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This book consists of survey and research articles expanding on the theme of the "International Conference on Reaction-Diffusion Systems and Viscosity Solutions", held at Providence University, Taiwan, during January 3-6, 2007. It is a carefully selected collection of articles representing the recent progress of some important areas of nonlinear partial differential equations. The book is aimed for researchers and postgraduate students who want to learn about or follow some of the current research topics in nonlinear partial differential equations. The contributors consist of international exp

Reaction-diffusion equations --- Differential equations, Parabolic

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In this book, stagnation flows on a catalytic porous plate is modeled one-dimensionally coupled with multi-step surface reaction mechanisms and molecular transport (diffusion and conduction) in the flow field and in the porous catalyst. Internal and external mass transfer limitations as well as possible reaction routes in the catalyst are investigated for CO oxidation, WGS reaction, partial and steam reforming of methane over Rh/Al?O?.

Heterogeneous catalysis --- Stofftransportlimitierungen --- Reaktion-DiffusionStagnation-flow reactor --- Staupunktreaktor --- Reaction-Diffusion --- Heterogenen Katalyse --- External and internal mass transfer limitation

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This book presents several fundamental results in solving nonlinear reaction-diffusion equations and systems using symmetry-based methods. Reaction-diffusion systems are fundamental modeling tools for mathematical biology with applications to ecology, population dynamics, pattern formation, morphogenesis, enzymatic reactions and chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems, which are relevant for biological applications, from the symmetry point of view, providing rigorous definitions and constructive algorithms to search for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry) of nonlinear reaction-diffusion systems. In order to present applications to population dynamics, it focuses mainly on two- and three-component diffusive Lotka-Volterra systems. While it is primarily a valuable guide for researchers working with reaction-diffusion systems and those developing the theoretical aspects of conditional symmetry conception, parts of the book can also be used in master’s level mathematical biology courses.

Mathematics. --- Partial differential equations. --- Biomathematics. --- Mathematical physics. --- Mathematical and Computational Biology. --- Partial Differential Equations. --- Mathematical Physics. --- Biology --- Mathematics --- Partial differential equations --- Physical mathematics --- Physics --- Math --- Science --- Differential equations, partial. --- Reaction-diffusion equations. --- Diffusion-reaction equations --- Equations, Reaction-diffusion --- Differential equations, Parabolic

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This monograph is concerned with the mathematical analysis of patterns which are encountered in biological systems. It summarises, expands and relates results obtained in the field during the last fifteen years. It also links the results to biological applications and highlights their relevance to phenomena in nature. Of particular concern are large-amplitude patterns far from equilibrium in biologically relevant models. The approach adopted in the monograph is based on the following paradigms: • Examine the existence of spiky steady states in reaction-diffusion systems and select as observable patterns only the stable ones • Begin by exploring spatially homogeneous two-component activator-inhibitor systems in one or two space dimensions • Extend the studies by considering extra effects or related systems, each motivated by their specific roles in developmental biology, such as spatial inhomogeneities, large reaction rates, altered boundary conditions, saturation terms, convection, many-component systems. Mathematical Aspects of Pattern Formation in Biological Systems will be of interest to graduate students and researchers who are active in reaction-diffusion systems, pattern formation and mathematical biology.

Pattern formation (Biology) --- Reaction-diffusion equations. --- Diffusion-reaction equations --- Equations, Reaction-diffusion --- Biological pattern formation --- Mathematics. --- Partial differential equations. --- Biomathematics. --- Partial Differential Equations. --- Mathematical and Computational Biology. --- Genetics and Population Dynamics. --- Physiological, Cellular and Medical Topics. --- Biology --- Mathematics --- Partial differential equations --- Math --- Science --- Differential equations, Parabolic --- Developmental biology --- Differential equations, partial. --- Genetics --- Physiology --- Animal physiology --- Animals --- Anatomy --- Embryology --- Mendel's law --- Adaptation (Biology) --- Breeding --- Chromosomes --- Heredity --- Mutation (Biology) --- Variation (Biology) --- Biological systems --- Mathematical models.

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“Symmetry Breaking in Cells and Tissues” presents a collection of seventeen reviews, opinions and original research papers contributed by theoreticians, physicists and mathematicians, as well as experimental biologists, united by a common interest in biological pattern formation and morphogenesis. The contributors discuss diverse manifestations of symmetry breaking in biology and showcase recent developments in experimental and theoretical approaches to biological morphogenesis and pattern formation on multiple scales.

actin waves --- curved proteins --- dynamic instability --- podosomes --- diffusion --- cell polarity --- Cdc42 --- stress --- cellular memory --- phase separation --- prions --- apoptotic extrusion --- oncogenic extrusion --- contractility --- actomyosin --- bottom-up synthetic biology --- motor proteins --- pattern formation --- self-organization --- cell motility --- signal transduction --- actin dynamics --- intracellular waves --- polarization --- direction sensing --- symmetry-breaking --- biphasic responses --- reaction-diffusion --- membrane and cortical tension --- cell fusion --- cortexillin --- cytokinesis --- Dictyostelium --- myosin --- symmetry breaking --- cytoplasmic flow --- phase-space analysis --- nonlinear waves --- actin polymerization --- bifurcation theory --- mass conservation --- spatial localization --- activator–inhibitor models --- developmental transitions --- cell polarization --- mathematical model --- fission yeast --- reaction–diffusion model --- small GTPases --- Cdc42 oscillations --- pseudopod --- Ras activation --- cytoskeleton --- chemotaxis --- neutrophils --- natural variation --- modelling --- activator-substrate mechanism --- mass-conserved models --- intracellular polarization --- partial differential equations --- sensitivity analysis --- GTPase activating protein (GAP) --- fission yeast Schizosaccharomyces pombe --- CRY2-CIBN --- optogenetics --- clustering --- positive feedback --- network evolution --- Saccharomyces cerevisiae --- polarity --- modularity --- neutrality --- n/a