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9783764366094

The Symmetry Perspective

by ;
  • ISBN13:

    9783764366094

  • ISBN10:

    3764366095

  • Format: Hardcover
  • Copyright: 2002-04-01
  • Publisher: Birkhauser

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Summary

Pattern formation in physical systems is one of the major research frontiers of mathematics. A central theme of this book is that many instances of pattern formation can be understood within a single framework: symmetry. This book applies symmetry methods to increasingly complex kinds of dynamic behavior: equilibria, period-doubling, time-periodic states, homoclinic and heteroclinic orbits, and chaos. Examples are drawn from both ODEs and PDEs. In each case the type of dynamical behavior being studied is motivated through applications, drawn from a wide variety of scientific disciplines ranging from theoretical physics to evolutionary biology.

Table of Contents

Continuum Mechanicsp. 1
Balance Equations of Fluid Mechanicsp. 3
Turbulencep. 29
Porous Mediap. 45
Problem Classificationp. 63
Numerical Methodsp. 79
Numerical Methodsp. 81
Finite Difference Methodp. 97
Finite Element Methodp. 129
Finite Volume Methodp. 173
Software-Engineeringp. 191
Object-Oriented Methods for Hydrosystem Modelingp. 193
Object-Oriented Programming Techniquesp. 207
Element Implementationp. 233
Selected Topicsp. 239
Non-Linear Flow in Fractured Mediap. 241
Heat Transport in Fractured-Porous Mediap. 271
Density Dependent Flow in Porous Mediap. 301
Multiphase Flow in Deformable Porous Mediap. 333
Indexp. 373
Table of Contents provided by Blackwell. All Rights Reserved.

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