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An interdisciplinary study explaining the dynamics underlying biological motion – one of the most obvious expressions of self-organization. Designed for a broad audience from bioscientists to applied mathematicians, this book considers possible synergetic mechanisms of interaction and cooperation on different microscopic levels.
Polymer and cell dynamics play an important role in processes like tumor growth, metastasis, embryogenesis, immune reactions and regeneration. Based on an international workshop on numerical simulations of polymer and cell dynamics in Bad Honnef (Germany) in 2000, this volume provides an overview of the relevant mathematical and numerical methods, their applications and limits. Polymer and Cell Dynamics will be of interest to scientists and advanced undergraduates.
" . . . behavior is not, what an organism does itself, but to what we point. Therefore, whether a type of behavior of an organism is adequate as a certain configuration of movements, will depend on the environment in which we de scribe it. " (Humberto Maturana, Francisco Varela: El arbol del conocimiento, 1984) "A thorough analysis of behavior must result in a scheme, that shows all regularities that are to be found between the sensorical input and the motorical output of an animal. This scheme is an abstract representation of the brain. " (Valentin Braitenberg: Gehirngespinste, 1973) During the 70ies, when Biomathematics (beyond Biomedical Statistics and Com puting) became more popular at u...
This book is not a textbook, but rather a coherent collection of papers from the field of partial differential equations. Nevertheless we believe that it may very well serve as a good introduction into some topics of this classical field of analysis which, despite of its long history, is highly modem and well prospering. Richard Courant wrote in 1950: "It has always been a temptationfor mathematicians to present the crystallized product of their thought as a deductive general theory and to relegate the individual mathematical phenomenon into the role of an example. The reader who submits to the dogmatic form will be easily indoctrinated. Enlightenment, however, must come from an understandin...
The book integrates theoretical analysis, numerical simulation and modeling approaches for the treatment of singular phenomena. The projects covered focus on actual applied problems, and develop qualitatively new and mathematically challenging methods for various problems from the natural sciences. Ranging from stochastic and geometric analysis over nonlinear analysis and modelling to numerical analysis and scientific computation, the book is divided into the three sections: A) Scaling limits of diffusion processes and singular spaces, B) Multiple scales in mathematical models of materials science and biology and C) Numerics for multiscale models and singular phenomena. Each section addresses the key aspects of multiple scales and model hierarchies, singularities and degeneracies, and scaling laws and self-similarity.
The tendency of a living organism to move to a more favourable environment is a natural but complex reaction, involving the integration of sometimes conflicting environmental stimuli as well as a coordinated mechanical response. The response of motile, single cell organisms to environmental stimuli provides a useful model for understanding first of all how the environment is monitored and sensed, and secondly how this information is processed to result in an integrated and coordinated response. The volume looks at a large number of well-studied examples of the chemotactic response, in prokaryotes and eukaryotes, and casts new light on how cells process information and react to their environment. This fundamental response is of great importance in understanding one of the characteristic features of living organisms.
Current biological research demands the extensive use of sophisticated mathematical methods and computer-aided analysis of experiments and data. This highly interdisciplinary volume focuses on structural, dynamical and functional aspects of cellular systems and presents corresponding experiments and mathematical models. The book may serve as an introduction for biologists, mathematicians and physicists to key questions in cellular systems which can be studied with mathematical models. Recent model approaches are presented with applications in cellular metabolism, intra- and intercellular signaling, cellular mechanics, network dynamics and pattern formation. In addition, applied issues such as tumor cell growth, dynamics of the immune system and biotechnology are included.