Singular Phenomena and Scaling in Mathematical Model
[Book]
/ electronic resource
Cham
: Springer International Publishing :Imprint: Springer,
, 2014.
VIII, 434 s. 86 illus., 58 illus. in color. , online resource..
9783319007854.
Electronic
Summary: 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.
Preface -- Area A @2013 Scaling Limits of Diffusion Processes and Singular Spaces -- Area B @2013 Multiple Scales in Mathematical Models of Materials Science and Biology -- Area C @2013 Numerics for Multiscale Models and Singular Phenomena.