Mathematical Theory Of Elasticity Of Quasicrystals And Its Applications
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Mathematical Theory Of Elasticity Of Quasicrystals And Its Applications
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Author : Tianyou Fan
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-25
Mathematical Theory Of Elasticity Of Quasicrystals And Its Applications written by Tianyou Fan 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 2011-05-25 with Science categories.
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.
Mathematical Theory Of Elasticity And Generalized Dynamics Of Quasicrystals And Its Applications
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Author : Tian-you Fan
language : en
Publisher: World Scientific
Release Date : 2023-12-27
Mathematical Theory Of Elasticity And Generalized Dynamics Of Quasicrystals And Its Applications written by Tian-you Fan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-27 with Science categories.
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.
Mathematical Theory Of Elasticity Of Quasicrystals And Its Applications
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Author : Tian-You Fan
language : en
Publisher: Springer
Release Date : 2016-09-20
Mathematical Theory Of Elasticity Of Quasicrystals And Its Applications written by Tian-You Fan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-20 with Science categories.
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.
Mathematical Theory Of Elasticity And Generalized Dynamics Of Quasicrystals And Its Applications
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Author : Tian-You Fan
language : en
Publisher: World Scientific Publishing Company
Release Date : 2023-12-29
Mathematical Theory Of Elasticity And Generalized Dynamics Of Quasicrystals And Its Applications written by Tian-You Fan and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-29 with Science categories.
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.
Generalized Dynamics Of Soft Matter Quasicrystals
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Author : Tian-You Fan
language : en
Publisher: Springer
Release Date : 2017-10-14
Generalized Dynamics Of Soft Matter Quasicrystals written by Tian-You Fan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-14 with Science categories.
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.
Generalized Dynamics Of Soft Matter Quasicrystals
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Author : Tian-You Fan
language : en
Publisher: Springer Nature
Release Date : 2022-01-17
Generalized Dynamics Of Soft Matter Quasicrystals written by Tian-You Fan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-17 with Science categories.
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.
The Mathematical Theory Of Elasticity
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Author : Richard B. Hetnarski
language : en
Publisher: CRC Press
Release Date : 2016-04-19
The Mathematical Theory Of Elasticity written by Richard B. Hetnarski and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.
Through its inclusion of specific applications, The Mathematical Theory of Elasticity, Second Edition continues to provide a bridge between the theory and applications of elasticity. It presents classical as well as more recent results, including those obtained by the authors and their colleagues. Revised and improved, this edition incorporates add
Mathematical Theory Of Elasticity
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Author : Richa Hetnarski
language : en
Publisher: CRC Press
Release Date : 2003-12-16
Mathematical Theory Of Elasticity written by Richa Hetnarski and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-16 with Mathematics categories.
The purpose of this book is to present Mathematical Theory of Elasticity and its applications to a wide range of readers, including graduate students and researchers in modern theory of continuum mechanics. The book provides classical results on elasticity as well as the new findings of classical type obtained in recent years by various researchers
Applied Mechanics Reviews
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Author :
language : en
Publisher:
Release Date : 2004
Applied Mechanics Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mechanical engineering categories.
Integral Equations Boundary Value Problems And Related Problems
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Author : Xing Li
language : en
Publisher: World Scientific
Release Date : 2013
Integral Equations Boundary Value Problems And Related Problems written by Xing Li and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
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.