Singular Phenomena and Scaling in Mathematical Models

Singular Phenomena and Scaling in Mathematical Models

Author: Michael Griebel

Publisher: Springer Science & Business Media

ISBN: 3319007866

Page: 434

View: 6585

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.
Categories: Computers

Multiscale Modeling in Epitaxial Growth

Multiscale Modeling in Epitaxial Growth

Author: Axel Voigt

Publisher: Springer Science & Business Media

ISBN: 3764373431

Page: 240

View: 7235

Epitaxy is relevant for thin film growth and is a very active area of theoretical research since several years. Recently powerful numerical techniques have been used to link atomistic effects at the film's surface to its macroscopic morphology. This book also serves as an introduction into this highly active interdisciplinary field of research for applied mathematicians, theoretical physicists and computational materials scientists.
Categories: Mathematics

Polymer and Cell Dynamics

Multiscale Modelling and Numerical Simulations

Polymer and Cell Dynamics

Author: Wolfgang Alt,Mark Chaplain,Michael Griebel,Jürgen Lenz

Publisher: Birkhäuser

ISBN: 303488043X

Page: 308

View: 2136

Polymer and cell dynamics play an important role in processes like tumor growth, metastasis, embryogenesis, immune reactions and regeneration. Based on an international workshop on numerical simulations of polymer and cell dynamics in Bad Honnef (Germany) in 2000, this volume provides an overview of the relevant mathematical and numerical methods, their applications and limits. Polymer and Cell Dynamics will be of interest to scientists and advanced undergraduates.
Categories: Mathematics

Meshfree Methods for Partial Differential Equations V

Meshfree Methods for Partial Differential Equations V

Author: Michael Griebel,Marc Alexander Schweitzer

Publisher: Springer Science & Business Media

ISBN: 9783642162299

Page: 270

View: 8769

The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is an extremely active research field, both in the mathematics and engineering communities. Meshfree methods are becoming increasingly mainstream in various applications. Due to their independence of a mesh, particle schemes and meshfree methods can deal with large geometric changes of the domain more easily than classical discretization techniques. Furthermore, meshfree methods offer a promising approach for the coupling of particle models to continuous models. This volume of LNCSE is a collection of the papers from the proceedings of the Fifth International Workshop on Meshfree Methods, held in Bonn in August 2009. The articles address the different meshfree methods and their use in applied mathematics, physics and engineering. The volume is intended to foster this highly active and exciting area of interdisciplinary research and to present recent advances and findings in this field.
Categories: Mathematics

Current Trends in Potential Theory

Conference Proceedings, Bucharest (Romania), September 2002 and 2003

Current Trends in Potential Theory

Author: Dominique Bakry

Publisher: Fundatia Theta Editura

ISBN: N.A

Page: 173

View: 1436

This is the proceedings volume of two mathematical meetings on Potential Theory organized in Bucharest, Romania, in September 2002 and September 2003. It includes six survey articles and seven selected research papers, covering the main topics of the conferences: geometric aspects in potential theory, Dirichlet structures, stochastic analysis, potential theory, and Markov processes.
Categories: Mathematics

Analyzing Multiscale Phenomena Using Singular Perturbation Methods

American Mathematical Society Short Course, January 5-6, 1998, Baltimore, Maryland

Analyzing Multiscale Phenomena Using Singular Perturbation Methods

Author: Jane Cronin

Publisher: American Mathematical Soc.

ISBN: 0821809296

Page: 187

View: 674

To understand multiscale phenomena, it is essential to employ asymptotic methods to construct approximate solutions and to design effective computational algorithms. This volume consists of articles based on the AMS Short Course in Singular Perturbations held at the annual Joint Mathematics Meetings in Baltimore (MD). Leading experts discussed the following topics which they expand upon in the book: boundary layer theory, matched expansions, multiple scales, geometric theory, computational techniques, and applications in physiology and dynamic metastability. Readers will find that this text offers an up-to-date survey of this important field with numerous references to the current literature, both pure and applied.
Categories: Mathematics

Mathematical Modelling of Wave Phenomena

2nd Conference on Mathematical Modeling of Wave Phenomena

Mathematical Modelling of Wave Phenomena

Author: Börje Nilsson,Louis Fishman

Publisher: American Institute of Physics

ISBN: N.A

Page: 378

View: 3463

This conference series intends to illuminate the relationship between different types of waves. This second conference focused primarily on classical wave modeling of acoustic waves in solids and fluids, electromagnetic waves, as well as elastic wave modeling, and both direct and inverse problems are addressed. Topics included are: (1) Classical linear wave propagation modeling, analysis and computation: general, electromagnetic applications, acoustics of fluids, acoustics of solids; (2) classical nonlinear wave propagation modeling, analysis, and computation; (3) inverse scattering modeling: gneral and electromagnetic imaging, wood imaging, seismic imaging; (4) quantum and statistical mechanics; (5) signal processing and analysis.
Categories: Science

Macroscopic Models for Vehicular Flows and Crowd Dynamics: Theory and Applications

Classical and Non–Classical Advanced Mathematics for Real Life Applications

Macroscopic Models for Vehicular Flows and Crowd Dynamics: Theory and Applications

Author: Massimiliano Daniele Rosini

Publisher: Springer

ISBN: 3319001558

Page: 242

View: 8437

This monograph presents a systematic treatment of the theory for hyperbolic conservation laws and their applications to vehicular traffics and crowd dynamics. In the first part of the book, the author presents very basic considerations and gradually introduces the mathematical tools necessary to describe and understand the mathematical models developed in the following parts focusing on vehicular and pedestrian traffic. The book is a self-contained valuable resource for advanced courses in mathematical modeling, physics and civil engineering. A number of examples and figures facilitate a better understanding of the underlying concepts and motivations for the students. Important new techniques are presented, in particular the wave front tracking algorithm, the operator splitting approach, the non-classical theory of conservation laws and the constrained problems. This book is the first to present a comprehensive account of these fundamental new mathematical advances.
Categories: Technology & Engineering