Description
Book SynopsisUnderstanding the spontaneous formation and dynamics of spatiotemporal patterns in dissipative nonequilibrium systems is one of the major challenges in nonlinear science. This collection of expository papers and advanced research articles, written by leading experts, provides an overview of the state of the art. The topics include new approaches to the mathematical characterization of spatiotemporal complexity, with special emphasis on the role of symmetry, as well as analysis and experiments of patterns in a remarkable variety of applied fields such as magnetoconvection, liquid crystals, granular media, Faraday waves, multiscale biological patterns, visual hallucinations, and biological pacemakers. The unitary presentations, guiding the reader from basic fundamental concepts to the most recent research results on each of the themes, make the book suitable for a wide audience.
Table of ContentsInstabilities, Bifurcation, and the Role of Symmetry: Symmetry and Pattern Formation in the Visual Cortex (M Golubitsky et al.); Validity of the Ginzburg-Landau Approximation in Pattern Forming Systems with Time Periodic Forcing (N Breindl et al.); Pattern Formation on a Sphere (P C Matthews); Convergence Properties of Fourier Mode Representations of Quasipatterns (A M Rucklidge); Localized Patterns, Waves, and Weak Turbulence: Phase Diffusion and Weak Turbulence (J Lega); Pattern Formation and Parametric Resonance (D Armbruster & T-C Jo); Rogue Waves and the Benjamin-Feir Instability (C M Schober); Modelling and Characterization of Spatio-Temporal Complexity: A Finite-Dimensional Mechanism Responsible for Bursts in Fluid Mechanics (E Knobloch); Biological Lattice Gas Models (M S Alber et al.); Characterizations of Far from Equilibrium Structures Using Their Contours (G Nathan and G H Gunaratne); Internal Dynamics of Intermittency (R Sturman & P Ashwin); and other articles.
