The Cahn Hilliard Equation Recent Advances And Applications

Author : Alain Miranville
Publisher : SIAM
Page : 216 pages
File Size : 43,8 Mb
Release : 2019-09-09
Category : Mathematics
ISBN : 9781611975925

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

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.

Author : Fioralba Cakoni,David Colton,Houssem Haddar
Publisher : SIAM
Page : 259 pages
File Size : 51,8 Mb
Release : 2022-12-07
Category : Mathematics
ISBN : 9781611977424

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Inverse Scattering Theory and Transmission Eigenvalues by Fioralba Cakoni,David Colton,Houssem Haddar Pdf

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.

Author : Xiaobing Feng,Tim P. Schulze
Publisher : American Mathematical Soc.
Page : 177 pages
File Size : 50,5 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821829707

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Recent Advances in Numerical Methods for Partial Differential Equations and Applications by Xiaobing Feng,Tim P. Schulze Pdf

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.

Author : Darren Crowdy
Publisher : SIAM
Page : 456 pages
File Size : 50,6 Mb
Release : 2020-04-20
Category : Mathematics
ISBN : 9781611976151

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Solving Problems in Multiply Connected Domains by Darren Crowdy Pdf

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.

Author : Per-Gunnar Martinsson
Publisher : SIAM
Page : 332 pages
File Size : 44,7 Mb
Release : 2019-12-16
Category : Mathematics
ISBN : 9781611976045

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Fast Direct Solvers for Elliptic PDEs by Per-Gunnar Martinsson Pdf

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.

Author : Xiaobing Feng,Tim P. Schulze
Publisher : American Mathematical Soc.
Page : 196 pages
File Size : 47,9 Mb
Release : 2002
Category : Mathematics
ISBN : 0821856421

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Recent Advances in Numerical Methods for Partial Differential Equations and Applications by Xiaobing Feng,Tim P. Schulze Pdf

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.

Author : Jichun Li,Hongtao Yang,Eric Alexander Machorro
Publisher : American Mathematical Soc.
Page : 397 pages
File Size : 44,6 Mb
Release : 2013-04-24
Category : Mathematics
ISBN : 9780821887370

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Recent Advances in Scientific Computing and Applications by Jichun Li,Hongtao Yang,Eric Alexander Machorro Pdf

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.

Author : Palle E. T. J0rgensen
Publisher : World Scientific
Page : 395 pages
File Size : 43,6 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812792389

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Recent Advances in Computational Sciences by Palle E. T. J0rgensen Pdf

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.

Author : Xiaoping Shen,Chi-wang Shu,Palle Jorgensen
Publisher : World Scientific
Page : 395 pages
File Size : 53,8 Mb
Release : 2008-07-31
Category : Mathematics
ISBN : 9789814475365

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Recent Advances In Computational Sciences: Selected Papers From The International Workshop On Computational Sciences And Its Education by Xiaoping Shen,Chi-wang Shu,Palle Jorgensen Pdf

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.

Author : Hannes Uecker
Publisher : SIAM
Page : 380 pages
File Size : 49,9 Mb
Release : 2021-08-19
Category : Mathematics
ISBN : 9781611976618

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Numerical Continuation and Bifurcation in Nonlinear PDEs by Hannes Uecker Pdf

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.

Author : Anna Maria Candela,Mirella Cappelletti Montano,Elisabetta Mangino
Publisher : Springer Nature
Page : 470 pages
File Size : 48,6 Mb
Release : 2023-06-21
Category : Mathematics
ISBN : 9783031200212

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Recent Advances in Mathematical Analysis by Anna Maria Candela,Mirella Cappelletti Montano,Elisabetta Mangino Pdf

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.

Author : Eberhard Bänsch,Klaus Deckelnick,Harald Garcke,Paola Pozzi
Publisher : Springer Nature
Page : 186 pages
File Size : 43,9 Mb
Release : 2023-11-11
Category : Mathematics
ISBN : 9783031355509

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Interfaces: Modeling, Analysis, Numerics by Eberhard Bänsch,Klaus Deckelnick,Harald Garcke,Paola Pozzi Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 422 pages
File Size : 40,5 Mb
Release : 2003
Category : Mathematical analysis
ISBN : UOM:39015057376082

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Advances in Mathematical Sciences and Applications by Anonim Pdf

Author : Luis Rodrigues ,Behzad Samadi ,Miad Moarref
Publisher : SIAM
Page : 224 pages
File Size : 42,8 Mb
Release : 2019-11-06
Category : Mathematics
ISBN : 9781611975901

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Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems by Luis Rodrigues ,Behzad Samadi ,Miad Moarref Pdf

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.

Author : Norbert Huber,Surya R. Kalidindi,Stefan Blügel,Wolfgang Wenzel
Publisher : Frontiers Media SA
Page : 197 pages
File Size : 48,9 Mb
Release : 2022-08-02
Category : Technology & Engineering
ISBN : 9782889766772

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Virtual Materials Design by Norbert Huber,Surya R. Kalidindi,Stefan Blügel,Wolfgang Wenzel Pdf