This new volume introduces readers to the current topics of industrial and applied mathematics in China, with applications to material science, information science, mathematical finance and engineering. The authors utilize mathematics for the solution of problems. The purposes of the volume are to promote research in applied mathematics and computational science; further the application of mathematics to new methods and techniques useful in industry and science; and provide for the exchange of information between the mathematical, industrial, and scientific communities.
This collection of articles covers the hottest topics in contemporary applied mathematics. Multiscale modeling, material computing, symplectic methods, parallel computing, mathematical biology, applied differential equations and engineering computing problems are all included. The book contains the latest results of many leading scientists and provides a window on new trends in research in the field. Sample Chapter(s). Chapter 1: An Iterative BEM for the Inverse Problem of Detecting Corrosion in a Pipe (467 KB). Contents: An Iterative BEM for the Inverse Problem of Detecting Corrosion in a Pipe (J Cheng et al.); Optimal Order Integration on the Sphere (K Hesse & I H Sloan); Inverse Problems in Bioluminescence Tomography (M Jiang et al.); Global Dynamic Properties of Protein Networks (F-T Li et al.); Distance Geometry Problem and Algorithm Based on Barycentric Coordinates (H-X Huang & C-J Wang); On Ill-Posedness and Inversion Scheme for 2-D Backward Heat Conduction (J-J Liu); Error Analysis on Scrambled Quasi-Monte Carlo Quadrature Rules Using Sobol Points (R-X Yue); and other papers. Readership: Graduate students and researchers in applied mathematics.
This invaluable volume is a collection of articles in memory ofJacques-Louis Lions, a leading mathematician and the founder of theContemporary French Applied Mathematics School. The contributions havebeen written by his friends, colleagues and students, including CBardos, A Bensoussan, S S Chern, P G Ciarlet, R Glowinski, Gu Chaohao, B Malgrange, G Marchuk, O Pironneau, W Strauss, R Temam, etc
The Ginzburg-Landau equation us a mathematical model of superconductors has become an extremely useful tool in many areas of physics where vortices carrying a topological charge appear. The remarkable progress in the mathematical understanding of this equation involves a combined use of mathematical tools from many branches of mathematics. The Ginzburg-Landau model has been an amazing source of new problems and new ideas in analysis, geometry and topology. This collection will meet the urgent needs of the specialists, scholars and graduate students working in this area or related areas.
This monograph describes global propagation of regular nonlinear hyperbolic waves described by first-order quasilinear hyperbolic systems in one dimension. The exposition is clear, concise, and unfolds systematically beginning with introductory material and leading to the original research of the authors. Topics are motivated with a number of physical examples from the areas of elastic materials, one-dimensional gas dynamics, and waves. Aimed at researchers and graduate students in partial differential equations and related topics, this book will stimulate further research and help readers further understand important aspects and recent progress of regular nonlinear hyperbolic waves.
This book contains a selection of more than 500 mathematical problems and their solutions from the PhD qualifying examination papers of more than ten famous American universities. The problems cover six aspects of graduate school mathematics: Algebra, Differential Geometry, Topology, Real Analysis, Complex Analysis and Partial Differential Equations. The depth of knowledge involved is not beyond the contents of the textbooks for graduate students, while solution of the problems requires deep understanding of the mathematical principles and skilled techniques. For students this book is a valuable complement to textbooks; for lecturers teaching graduate school mathematics, a helpful reference.
This first part of this book deals with the boundary value problem with equivalued surfaces, while the second part is concerned with the mathematical model and method, including the numerical method, of the resistivity well-logging for the three-lateral well-logging.
Within this carefully presented monograph, the authors extend the universal phenomenon of synchronization from finite-dimensional dynamical systems of ordinary differential equations (ODEs) to infinite-dimensional dynamical systems of partial differential equations (PDEs). By combining synchronization with controllability, they introduce the study of synchronization to the field of control and add new perspectives to the investigation of synchronization for systems of PDEs. With a focus on synchronization for a coupled system of wave equations, the text is divided into three parts corresponding to Dirichlet, Neumann, and coupled Robin boundary controls. Each part is then subdivided into chapters detailing exact boundary synchronization and approximate boundary synchronization, respectively. The core intention is to give artificial intervention to the evolution of state variables through appropriate boundary controls for realizing the synchronization in a finite time, creating a novel viewpoint into the investigation of synchronization for systems of partial differential equations, and revealing some essentially dissimilar characteristics from systems of ordinary differential equations. Primarily aimed at researchers and graduate students of applied mathematics and applied sciences, this text will particularly appeal to those interested in applied PDEs and control theory for distributed parameter systems.
Partial differential equations (PDEs) play a central role in modern physics as a tool to model many fundamental physical processes. This book provides a bridge between the problems addressed by physics and the mathematical tools used to solve them. The authors describe the connections between various physical disciplines and their related mathematical models, which are described by partial differential equations (PDEs) and establish the fundamental equations in areas such as electrodynamics; fluid dynamics; elastic mechanics; kinetic theory of gases; special relativity; and quantum mechanics. This is followed by in-depth explanations of how PDEs work as effective tools to express the basic concepts of physics. The book describes the features of these PDEs, including the types and characteristics of the equations, the behaviour of solutions and common approaches for solving PDEs. The chapters, which include exercises, are self-contained and are accessible to anyone with knowledge of basic undergraduate maths and physics.
This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
This text represents the results originally obtained by S. Lainerman, D. Christodoulou, Y. Choquet-Bruhat, T. Nishida and A. Matsumara on the global existence of classical solutions to the Cauchy problem with small initial data for nonlinear evolution equations.
The focus of this is on the latest developments related to the analysis of problems in which several scales are presented. After a theoretical presentation of the theory of homogenization in the periodic case, the other contributions address a wide range of applications in the fields of elasticity (asymptotic behavior of nonlinear elastic thin structures, modeling of junction of a periodic family of rods with a plate) and fluid mechanics (stationary NavierStokes equations in porous media). Other applications concern the modeling of new composites (electromagnetic and piezoelectric materials) a.
Fuzzy logic has found many applications in the field of control and systems engineering. This book focuses on how fuzzy sets principles are employed for modelling and controlling a variety of dynamic systems. It also discusses the use of fuzzy logic techniques for fault diagnosis in processes and machines.
This collection of articles covers the hottest topics in contemporary applied mathematics. Multiscale modeling, material computing, symplectic methods, parallel computing, mathematical biology, applied differential equations and engineering computing problems are all included. The book contains the latest results of many leading scientists and provides a window on new trends in research in the field. Sample Chapter(s). Chapter 1: An Iterative BEM for the Inverse Problem of Detecting Corrosion in a Pipe (467 KB). Contents: An Iterative BEM for the Inverse Problem of Detecting Corrosion in a Pipe (J Cheng et al.); Optimal Order Integration on the Sphere (K Hesse & I H Sloan); Inverse Problems in Bioluminescence Tomography (M Jiang et al.); Global Dynamic Properties of Protein Networks (F-T Li et al.); Distance Geometry Problem and Algorithm Based on Barycentric Coordinates (H-X Huang & C-J Wang); On Ill-Posedness and Inversion Scheme for 2-D Backward Heat Conduction (J-J Liu); Error Analysis on Scrambled Quasi-Monte Carlo Quadrature Rules Using Sobol Points (R-X Yue); and other papers. Readership: Graduate students and researchers in applied mathematics.
This volume is a collection of articles in memory of Jacques-Louis Lions, a leading mathematician and the founder of the Contemporary French Applied Mathematics School. The contributions have been written by his friends, colleagues and students. The book concerns many important results in analysis, geometry, numerical methods, fluid mechanics, control theory, etc.
The focus of this is on the latest developments related to the analysis of problems in which several scales are presented. After a theoretical presentation of the theory of homogenization in the periodic case, the other contributions address a wide range of applications in the fields of elasticity (asymptotic behavior of nonlinear elastic thin structures, modeling of junction of a periodic family of rods with a plate) and fluid mechanics (stationary Navier?Stokes equations in porous media). Other applications concern the modeling of new composites (electromagnetic and piezoelectric materials) and imperfect transmission problems. A detailed approach of numerical finite element methods is also investigated.
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