Singular Phenomena and Scaling in Mathematical Models

Nonfiction, Science & Nature, Mathematics, Counting & Numeration, Computers, Advanced Computing, Computer Science, Science
Cover of the book Singular Phenomena and Scaling in Mathematical Models by , Springer International Publishing
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Author: ISBN: 9783319007861
Publisher: Springer International Publishing Publication: November 18, 2013
Imprint: Springer Language: English
Author:
ISBN: 9783319007861
Publisher: Springer International Publishing
Publication: November 18, 2013
Imprint: Springer
Language: English

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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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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