Singular Phenomena and Scaling in Mathematical Models, 1st Edition

  • Published By:
  • ISBN-10: 3319007866
  • ISBN-13: 9783319007861
  • DDC: 511.8
  • Grade Level Range: College Freshman - College Senior
  • 434 Pages | eBook
  • Original Copyright 2014 | Published/Released June 2014
  • This publication's content originally published in print form: 2014

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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.

Table of Contents

Front Cover.
Half Title Page.
Title Page.
Copyright Page.
1: Scaling Limits of Diffusion Processes and Singular Spaces.
2: Ricci Bounds for Euclidean and Spherical Cones.
3: A Monotone Approximation to the Wasserstein Diffusion.
4: Adapted Function Spaces for Dispersive Equations.
5: A Note on Metastable Behaviour in the Zero-Range Process.
6: Convergence of the Two-Point Function of the Stationary TASEP.
7: Multiple Scales in Mathematical Models of Materials Science and Biology.
8: Vortex Motion for the Landau-Lifshitz-Gilbert Equation with Applied Magnetic Field.
9: On Prandtl-Reuss Mixtures.
10: Modeling and Simulation of Lipid Monolayers as Surfactant in Lung Alveoli.
11: Fluid Mixtures and Applications to Biological Systems.
12: A Nested Variational Time Discretization for Parametric Anisotropic Willmore Flow.
13: Energy Scaling and Domain Branching in Solid-Solid Phase Transitions.
14: Numerics for Multiscale Models and Singular Phenomena.
15: On a Multilevel Preconditioner and Its Condition Numbers for the Discretized Laplacian on Full and Sparse Grids in Higher Dimensions.
16: Simulation of Droplet Impact with Dynamic Contact Angle Boundary Conditions.
17: A Parallel Multiscale Simulation Toolbox for Coupling Molecular Dynamics and Finite Elements.
18: A Moving Least Squares Approach to the Construction of Discontinuous Enrichment Functions.
19: Second Moment Analysis for Robin Boundary Value Problems on Random Domains.
20: Simulation of Q-Tensor Fields with Constant Orientational Order Parameter in the Theory of Uniaxial Nematic Liquid Crystals.
21: A Fast and Accurate Numerical Method for the Computation of Unstable Micromagnetic Configurations.