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.
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