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Singular Phenomena and Scaling in Mathematical Models

  • Book
  • © 2014

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Editors:
  1. Michael Griebel

    1. Universität Bonn Institut für Numerische Simulation, Bonn, Germany

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Table of contents (18 chapters)

  1. Front Matter

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

    1. Front Matter

      Pages 1-1
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    2. Ricci Bounds for Euclidean and Spherical Cones

      • Kathrin Bacher, Karl-Theodor Sturm
      Pages 3-23

    3. A Monotone Approximation to the Wasserstein Diffusion

      • Karl-Theodor Sturm
      Pages 25-48

    4. Adapted Function Spaces for Dispersive Equations

      • Herbert Koch
      Pages 49-67

    5. A Note on Metastable Behaviour in the Zero-Range Process

      • Anton Bovier, Rebecca Neukirch
      Pages 69-90

    6. Convergence of the Two-Point Function of the Stationary TASEP

      • 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
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    2. Vortex Motion for the Landau-Lifshitz-Gilbert Equation with Applied Magnetic Field

      • Matthias Kurzke, Christof Melcher, Roger Moser
      Pages 113-132

    3. On Prandtl-Reuss Mixtures

      • Jens Frehse, Josef Málek
      Pages 133-169

    4. Modeling and Simulation of Lipid Monolayers as Surfactant in Lung Alveoli

      • Annelene Wittenfeld, Andrey Ryskin, Wolfgang Alt
      Pages 171-189

    5. Fluid Mixtures and Applications to Biological Systems

      • Hans Wilhelm Alt, Wolfgang Alt
      Pages 191-219

    6. A Nested Variational Time Discretization for Parametric Anisotropic Willmore Flow

      • Ricardo Perl, Paola Pozzi, Martin Rumpf
      Pages 221-241

    7. Energy Scaling and Domain Branching in Solid-Solid Phase Transitions

      • Allan Chan, Sergio Conti
      Pages 243-260

  4. Numerics for Multiscale Models and Singular Phenomena

    1. Front Matter

      Pages 261-261
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    2. On a Multilevel Preconditioner and its Condition Numbers for the Discretized Laplacian on Full and Sparse Grids in Higher Dimensions

      • Michael Griebel, Alexander Hullmann
      Pages 263-296

    3. Simulation of Droplet Impact with Dynamic Contact Angle Boundary Conditions

      • Michael Griebel, Margrit Klitz
      Pages 297-325

    4. A Parallel Multiscale Simulation Toolbox for Coupling Molecular Dynamics and Finite Elements

      • Dorian Krause, Konstantin Fackeldey, Rolf Krause
      Pages 327-346

    5. A Moving Least Squares Approach to the Construction of Discontinuous Enrichment Functions

      • Marc Alexander Schweitzer, Sa Wu
      Pages 347-360

    6. Second Moment Analysis for Robin Boundary Value Problems on Random Domains

      • Helmut Harbrecht
      Pages 361-381
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Keywords

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.

Editors and Affiliations

  • Universität Bonn Institut für Numerische Simulation, Bonn, Germany

    Michael Griebel

About the editor

Michael Griebel is Editor-in-Chief of the journal Numerische Mathematik, and is in the LNCSE Editorial Board. He is also co-editor with Marc Alexander Schweitzer of several LNCSE volumes on Meshfree Methods for Partial Differential Equations, which have been published regularly every two year.

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