Solving Problems In Multiply Connected Domains

Author : Darren Crowdy
Publisher : SIAM
Page : 456 pages
File Size : 46,8 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 : Piotr Drygaś,Sergei Rogosin
Publisher : Birkhäuser
Page : 214 pages
File Size : 54,8 Mb
Release : 2018-03-21
Category : Mathematics
ISBN : 9783319726403

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Modern Problems in Applied Analysis by Piotr Drygaś,Sergei Rogosin Pdf

This book features a collection of recent findings in Applied Real and Complex Analysis that were presented at the 3rd International Conference “Boundary Value Problems, Functional Equations and Applications” (BAF-3), held in Rzeszow, Poland on 20-23 April 2016. The contributions presented here develop a technique related to the scope of the workshop and touching on the fields of differential and functional equations, complex and real analysis, with a special emphasis on topics related to boundary value problems. Further, the papers discuss various applications of the technique, mainly in solid mechanics (crack propagation, conductivity of composite materials), biomechanics (viscoelastic behavior of the periodontal ligament, modeling of swarms) and fluid dynamics (Stokes and Brinkman type flows, Hele-Shaw type flows). The book is addressed to all readers who are interested in the development and application of innovative research results that can help solve theoretical and real-world problems.

Author : Karl K. Sabelfeld,Nikolai A. Simonov
Publisher : Walter de Gruyter
Page : 148 pages
File Size : 48,7 Mb
Release : 2013-07-05
Category : Mathematics
ISBN : 9783110942026

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Random Walks on Boundary for Solving PDEs by Karl K. Sabelfeld,Nikolai A. Simonov Pdf

This monograph presents new probabilistic representations for classical boundary value problems of mathematical physics and is the first book devoted to the walk on boundary algorithms. Compared to the well-known Wiener and diffusion path integrals, the trajectories of random walks in this publication are simlated on the boundary of the domain as Markov chains generated by the kernels of the boundary integral equations equivalent to the original boundary value problem. The book opens with an introduction for solving the interior and exterior boundary values for the Laplace and heat equations, which is followed by applying this method to all main boundary value problems of the potential and elasticity theories.

Author : F. D. Gakhov
Publisher : Courier Corporation
Page : 596 pages
File Size : 48,8 Mb
Release : 1990-01-01
Category : Mathematics
ISBN : 0486662756

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Boundary Value Problems by F. D. Gakhov Pdf

A brilliant monograph, directed to graduate and advanced-undergraduate students, on the theory of boundary value problems for analytic functions and its applications to the solution of singular integral equations with Cauchy and Hilbert kernels. With exercises.

Author : Foluso Ladeinde
Publisher : Walter de Gruyter GmbH & Co KG
Page : 604 pages
File Size : 53,6 Mb
Release : 2024-05-06
Category : Mathematics
ISBN : 9783111351179

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Applications of Complex Variables by Foluso Ladeinde Pdf

The subject of applied complex variables is so fundamental that most of the other topics in advanced engineering mathematics (AEM) depend on it. The present book contains complete coverage of the subject, summarizing the more elementary aspects that you find in most AEM textbooks and delving into the more specialized topics that are less commonplace. The book represents a one-stop reference for complex variables in engineering. The applications of conformal mapping in this book are significantly more extensive than in other AEM textbooks. The treatments of complex integral transforms enable a much larger class of functions that can be transformed, resulting in an expanded use of complex-transform techniques in engineering analysis. The inclusion of the asymptotics of complex integrals enables the analysis of models with irregular singular points. The book, which has more than 300 illustrations, is generous with realistic example problems.

Author : Peter Jonathan Baddoo
Publisher : Springer Nature
Page : 269 pages
File Size : 51,9 Mb
Release : 2020-08-31
Category : Science
ISBN : 9783030557812

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Analytic Solutions for Flows Through Cascades by Peter Jonathan Baddoo Pdf

This thesis is concerned with flows through cascades, i.e. periodic arrays of obstacles. Such geometries are relevant to a range of physical scenarios, chiefly the aerodynamics and aeroacoustics of turbomachinery flows. Despite the fact that turbomachinery is of paramount importance to a number of industries, many of the underlying mechanisms in cascade flows remain opaque. In order to clarify the function of different physical parameters, the author considers six separate problems. For example, he explores the significance of realistic blade geometries in predicting turbomachinery performance, and the possibility that porous blades can achieve noise reductions. In order to solve these challenging problems, the author deploys and indeed develops techniques from across the spectrum of complex analysis: the Wiener–Hopf method, Riemann–Hilbert problems, and the Schottky–Klein prime function all feature prominently. These sophisticated tools are then used to elucidate the underlying mathematical and physical structures present in cascade flows. The ensuing solutions greatly extend previous works and offer new avenues for future research. The results are not of simply academic value but are also useful for aircraft designers seeking to balance aeroacoustic and aerodynamic effects.

Author : David E. Keyes,Yousef Saad,Donald G. Truhlar
Publisher : SIAM
Page : 339 pages
File Size : 51,9 Mb
Release : 1995-01-01
Category : Mathematics
ISBN : 1611971500

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Domain-based Parallelism and Problem Decomposition Methods in Computational Science and Engineering by David E. Keyes,Yousef Saad,Donald G. Truhlar Pdf

This refereed volume arose from the editors' recognition that physical scientists, engineers, and applied mathematicians are developing, in parallel, solutions to problems of parallelization. The cross-disciplinary field of scientific computation is bringing about better communication between heterogeneous computational groups, as they face this common challenge. This volume is one attempt to provide cross-disciplinary communication. Problem decomposition and the use of domain-based parallelism in computational science and engineering was the subject addressed at a workshop held at the University of Minnesota Supercomputer Institute in April 1994. The authors were subsequently able to address the relationships between their individual applications and independently developed approaches. This book is written for an interdisciplinary audience and concentrates on transferable algorithmic techniques, rather than the scientific results themselves. Cross-disciplinary editing was employed to identify jargon that needed further explanation and to ensure provision of a brief scientific background for each chapter at a tutorial level so that the physical significance of the variables is clear and correspondences between fields are visible.

Author : Anonim
Publisher : Unknown
Page : 650 pages
File Size : 44,9 Mb
Release : 1950
Category : Mathematics
ISBN : UOM:39015053962679

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Projects and Publications of the National Applied Mathematics Laboratories by Anonim Pdf

Author : United States. National Bureau of Standards. National Applied Mathematics Laboratories
Publisher : Unknown
Page : 650 pages
File Size : 41,9 Mb
Release : 1949
Category : Mathematics
ISBN : MINN:31951D00036569N

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Projects and Publications by United States. National Bureau of Standards. National Applied Mathematics Laboratories Pdf

Author : Guo-Chun Wen
Publisher : American Mathematical Soc.
Page : 318 pages
File Size : 55,5 Mb
Release : 2024-06-13
Category : Mathematics
ISBN : 0821886800

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Conformal Mappings and Boundary Value Problems by Guo-Chun Wen Pdf

Translated from the Chinese. Conformal mapping and boundary value problems are two major branches of complex function theory. The former is the geometric theory of analytic functions, and the latter is the analysis theory governing the close relationship between abstract theory and many concrete problems. Topics include applications of Cauchy type integrals, the Hilbert boundary value problem, quasiconformal mappings, and basic boundary value problems for harmonic functions. Annotation copyright by Book News, Inc., Portland, OR

Author : V. P. Kompaniec
Publisher : American Mathematical Soc.
Page : 268 pages
File Size : 43,7 Mb
Release : 1968
Category : Algebra
ISBN : 0821817736

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Fourteen Papers on Algebra, Topology, Algebraic and Differential Geometry by V. P. Kompaniec Pdf

Author : Fioralba Cakoni,David Colton,Houssem Haddar
Publisher : SIAM
Page : 259 pages
File Size : 40,8 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 : Peter Duren,Lawrence Zalcman
Publisher : Springer Science & Business Media
Page : 555 pages
File Size : 47,7 Mb
Release : 2013-10-17
Category : Mathematics
ISBN : 9781461479499

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Menahem Max Schiffer: Selected Papers Volume 2 by Peter Duren,Lawrence Zalcman Pdf

This two volume set presents over 50 of the most groundbreaking contributions of Menahem M Schiffer. All of the reprints of Schiffer’s works herein have extensive annotation and invited commentaries, giving new clarity and insight into the impact and legacy of Schiffer's work. A complete bibliography and brief biography make this a rounded and invaluable reference.

Author : Dr. Marius Rosu,Dr. Ping Zhou,Dr. Dingsheng Lin,Dr. Dan M. Ionel,Dr. Mircea Popescu,Frede Blaabjerg,Dr. Vandana Rallabandi,Dr. David Staton
Publisher : John Wiley & Sons
Page : 320 pages
File Size : 49,7 Mb
Release : 2017-11-10
Category : Science
ISBN : 9781119103479

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Multiphysics Simulation by Design for Electrical Machines, Power Electronics and Drives by Dr. Marius Rosu,Dr. Ping Zhou,Dr. Dingsheng Lin,Dr. Dan M. Ionel,Dr. Mircea Popescu,Frede Blaabjerg,Dr. Vandana Rallabandi,Dr. David Staton Pdf

Presents applied theory and advanced simulation techniques for electric machines and drives This book combines the knowledge of experts from both academia and the software industry to present theories of multiphysics simulation by design for electrical machines, power electronics, and drives. The comprehensive design approach described within supports new applications required by technologies sustaining high drive efficiency. The highlighted framework considers the electric machine at the heart of the entire electric drive. The book also emphasizes the simulation by design concept—a concept that frames the entire highlighted design methodology, which is described and illustrated by various advanced simulation technologies. Multiphysics Simulation by Design for Electrical Machines, Power Electronics and Drives begins with the basics of electrical machine design and manufacturing tolerances. It also discusses fundamental aspects of the state of the art design process and includes examples from industrial practice. It explains FEM-based analysis techniques for electrical machine design—providing details on how it can be employed in ANSYS Maxwell software. In addition, the book covers advanced magnetic material modeling capabilities employed in numerical computation; thermal analysis; automated optimization for electric machines; and power electronics and drive systems. This valuable resource: Delivers the multi-physics know-how based on practical electric machine design methodologies Provides an extensive overview of electric machine design optimization and its integration with power electronics and drives Incorporates case studies from industrial practice and research and development projects Multiphysics Simulation by Design for Electrical Machines, Power Electronics and Drives is an incredibly helpful book for design engineers, application and system engineers, and technical professionals. It will also benefit graduate engineering students with a strong interest in electric machines and drives.

Author : Włodzimierz J. Prosnak
Publisher : Unknown
Page : 356 pages
File Size : 41,5 Mb
Release : 1987
Category : Conformal mapping
ISBN : UCSD:31822003107018

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Computation of Fluid Motions in Multiply Connected Domains by Włodzimierz J. Prosnak Pdf