Singular Phenomena and Scaling in Mathematical Models

  • Michael Griebel

Table of contents

  1. Front Matter
    Pages i-viii
  2. Scaling Limits of Diffusion Processes and Singular Spaces

    1. Front Matter
      Pages 1-1
    2. Kathrin Bacher, Karl-Theodor Sturm
      Pages 3-23
    3. Anton Bovier, Rebecca Neukirch
      Pages 69-90
    4. Jinho Baik, Patrik Lino Ferrari, Sandrine Péché
      Pages 91-110
  3. Multiple Scales in Mathematical Models of Materials Science and Biology

    1. Front Matter
      Pages 111-111
    2. Matthias Kurzke, Christof Melcher, Roger Moser
      Pages 113-132
    3. Jens Frehse, Josef Málek
      Pages 133-169
    4. Annelene Wittenfeld, Andrey Ryskin, Wolfgang Alt
      Pages 171-189
    5. Hans Wilhelm Alt, Wolfgang Alt
      Pages 191-219
    6. Ricardo Perl, Paola Pozzi, Martin Rumpf
      Pages 221-241
  4. Numerics for Multiscale Models and Singular Phenomena

About this book


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.


mathematical modelling multiscale methods numerics scaling limits singular phenomena

Editors and affiliations

  • Michael Griebel
    • 1
  1. 1.Universität Bonn Institut für Numerische SimulationBonnGermany

Bibliographic information