The Cahn Hilliard Equation Recent Advances And Applications

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The Cahn–Hilliard Equation: Recent Advances and Applications

Author : Alain Miranville
Publisher : SIAM
ISBN 13 : 1611975921
Total Pages : 216 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis The Cahn–Hilliard Equation: Recent Advances and Applications by : Alain Miranville

Download or read book The Cahn–Hilliard Equation: Recent Advances and Applications written by Alain Miranville and published by SIAM. This book was released on 2019-09-09 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to present a detailed discussion of both classical and recent results on the popular Cahn–Hilliard equation and some of its variants. The focus is on mathematical analysis of Cahn–Hilliard models, with an emphasis on thermodynamically relevant logarithmic nonlinear terms, for which several questions are still open. Initially proposed in view of applications to materials science, the Cahn–Hilliard equation is now applied in many other areas, including image processing, biology, ecology, astronomy, and chemistry. In particular, the author addresses applications to image inpainting and tumor growth. Many chapters include open problems and directions for future research. The Cahn-Hilliard Equation: Recent Advances and Applications is intended for graduate students and researchers in applied mathematics, especially those interested in phase separation models and their generalizations and applications to other fields. Materials scientists also will find this text of interest.

Recent Advances in Numerical Methods for Partial Differential Equations and Applications

Author : Xiaobing Feng
Publisher : American Mathematical Soc.
ISBN 13 : 9780821856420
Total Pages : 196 pages
Book Rating : 4.8/5 (564 download)

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Book Synopsis Recent Advances in Numerical Methods for Partial Differential Equations and Applications by : Xiaobing Feng

Download or read book Recent Advances in Numerical Methods for Partial Differential Equations and Applications written by Xiaobing Feng and published by American Mathematical Soc.. This book was released on 2002 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is derived from lectures presented at the 2001 John H. Barrett Memorial Lectures at the University of Tennessee, Knoxville. The topic was computational mathematics, focusing on parallel numerical algorithms for partial differential equations, their implementation and applications in fluid mechanics and material science. Compiled here are articles from six of nine speakers. Each of them is a leading researcher in the field of computational mathematics and its applications. A vast area that has been coming into its own over the past 15 years, computational mathematics has experienced major developments in both algorithmic advances and applications to other fields. These developments have had profound implications in mathematics, science, engineering and industry. With the aid of powerful high performance computers, numerical simulation of physical phenomena is the only feasible method for analyzing many types of important phenomena, joining experimentation and theoretical analysis as the third method of scientific investigation. The three aspects: applications, theory, and computer implementation comprise a comprehensive overview of the topic. Leading lecturers were Mary Wheeler on applications, Jinchao Xu on theory, and David Keyes on computer implementation. Following the tradition of the Barrett Lectures, these in-depth articles and expository discussions make this book a useful reference for graduate students as well as the many groups of researchers working in advanced computations, including engineering and computer scientists.

Inverse Scattering Theory and Transmission Eigenvalues

Author : Fioralba Cakoni
Publisher : SIAM
ISBN 13 : 1611977428
Total Pages : 259 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Inverse Scattering Theory and Transmission Eigenvalues by : Fioralba Cakoni

Download or read book Inverse Scattering Theory and Transmission Eigenvalues written by Fioralba Cakoni and published by SIAM. This book was released on 2022-12-07 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse scattering theory is a major theme in applied mathematics, with applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting challenges in the development of efficient inversion algorithms. A further complication is that anisotropic materials cannot be uniquely determined from given scattering data. In the first edition of Inverse Scattering Theory and Transmission Eigenvalues, the authors discussed methods for determining the support of inhomogeneous media from measured far field data and the role of transmission eigenvalue problems in the mathematical development of these methods. In this second edition, three new chapters describe recent developments in inverse scattering theory. In particular, the authors explore the use of modified background media in the nondestructive testing of materials and methods for determining the modified transmission eigenvalues that arise in such applications from measured far field data. They also examine nonscattering wave numbers—a subset of transmission eigenvalues—using techniques taken from the theory of free boundary value problems for elliptic partial differential equations and discuss the dualism of scattering poles and transmission eigenvalues that has led to new methods for the numerical computation of scattering poles. This book will be of interest to research mathematicians and engineers and physicists working on problems in target identification. It will also be useful to advanced graduate students in many areas of applied mathematics.

Recent Advances in Numerical Methods for Partial Differential Equations and Applications

Author : Xiaobing Feng
Publisher : American Mathematical Soc.
ISBN 13 : 082182970X
Total Pages : 177 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Recent Advances in Numerical Methods for Partial Differential Equations and Applications by : Xiaobing Feng

Download or read book Recent Advances in Numerical Methods for Partial Differential Equations and Applications written by Xiaobing Feng and published by American Mathematical Soc.. This book was released on 2002 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: An emerging field over the past 15 years, computational mathematics is a vast area which has experienced major developments in both algorithmic advances and applications to other fields. These developments have had profound implications in mathematics, science, engineering and industry. Compiled here are six of nine in-depth survey papers with an expository discussion on computational mathematics that were presented at the 2001 John H. Barrett Memorial Lectures at the University of Tennessee, Knoxville. They focus on parallel numerical algorithms for partial differential equations, their implementation and applications in fluid mechanics and material science. Each of the lecturers is a leading researcher in the field of computational mathematics and its applications. This book will be a useful reference for graduate students as well as the many groups of researchers working in advanced computations, including engineering and computer scientists. Prior knowledge of partial differential equations and their numerical methods is helpful.

Solving Problems in Multiply Connected Domains

Author : Darren Crowdy
Publisher : SIAM
ISBN 13 : 1611976154
Total Pages : 456 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Solving Problems in Multiply Connected Domains by : Darren Crowdy

Download or read book Solving Problems in Multiply Connected Domains written by Darren Crowdy and published by SIAM. This book was released on 2020-04-20 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Whenever two or more objects or entities—be they bubbles, vortices, black holes, magnets, colloidal particles, microorganisms, swimming bacteria, Brownian random walkers, airfoils, turbine blades, electrified drops, magnetized particles, dislocations, cracks, or heterogeneities in an elastic solid—interact in some ambient medium, they make holes in that medium. Such holey regions with interacting entities are called multiply connected. This book describes a novel mathematical framework for solving problems in two-dimensional, multiply connected regions. The framework is built on a central theoretical concept: the prime function, whose significance for the applied sciences, especially for solving problems in multiply connected domains, has been missed until recent work by the author. This monograph is a one-of-a-kind treatise on the prime function associated with multiply connected domains and how to use it in applications. The book contains many results familiar in the simply connected, or single-entity, case that are generalized naturally to any number of entities, in many instances for the first time. Solving Problems in Multiply Connected Domains is aimed at applied and pure mathematicians, engineers, physicists, and other natural scientists; the framework it describes finds application in a diverse array of contexts. The book provides a rich source of project material for undergraduate and graduate courses in the applied sciences and could serve as a complement to standard texts on advanced calculus, potential theory, partial differential equations and complex analysis, and as a supplement to texts on applied mathematical methods in engineering and science.

Fast Direct Solvers for Elliptic PDEs

Author : Per-Gunnar Martinsson
Publisher : SIAM
ISBN 13 : 1611976049
Total Pages : 332 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Fast Direct Solvers for Elliptic PDEs by : Per-Gunnar Martinsson

Download or read book Fast Direct Solvers for Elliptic PDEs written by Per-Gunnar Martinsson and published by SIAM. This book was released on 2019-12-16 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fast solvers for elliptic PDEs form a pillar of scientific computing. They enable detailed and accurate simulations of electromagnetic fields, fluid flows, biochemical processes, and much more. This textbook provides an introduction to fast solvers from the point of view of integral equation formulations, which lead to unparalleled accuracy and speed in many applications. The focus is on fast algorithms for handling dense matrices that arise in the discretization of integral operators, such as the fast multipole method and fast direct solvers. While the emphasis is on techniques for dense matrices, the text also describes how similar techniques give rise to linear complexity algorithms for computing the inverse or the LU factorization of a sparse matrix resulting from the direct discretization of an elliptic PDE. This is the first textbook to detail the active field of fast direct solvers, introducing readers to modern linear algebraic techniques for accelerating computations, such as randomized algorithms, interpolative decompositions, and data-sparse hierarchical matrix representations. Written with an emphasis on mathematical intuition rather than theoretical details, it is richly illustrated and provides pseudocode for all key techniques. Fast Direct Solvers for Elliptic PDEs is appropriate for graduate students in applied mathematics and scientific computing, engineers and scientists looking for an accessible introduction to integral equation methods and fast solvers, and researchers in computational mathematics who want to quickly catch up on recent advances in randomized algorithms and techniques for working with data-sparse matrices.

Advances and Trends in Optimization with Engineering Applications

Author : Tamas Terlaky
Publisher : SIAM
ISBN 13 : 1611974674
Total Pages : 730 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Advances and Trends in Optimization with Engineering Applications by : Tamas Terlaky

Download or read book Advances and Trends in Optimization with Engineering Applications written by Tamas Terlaky and published by SIAM. This book was released on 2017-04-26 with total page 730 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization is of critical importance in engineering. Engineers constantly strive for the best possible solutions, the most economical use of limited resources, and the greatest efficiency. As system complexity increases, these goals mandate the use of state-of-the-art optimization techniques. In recent years, the theory and methodology of optimization have seen revolutionary improvements. Moreover, the exponential growth in computational power, along with the availability of multicore computing with virtually unlimited memory and storage capacity, has fundamentally changed what engineers can do to optimize their designs. This is a two-way process: engineers benefit from developments in optimization methodology, and challenging new classes of optimization problems arise from novel engineering applications. Advances and Trends in Optimization with Engineering Applications reviews 10 major areas of optimization and related engineering applications, providing a broad summary of state-of-the-art optimization techniques most important to engineering practice. Each part provides a clear overview of a specific area and discusses a range of real-world problems. The book provides a solid foundation for engineers and mathematical optimizers alike who want to understand the importance of optimization methods to engineering and the capabilities of these methods.

Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems

Author : Luis Rodrigues
Publisher : SIAM
ISBN 13 : 1611975905
Total Pages : 224 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems by : Luis Rodrigues

Download or read book Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems written by Luis Rodrigues and published by SIAM. This book was released on 2019-11-06 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineering systems operate through actuators, most of which will exhibit phenomena such as saturation or zones of no operation, commonly known as dead zones. These are examples of piecewise-affine characteristics, and they can have a considerable impact on the stability and performance of engineering systems. This book targets controller design for piecewise affine systems, fulfilling both stability and performance requirements. The authors present a unified computational methodology for the analysis and synthesis of piecewise affine controllers, taking an approach that is capable of handling sliding modes, sampled-data, and networked systems. They introduce algorithms that will be applicable to nonlinear systems approximated by piecewise affine systems, and they feature several examples from areas such as switching electronic circuits, autonomous vehicles, neural networks, and aerospace applications. Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems is intended for graduate students, advanced senior undergraduate students, and researchers in academia and industry. It is also appropriate for engineers working on applications where switched linear and affine models are important.

Recent Advances in Scientific Computing and Applications

Author : Jichun Li
Publisher : American Mathematical Soc.
ISBN 13 : 0821887378
Total Pages : 397 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Recent Advances in Scientific Computing and Applications by : Jichun Li

Download or read book Recent Advances in Scientific Computing and Applications written by Jichun Li and published by American Mathematical Soc.. This book was released on 2013-04-24 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Eighth International Conference on Scientific Computing and Applications, held April 1-4, 2012, at the University of Nevada, Las Vegas. The papers in this volume cover topics such as finite element methods, multiscale methods, finite difference methods, spectral methods, collocation methods, adaptive methods, parallel computing, linear solvers, applications to fluid flow, nano-optics, biofilms, finance, magnetohydrodynamics flow, electromagnetic waves, the fluid-structure interaction problem, and stochastic PDEs. This book will serve as an excellent reference for graduate students and researchers interested in scientific computing and its applications.

Recent Advances in Computational Sciences

Author : Palle E. T. J0rgensen
Publisher : World Scientific
ISBN 13 : 9812792384
Total Pages : 395 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Recent Advances in Computational Sciences by : Palle E. T. J0rgensen

Download or read book Recent Advances in Computational Sciences written by Palle E. T. J0rgensen and published by World Scientific. This book was released on 2008 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents state-of-the-art lectures delivered by international academic and industrial experts in the field of computational science and its education, covering a wide spectrum from theory to practice. Topics include new developments in finite element method (FEM), finite volume method and Spline theory, such as Moving Mesh Methods, Galerkin and Discontinuous Galerkin Schemes, Shape Gradient Methods, Mixed FEMs, Superconvergence techniques and Fourier spectral approximations with applications in multidimensional fluid dynamics; Maxwell equations in discrepancy media; and phase-field equations. It also discusses some interesting topics related to Stokes equations, Schrodinger equations, wavelet analysis and approximation theory. Contemporary teaching issues in curriculum reform also form an integral part of the book. This book will therefore be of significant interest and value to all graduates, research scientists and practitioners facing complex computational problems. Administrators and policymakers will find it is an addition to their mathematics curriculum reform libraries.

Recent Advances In Computational Sciences: Selected Papers From The International Workshop On Computational Sciences And Its Education

Download Recent Advances In Computational Sciences: Selected Papers From The International Workshop On Computational Sciences And Its Education PDF Online Free

Author : Xiaoping Shen
Publisher : World Scientific
ISBN 13 : 981447536X
Total Pages : 395 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Recent Advances In Computational Sciences: Selected Papers From The International Workshop On Computational Sciences And Its Education by : Xiaoping Shen

Download or read book Recent Advances In Computational Sciences: Selected Papers From The International Workshop On Computational Sciences And Its Education written by Xiaoping Shen and published by World Scientific. This book was released on 2008-07-31 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents state-of-the-art lectures delivered by international academic and industrial experts in the field of computational science and its education, covering a wide spectrum from theory to practice. Topics include new developments in finite element method (FEM), finite volume method and Spline theory, such as Moving Mesh Methods, Galerkin and Discontinuous Galerkin Schemes, Shape Gradient Methods, Mixed FEMs, Superconvergence techniques and Fourier spectral approximations with applications in multidimensional fluid dynamics; Maxwell equations in discrepancy media; and phase-field equations. It also discusses some interesting topics related to Stokes equations, Schrödinger equations, wavelet analysis and approximation theory. Contemporary teaching issues in curriculum reform also form an integral part of the book.This book will therefore be of significant interest and value to all graduates, research scientists and practitioners facing complex computational problems. Administrators and policymakers will find it is an addition to their mathematics curriculum reform libraries.

Numerical Continuation and Bifurcation in Nonlinear PDEs

Author : Hannes Uecker
Publisher : SIAM
ISBN 13 : 1611976618
Total Pages : 380 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Numerical Continuation and Bifurcation in Nonlinear PDEs by : Hannes Uecker

Download or read book Numerical Continuation and Bifurcation in Nonlinear PDEs written by Hannes Uecker and published by SIAM. This book was released on 2021-08-19 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a hands-on approach to numerical continuation and bifurcation for nonlinear PDEs in 1D, 2D, and 3D. Partial differential equations (PDEs) are the main tool to describe spatially and temporally extended systems in nature. PDEs usually come with parameters, and the study of the parameter dependence of their solutions is an important task. Letting one parameter vary typically yields a branch of solutions, and at special parameter values, new branches may bifurcate. After a concise review of some analytical background and numerical methods, the author explains the free MATLAB package pde2path by using a large variety of examples with demo codes that can be easily adapted to the reader's given problem. Numerical Continuation and Bifurcation in Nonlinear PDEs will appeal to applied mathematicians and scientists from physics, chemistry, biology, and economics interested in the numerical solution of nonlinear PDEs, particularly the parameter dependence of solutions. It can be used as a supplemental text in courses on nonlinear PDEs and modeling and bifurcation.

Recent Advances in Mathematical Analysis

Author : Anna Maria Candela
Publisher : Springer Nature
ISBN 13 : 3031200217
Total Pages : 470 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Recent Advances in Mathematical Analysis by : Anna Maria Candela

Download or read book Recent Advances in Mathematical Analysis written by Anna Maria Candela and published by Springer Nature. This book was released on 2023-06-21 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects selected peer reviewed papers on the topics of Nonlinear Analysis, Functional Analysis, (Korovkin-Type) Approximation Theory, and Partial Differential Equations. The aim of the volume is, in fact, to promote the connection among those different fields in Mathematical Analysis. The book celebrates Francesco Altomare, on the occasion of his 70th anniversary.

Advances in Mathematical Sciences and Applications

Author :
Publisher :
ISBN 13 :
Total Pages : 422 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Advances in Mathematical Sciences and Applications by :

Download or read book Advances in Mathematical Sciences and Applications written by and published by . This book was released on 2003 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Interfaces: Modeling, Analysis, Numerics

Author : Eberhard Bänsch
Publisher : Springer Nature
ISBN 13 : 3031355504
Total Pages : 186 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Interfaces: Modeling, Analysis, Numerics by : Eberhard Bänsch

Download or read book Interfaces: Modeling, Analysis, Numerics written by Eberhard Bänsch and published by Springer Nature. This book was released on 2023-11-11 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes are dedicated to the mathematical modelling, analysis and computation of interfaces and free boundary problems appearing in geometry and in various applications, ranging from crystal growth, tumour growth, biological membranes to porous media, two-phase flows, fluid-structure interactions, and shape optimization. We first give an introduction to classical methods from differential geometry and systematically derive the governing equations from physical principles. Then we will analyse parametric approaches to interface evolution problems and derive numerical methods which will be thoroughly analysed. In addition, implicit descriptions of interfaces such as phase field and level set methods will be analysed. Finally, we will discuss numerical methods for complex interface evolutions and will focus on two phase flow problems as an important example of such evolutions.

Virtual Materials Design

Author : Norbert Huber
Publisher : Frontiers Media SA
ISBN 13 : 2889766772
Total Pages : 197 pages
Book Rating : 4.8/5 (897 download)

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Book Synopsis Virtual Materials Design by : Norbert Huber

Download or read book Virtual Materials Design written by Norbert Huber and published by Frontiers Media SA. This book was released on 2022-08-02 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Spectral Methods

Author : Jie Shen
Publisher : Springer Science & Business Media
ISBN 13 : 3540710418
Total Pages : 472 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Spectral Methods by : Jie Shen

Download or read book Spectral Methods written by Jie Shen and published by Springer Science & Business Media. This book was released on 2011-08-25 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of basic convergence theory and error analysis for spectral methods. Readers of this book will be exposed to a unified framework for designing and analyzing spectral algorithms for a variety of problems, including in particular high-order differential equations and problems in unbounded domains. The book contains a large number of figures which are designed to illustrate various concepts stressed in the book. A set of basic matlab codes has been made available online to help the readers to develop their own spectral codes for their specific applications.