This volume contains a selection of papers presented at the work­ shop "Modelling of Patterns in Space and Time", organized by the 80nderforschungsbereich 123, "8tochastische Mathematische Modelle", in Heidelberg, July 4-8, 1983. The main aim of this workshop was to bring together physicists, chemists, biologists and mathematicians for an exchange of ideas and results in modelling patterns. Since the mathe­ matical problems arising depend only partially on the particular field of applications the interdisciplinary cooperation proved very useful. The workshop mainly treated phenomena showing spatial structures. The special areas covered were morphogenesis, growth in cell cultures, competition systems, structured populations, chemotaxis, chemical precipitation, space-time oscillations in chemical reactors, patterns in flames and fluids and mathematical methods. The discussions between experimentalists and theoreticians were especially interesting and effective. The editors hope that these proceedings reflect at least partially the atmosphere of this workshop. For the convenience of the reader, the papers are ordered alpha­ betically according to authors. However, the table of contents can easily be grouped into the main topics of the workshop. For practical reasons it was not possible to reproduce in colour the beautiful pictures of patterns shown at the workshop. Since a larger number of half-tone pictures could be included in this volume, the loss of information has, however, been kept to a minimum. The workshop has already stimulated cooperation between its parti­ cipants and this volume is intended to spread this effect.

Inhalt

Contraction patterns in a viscous polymer system.- Formation and evolution of spatial structures in chemotactic bacterial systems.- Pattern formation in directional solidification: the nonlinear evolution of cellular melt/solid interfaces.- Evolution of 3-D chemical waves in the BZ reaction medium.- Patterns of bifurcations in plane layers and spherical shells.- Chemotactic collapse in two dimensions.- Singular bifurcation in reaction-diffusion systems.- How chemical structure determines spatial structure in flame profiles.- An age-dependent population model with applications to microbial growth processes.- Cell traction and the generation of anatomical structure.- A hysteresis model for bacterial growth patterns.- Chaos in simple three- and four-variable chemical systems.- Spatial structures induced by chemical reactions at interfaces: survey of some possible models and computerized pattern analysis.- Dynamic patterns in excitable media.- Head regeneration in hydra: biological studies and a model.- Pattern formation in aspect.- Chemotaxis and cell aggregation.- Turing structures, periodic and chaotic regimes in coupled cells.- Digits, segments, somites - the superposition of sequential and periodic structures.- Spatial pattern formation in thin layers of NADH-solutions.- Pattern formation in precipitation processes.- On a mechanical model for morphogenesis: mesenchymal patterns.- Every multi-mode singularly perturbed solution recovers its stability - from a global bifurcation view point.- A mechanochemical model for plasmodial oscillations in physarum.- Genomic control of global features in morphogenesis.- Patterns of starvation in a distributed predator-prey system.- Global branches of one dimensional stationary solutions to Chemotaxis systems and stability.- Analytical and topological methods for reaction-diffusion equations.- Branching processes with interaction as models of cellular pattern formation.- Periodic growth phenomena in spatially organized microbial systems.