Solving problems in multiply connected domains /

Solving problems in multiply connected domains /

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Bibliographic Details
Author / Creator:Crowdy, Darren, author.
Imprint:Philadelphia : Society for Industrial and Applied Mathematics, [2020]
Description:1 online resource (xxii, 434 pages).
Language:English
Series:CBMS-NSF regional conference series in applied math ; 97
CBMS-NSF regional conference series in applied mathematics ; 97.
Subject:
Problem solving.
Problem solving.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/12577682
Hidden Bibliographic Details
Other authors / contributors:Society for Industrial and Applied Mathematics, publisher.
ISBN:9781611976151
1611976154
9781611976144
1611976146
Notes:Includes bibliographical references and index.
Restricted to subscribers or individual electronic text purchasers.
Print version record and CIP data provided by publisher; resource not viewed.
Summary:"The aim of this monograph is to present a mathematical framework which makes solving problems in multiply connected domains a very natural generalization of solving them in simply connected ones"--
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. Solving Problems in Multiply Connected Domains is a one-of-a-kind treatise on the prime function associated with multiply connected domains and how to use it in a diverse range of applications; is the first monograph to focus on solving applied problems in multiply connected domains; and 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. This book is aimed at applied and pure mathematicians, engineers, physicists, and other natural scientists. It provides a rich source of project material for a range of 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.
Other form:Print version: Crowdy, Darren. Solving problems in multiply connected domains Philadelphia : Society for Industrial and Applied Mathematics, [2020] 9781611976144
Publisher's no.:CB97 SIAM
Table of Contents:
  • I. Mathematical framework. 1. Function theory and the prime function
  • 2. Function theory in multiply connected circular domains
  • 3. The Schottky double
  • 4. What is the prime function?
  • 5. Doubly connected domains
  • 6. Triply and higher connected domains
  • 7. Schwarz-Christoffel mappings
  • 8. Loxodromic functions
  • 9. Automorphic functions
  • 10. Polycircular arc domains
  • 11. Quadrature domains
  • 12. Cauchy transforms
  • 13. Schwarz problems in multiply connected domains
  • 14. Computing the prime function
  • II. Applications. 15. A calculus for potential theory
  • 16. Hamiltonian dynamics of point vortices
  • 17. Electric transport theory and the Hall effect
  • 18. Laminar flow in ducts
  • 19. Torsion of hollow prismatic rods
  • 20. Laminar convective heat transfer
  • 21. Mixed-type boundary value problems
  • 22. Slow viscous flow
  • 23. Plane elasticity
  • 24. Vortex patch equilibria of the Euler equations
  • 25. Free surface Euler flow
  • 26. Laplacian growth and Hele-Shaw flow
  • 27. Free surface Stokes flow
  • 28. Epilogue.

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