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 : 082182970X
Total Pages : 194 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 194 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.

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.

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.

Steady States of the One-dimensional Cahn-Hilliard Equation

Author : University of Minnesota. Institute for Mathematics and Its Applications
Publisher :
ISBN 13 :
Total Pages : 31 pages
Book Rating : 4.:/5 (123 download)

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Book Synopsis Steady States of the One-dimensional Cahn-Hilliard Equation by : University of Minnesota. Institute for Mathematics and Its Applications

Download or read book Steady States of the One-dimensional Cahn-Hilliard Equation written by University of Minnesota. Institute for Mathematics and Its Applications and published by . This book was released on 1992 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

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:

Energy Methods for the Cahn-Hilliard Equation

Author : University of Minnesota. Institute for Mathematics and Its Applications
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (123 download)

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Book Synopsis Energy Methods for the Cahn-Hilliard Equation by : University of Minnesota. Institute for Mathematics and Its Applications

Download or read book Energy Methods for the Cahn-Hilliard Equation written by University of Minnesota. Institute for Mathematics and Its Applications and published by . This book was released on 1985 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

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.

Solutions of the CAHN HILLIARD Equations

Author : Rahul Basu
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.2/5 (243 download)

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Book Synopsis Solutions of the CAHN HILLIARD Equations by : Rahul Basu

Download or read book Solutions of the CAHN HILLIARD Equations written by Rahul Basu and published by . This book was released on 2024-02-04 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Solutions of the Cahn Hilliard Equations" is a groundbreaking exploration of the Cahn Hilliard equations, a set of partial differential equations that describe the evolution of phase boundaries in materials. This comprehensive guide provides a thorough analysis of the equations and their solutions, offering valuable insights for researchers, engineers, and students in the field of materials science and engineering. The book begins with a detailed introduction to the Cahn-Hilliard equations, providing a clear and accessible overview of their mathematical formulation and physical significance. It then delves into the various analytical and numerical methods for solving the equations, offering step-by-step guidance on how to obtain accurate and reliable solutions. Throughout the book, the author presents a wealth of real-world examples and case studies, demonstrating the practical applications of the Cahn-Hilliard equations in materials science and engineering. From phase separation in polymers to microstructure evolution in alloys, readers will gain a deep understanding of how these equations can be used to model and predict the behavior of complex materials systems. With its comprehensive coverage and practical approach, "Solutions of the Cahn Hilliard Equations" is an indispensable resource for anyone seeking to understand and apply these important equations in their research or professional work. Whether you are a seasoned researcher or a student new to the field, this book will empower you to tackle challenging problems and make meaningful contributions to the advancement of materials science and engineering.

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.

Problems in Mathematical Biophysics

Author : Alberto d’Onofrio
Publisher : Springer Nature
ISBN 13 : 3031607732
Total Pages : 292 pages
Book Rating : 4.0/5 (316 download)

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Book Synopsis Problems in Mathematical Biophysics by : Alberto d’Onofrio

Download or read book Problems in Mathematical Biophysics written by Alberto d’Onofrio and published by Springer Nature. This book was released on with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Partial Differential Equations and Functional Analysis

Author : Erik Koelink
Publisher : Springer Science & Business Media
ISBN 13 : 3764376015
Total Pages : 294 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Partial Differential Equations and Functional Analysis by : Erik Koelink

Download or read book Partial Differential Equations and Functional Analysis written by Erik Koelink and published by Springer Science & Business Media. This book was released on 2006-08-18 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Capturing the state of the art of the interplay between partial differential equations, functional analysis, maximal regularity, and probability theory, this volume was initiated at the Delft conference on the occasion of the retirement of Philippe Clément. It will be of interest to researchers in PDEs and functional analysis.

Spectral Methods

Author : Jie Shen
Publisher : Springer Science & Business Media
ISBN 13 : 3540710418
Total Pages : 481 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 481 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.

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.

Partial Differential Equations in Ecology

Author : Sergei Petrovski
Publisher : MDPI
ISBN 13 : 3036502963
Total Pages : 238 pages
Book Rating : 4.0/5 (365 download)

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Book Synopsis Partial Differential Equations in Ecology by : Sergei Petrovski

Download or read book Partial Differential Equations in Ecology written by Sergei Petrovski and published by MDPI. This book was released on 2021-03-17 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Partial differential equations (PDEs) have been used in theoretical ecology research for more than eighty years. Nowadays, along with a variety of different mathematical techniques, they remain as an efficient, widely used modelling framework; as a matter of fact, the range of PDE applications has even become broader. This volume presents a collection of case studies where applications range from bacterial systems to population dynamics of human riots.