Mathematical Theory Of Elasticity Of Quasicrystals And Its Applications

Author : Tianyou Fan
Publisher : Springer Science & Business Media
Page : 350 pages
File Size : 54,8 Mb
Release : 2011-05-25
Category : Science
ISBN : 9783642146435

Get Book

Mathematical Theory of Elasticity of Quasicrystals and Its Applications by Tianyou Fan Pdf

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.

Author : Tian-you Fan
Publisher : World Scientific
Page : 636 pages
File Size : 53,8 Mb
Release : 2023-12-27
Category : Science
ISBN : 9789811279119

Get Book

Mathematical Theory Of Elasticity And Generalized Dynamics Of Quasicrystals And Its Applications by Tian-you Fan Pdf

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.

Author : Tian-You Fan
Publisher : Springer
Page : 452 pages
File Size : 47,8 Mb
Release : 2016-09-20
Category : Science
ISBN : 9789811019845

Get Book

Mathematical Theory of Elasticity of Quasicrystals and Its Applications by Tian-You Fan Pdf

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.

Author : Tian-You Fan
Publisher : World Scientific Publishing Company
Page : 0 pages
File Size : 52,9 Mb
Release : 2023-12-29
Category : Science
ISBN : 9811279098

Get Book

Mathematical Theory of Elasticity and Generalized Dynamics of Quasicrystals and Its Applications by Tian-You Fan Pdf

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.

Author : Tian-You Fan
Publisher : Springer
Page : 184 pages
File Size : 54,5 Mb
Release : 2017-10-14
Category : Science
ISBN : 9789811049507

Get Book

Generalized Dynamics of Soft-Matter Quasicrystals by Tian-You Fan Pdf

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.

Author : Tian-You Fan,Wenge Yang,Hui Cheng,Xiao-Hong Sun
Publisher : Springer Nature
Page : 246 pages
File Size : 50,8 Mb
Release : 2022-01-17
Category : Science
ISBN : 9789811666285

Get Book

Generalized Dynamics of Soft-Matter Quasicrystals by Tian-You Fan,Wenge Yang,Hui Cheng,Xiao-Hong Sun Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 604 pages
File Size : 51,9 Mb
Release : 2004
Category : Mechanical engineering
ISBN : OSU:32435075915058

Get Book

Applied Mechanics Reviews by Anonim Pdf

Author : Richard B. Hetnarski,Jozef Ignaczak
Publisher : CRC Press
Page : 837 pages
File Size : 50,8 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781439828892

Get Book

The Mathematical Theory of Elasticity by Richard B. Hetnarski,Jozef Ignaczak Pdf

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

Author : Xing Li
Publisher : World Scientific
Page : 298 pages
File Size : 48,9 Mb
Release : 2013
Category : Mathematics
ISBN : 9789814452885

Get Book

Integral Equations, Boundary Value Problems and Related Problems by Xing Li Pdf

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.

Author : Gérard A. Maugin
Publisher : Springer
Page : 259 pages
File Size : 48,8 Mb
Release : 2016-09-24
Category : Science
ISBN : 9789811024344

Get Book

Non-Classical Continuum Mechanics by Gérard A. Maugin Pdf

This dictionary offers clear and reliable explanations of over 100 keywords covering the entire field of non-classical continuum mechanics and generalized mechanics, including the theory of elasticity, heat conduction, thermodynamic and electromagnetic continua, as well as applied mathematics. Every entry includes the historical background and the underlying theory, basic equations and typical applications. The reference list for each entry provides a link to the original articles and the most important in-depth theoretical works. Last but not least, ever y entry is followed by a cross-reference to other related subject entries in the dictionary.

Author : Harry Schulz,André Simoes,Raquel Lobosco
Publisher : BoD – Books on Demand
Page : 462 pages
File Size : 49,6 Mb
Release : 2011-12-22
Category : Science
ISBN : 9789533075969

Get Book

Hydrodynamics by Harry Schulz,André Simoes,Raquel Lobosco Pdf

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.

Author : Richa Hetnarski,Jozef Ignaczak
Publisher : CRC Press
Page : 868 pages
File Size : 49,5 Mb
Release : 2003-12-16
Category : Mathematics
ISBN : 0203502485

Get Book

Mathematical Theory of Elasticity by Richa Hetnarski,Jozef Ignaczak Pdf

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

Author : J. N. Reddy,Chien Ming Wang,Van Hai Luong,Anh Tuan Le
Publisher : Springer Nature
Page : 1973 pages
File Size : 53,9 Mb
Release : 2024-01-12
Category : Architecture
ISBN : 9789819974344

Get Book

Proceedings of the Third International Conference on Sustainable Civil Engineering and Architecture by J. N. Reddy,Chien Ming Wang,Van Hai Luong,Anh Tuan Le Pdf

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.

Author : Marko V. Jaric
Publisher : Elsevier
Page : 238 pages
File Size : 45,5 Mb
Release : 2012-12-02
Category : Science
ISBN : 9780323159470

Get Book

Introduction to the Mathematics of Quasicrystals by Marko V. Jaric Pdf

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.

Author : Taylor & Francis Group
Publisher : Unknown
Page : 128 pages
File Size : 48,8 Mb
Release : 2018-09-18
Category : Electronic
ISBN : 1138374350

Get Book

The Mathematical Theory of Elasticity Second Edition by Taylor & Francis Group Pdf