Focus on Pattern Formation

Abstract

Pattern formation is a subfield of nonlinear dynamics in spatially extended systems. Although the latter term is often used narrowly to describe nonlinear systems with not too many degrees of freedom, in general it may be applied to describe more or less everything that happens in the Universe. Thus this statement can hardly be used as a definition. More precisely, the field of pattern formation focuses on systems where the nonlinearities conspire to form spatial patterns that sometimes are stationary, travelling or disordered in space and time. The latter is often referred to as spatio-temporal chaos.The past two decades have provided major progress in the field of pattern formation. We now have a well-developed theoretical framework for understanding weakly nonlinear patterns that can be described by Ginzburg-Landau-type theories. Close to the onset of instability, our understanding of time-independent or simple time-dependent patterns is quite advanced. Phase field models for the investigation of interfacial instabilities are leading to a breakthrough. Nonlinear phase diffusion equations that are derived from first principles allow the investigation of the `elastic' properties of pattern dynamics even in the fully nonlinear region.Rapid progress continues to be made possible by a close collaboration of experiment and theory. Advances in computational power are enabling the study of complex spatio-temporal patterns in systems of large spatial extent. In experiment, the increase in computational power combined with novel imaging technology allows the analysis of millions of high-resolution digital images. For instance, novel visualization and data analysis techniques have yielded progress in identifying and studying the nonequilibrium dynamics of extended systems in terms of the spatial and temporal evolution of defect structures that are found in many spatio-temporal chaotic systems. Numerical simulations based on first principles or on general higher-order equations can now be conducted in large systems under realistic boundary conditions.Pattern formation is a truly interdisciplinary science. The similarity in fundamental mechanisms and the accompanying mathematics brings together scientists from many disciplines, such as biology, chemistry, fluid dynamics, material science, mathematics, medicine, geophysics, ecology, physics and surface science. We believe that the articles collected here provide an overview of the widespread activities within this field.We feel that New Journal of Physics, as a purely electronic journal, isparticularly useful for our field of research: if a picture says athousand words, a movie can say many more about the spatio-temporaldynamics of a pattern. We would like to thank all of the authors fortheir contributions and, in many cases, for bearing the additionalburden of including moving pictures for the undoubted benefit of readers. Focus on Pattern Formation Contents Ferrofluid drops in rotating magnetic fields Alexander V Lebedev, Andreas Engel, Konstantin I Morozov and Heiko Bauke Excitation waves in reaction-diffusion media with non-monotonic dispersion relations Chad T Hamik and Oliver Steinbock Formation of a drop: viscosity dependence of three flow regimes Alexander Rothert, Reinhard Richter and Ingo Rehberg Local periodic forcing of CO oxidation on a Pt(110) surface J Wolff and H H Rotermund Localized nonequilibrium nanostructures in surface chemical reactions M Hildebrand, M Ipsen, A S Mikhailov and G Ertl Fluctuations in catalytic surface reactions R Imbihl The corkscrew instability of a Fréedericksz domain wall in a nematic liquid crystal Alberto de Lózar Muñoz, Thomas Bock, Matthias Müller, Wolfgang Schöpf and Ingo Rehberg Dark-in-bright solitons in Bose-Einstein condensates with attractive interactions P G Kevrekidis, D J Frantzeskakis, Boris A Malomed, A R Bishop and I G Kevrekidis Photo-induced travelling waves in condensed Langmuir monolayers Y Tabe, T Yamamoto and H Yokoyama Deterministic and stochastic models of intracellular Ca2+waves M Falcke Patterns of convection in rotating spherical shells R Simitev and F H Busse Dynamic mechanism for conduction block in heart tissue Jeffrey J Fox, Mark L Riccio, Paul Drury, Amanda Werthman and Robert FGilmour Jr Plume patterns in radiative–convective flows A Parodi, K A Emanuel and A Provenzale Sub-threshold Ca2+ waves J W Shuai and P Jung Whirling hexagons and defect chaos in hexagonal non-Boussinesq convection Yuan-Nan Young, Hermann Riecke and Werner Pesch Breakup of spiral waves caused by radial dynamics: Eckhaus and finite wavenumber instabilities Markus Bär and Lutz Brusch Eberhard Bodenschatz, Cornell University, USA Ronald Imbihl, Universität Hannover, Germany Ingo Rehberg, Universität Bayreuth, Germany