The Physics of Structure Formation: Theory and Simulation

ISBN-13: 9783642730030 / Angielski / Miękka / 2011 / 427 str.

Werner Güttinger;Gerhard Dangelmayr

Opis

The formation and evolution of complex dynamical structures is one of the most exciting areas of nonlinear physics. Such pattern formation problems are common in practically all systems involving a large number of interacting components. Here, the basic problem is to understand how competing physical forces can shape stable geometries and to explain why nature prefers just these. Motivation for the intensive study of pattern formation phenomena during the past few years derives from an increasing appreciation of the remarkable diversity of behaviour encountered in nonlinear systems and of universal features shared by entire classes of nonlinear processes. As physics copes with ever more ambi- tious problems in pattern formation, summarizing our present state of knowledge becomes a pressing issue. This volume presents an overview of selected topics in this field of current interest. It deals with theoretical models of pattern formation and with simulations that bridge the gap between theory and experiment. The book is a product of the International Symposium on the Physics of Structure Formation, held from October 27 through November 2, 1986, at the Institute for Information Sciences of the University of Tiibingen. The symposium brought together a group of distinguished scientists from various disciplines to exchange ideas about recent advances in pattern formation in the physical sciences, and also to introduce young scientists to the fi

Spis treści

I Disordered Systems, Networks and Patterns.- Neural Networks — Achievements, Prospects, Difficulties.- Pattern Recognition in Nonlinear Neural Networks.- Formation of Ordered Structures in Quenching Experiments: Scaling Theory and Simulations.- Patterns in Random Boolean Nets.- The Structure of the Visual Field.- Patterns of Maximal Entropy.- II Structure Formation in Nonlinear Systems.- Patterns of Bifurcation from Spherically Symmetric States.- Structure Formation by Propagating Fronts.- Oscillatory Doubly Diffusive Convection: Theory and Experiment.- Pattern Selection in Anisotropic Systems.- Rayleigh Number Ramps Cause Moving Convection Patterns.- Interactions of Stationary Modes in Systems with Two and Three Spatial Degrees of Freedom.- The Basic (n,2n)-Fold of Steady Axisymmetric Taylor Vortex Flows.- III Interfacial Patterns.- Nonlinear Interactions of Interface Structures of Differing Wavelength in Directional Solidification.- Velocity Selection in Dendritic Growth.- Interfacial Pattern Formation: Dynamical Effects.- IV Diffusion Limited Aggregation and Fractals.- Role of Fluctuations in Fluid Mechanics and Dendritic Solidification.- A Stochastic Model for Arborescent and Dendritic Growth.- Electrodeposition: Pattern Formation and Fractal Growth.- Anisotropy and Fluctuation in Diffusion Limited Aggregation.- The Classes of Fractals.- Structural Characterization of Aluminum Hydroxide Aggregates by S.A.X.S.: Comparison Between Simulations of Fractal Structures and Experiments.- V Chaos and Turbulence.- Spatial Disorder in Extended Systems.- Nonlinear Gravity Waves and Resonant Forcing.- Transitions to Chaos in a Finite Macroscopic System: Direct Numerical Simulations Versus Normal Form Predictions.- Time-Dependent and Chaotic Behaviour in Systems with O(3)-Symmetry.- Selfsimilarity of Developed Turbulence.- VI Bifurcations and Symmetry.- Nonlinear Normal Modes of Symmetric Hamiltonian Systems.- The Ubiquitous Astroid.- On the Hopf Bifurcation with Broken O(2) Symmetry.- Generic Spontaneous Symmetry Breaking in SU(n) — Equivariant Bifurcation Problems.- Computer Algebraic Tools for Applications of Catastrophe Theory.- Computer Algebra Programs for Dynamical Systems Theory.- Index of Contributors.