Architecture by : J. N. Reddy
Download or read book Proceedings of the Third International Conference on Sustainable Civil Engineering and Architecture written by J. N. Reddy and published by Springer Nature. This book was released on 2024-01-12 with total page 1973 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes articles from the Third International Conference on Sustainable Civil Engineering and Architecture (ICSSEA 2023), held at Da Nang City, Vietnam, on July 19-21, 2023. The conference brings together international experts from both academia and industry to share their knowledge and expertise, facilitate collaboration, and improve cooperation in the field. The book focuses on the most recent developments in sustainable architecture and civil engineering, including offshore structures, structural engineering, building materials, and architecture.
Download or read book Mathematical Elasticity written by and published by Elsevier. This book was released on 1997-07-22 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of Volume II is to show how asymptotic methods, with the thickness as the small parameter, indeed provide a powerful means of justifying two-dimensional plate theories. More specifically, without any recourse to any a priori assumptions of a geometrical or mechanical nature, it is shown that in the linear case, the three-dimensional displacements, once properly scaled, converge in H1 towards a limit that satisfies the well-known two-dimensional equations of the linear Kirchhoff-Love theory; the convergence of stress is also established. In the nonlinear case, again after ad hoc scalings have been performed, it is shown that the leading term of a formal asymptotic expansion of the three-dimensional solution satisfies well-known two-dimensional equations, such as those of the nonlinear Kirchhoff-Love theory, or the von Kármán equations. Special attention is also given to the first convergence result obtained in this case, which leads to two-dimensional large deformation, frame-indifferent, nonlinear membrane theories. It is also demonstrated that asymptotic methods can likewise be used for justifying other lower-dimensional equations of elastic shallow shells, and the coupled pluri-dimensional equations of elastic multi-structures, i.e., structures with junctions. In each case, the existence, uniqueness or multiplicity, and regularity of solutions to the limit equations obtained in this fashion are also studied.
Book Synopsis A Treatise on the Mathematical Theory of Elasticity by :
Download or read book A Treatise on the Mathematical Theory of Elasticity written by and published by CUP Archive. This book was released on with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to the Mathematics of Quasicrystals by : Marko V. Jaric
Download or read book Introduction to the Mathematics of Quasicrystals written by Marko V. Jaric and published by Elsevier. This book was released on 2012-12-02 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to the Mathematics of Quasicrystals provides a pedagogical introduction to mathematical concepts and results necessary for a quantitative description or analysis of quasicrystals. This book is organized into five chapters that cover the three mathematical areas most relevant to quasicrystals, namely, the theory of almost periodic functions, the theory of aperiodic tilings, and group theory. Chapter 1 describes the aspects of the theory of tiling in two- and three-dimensional space that are important for understanding some of the ways in which “classical mathematical crystallography is being generalized; this process is to include possible models for aperiodic crystals. Chapter 2 examines the non-local nature of assembly “mistakes that might have significance to the quasicrystals growth. This chapter also describes how closely a physical quasicrystal might be able to approximate a three-dimensional version of tilings. Chapter 3 discusses the theoretical background and concepts of group theory of icosahedral quasicrystals. Chapter 4 presents the local properties of the three-dimensional Penrose tilings and their global construction is described through the projection method. This chapter emphasizes the relationship between quasiperiodic sets of points and quasiperiodic tiling. Chapter 5 explores the analysis of defects in quasicrystals and their kinetics, as well as some properties of the perfect system. This book is of great value to physicists, crystallographers, metallurgists, and beginners in the field of quasicrystals.
Book Synopsis Advanced Technology for Manufacturing Systems and Industry by : Wei Deng
Download or read book Advanced Technology for Manufacturing Systems and Industry written by Wei Deng and published by Trans Tech Publications Ltd. This book was released on 2012-11-29 with total page 1480 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 3rd International Conference on Information Technology for Manufacturing Systems (ITMS 2012) was held on the 8 and 9th September 2012 in Qingdao, China. It was intended to bring together researchers and engineers/technologists working on various aspects of materials, mechanical, electronic, computer, information and other topics.
Book Synopsis Directions in Mathematical Quasicrystals by : Michael Baake
Download or read book Directions in Mathematical Quasicrystals written by Michael Baake and published by American Mathematical Soc.. This book was released on 2000 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume includes twelve solicited articles which survey the current state of knowledge and some of the open questions on the mathematics of aperiodic order. A number of the articles deal with the sophisticated mathematical ideas that are being developed from physical motivations. Many prominent mathematical aspects of the subject are presented, including the geometry of aperiodic point sets and their diffractive properties, self-affine tilings, the role of $C*$-algebras in tiling theory, and the interconnections between symmetry and aperiodic point sets. Also discussed are the question of pure point diffraction of general model sets, the arithmetic of shelling icosahedral quasicrystals, and the study of self-similar measures on model sets. From the physical perspective, articles reflect approaches to the mathematics of quasicrystal growth and the Wulff shape, recent results on the spectral nature of aperiodic Schrödinger operators with implications to transport theory, the characterization of spectra through gap-labelling, and the mathematics of planar dimer models. A selective bibliography with comments is also provided to assist the reader in getting an overview of the field. The book will serve as a comprehensive guide and an inspiration to those interested in learning more about this intriguing subject.
Book Synopsis The Physics of Quasicrystals by : P J Steinhardt
Download or read book The Physics of Quasicrystals written by P J Steinhardt and published by World Scientific Publishing Company. This book was released on 1987-12-31 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises an introductory lecture outlining the basic concepts and challenges in the field. This is followed by a collection of reprinted articles which are important in understanding the subject. The book will focus mainly on mathematical and physical foundations of the subject rather than experimental progress. By concentrating on theoretical topics, this volume has long-lasting as well as immediate value to physicists, crystallographers, metallurgists and mathematicians. Request Inspection Copy
Book Synopsis Quasicrystals: The State Of The Art by : David Divincenzo
Download or read book Quasicrystals: The State Of The Art written by David Divincenzo and published by World Scientific. This book was released on 1991-10-22 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This review volume provides the most up-to-date and authoritative description of research on icosahedral solids, which has advanced rapidly since the discovery of these unique materials in 1984. The present book, intended as a companion volume to the reprint volume on The Physics of Quasicrystals edited by P Steinhardt and S Ostlund, will be invaluable to graduate students and workers in the field as a comprehensive reference. Scientists in related fields can use it as a readable introduction to the important current problems in quasicrystals. The chapters have been written by many of the most prominent theorists and experimentalists on quasicrystals, both physicists and materials scientists, from around the world. Especially exciting are the details of the recent discovery of “perfect quasi-crystals”, new materials which promise to be an ideal form of quasiperiodic matter with little or no disorder. Other topics include: electron, X-ray and neutron quasi-crystallography, scanning tunneling microscopy studies, electronic transport experiments, quasicrystal faceting and statistical mechanics, growth rules and matching rules for quasicrystals, group theory and elasticity theory.
