Singular Phenomena And Scaling In Mathematical Models

Author : Michael Griebel
Publisher : Springer Science & Business Media
ISBN 13 : 3319007866
Total Pages : 434 pages
Book Rating : 4.61/5 ( download)

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Download or read book Singular Phenomena and Scaling in Mathematical Models written by Michael Griebel and published by Springer Science & Business Media. This book was released on 2013-11-18 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Axel Voigt
Publisher : Springer Science & Business Media
ISBN 13 : 3764373431
Total Pages : 240 pages
Book Rating : 4.36/5 ( download)

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Download or read book Multiscale Modeling in Epitaxial Growth written by Axel Voigt and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Malena I. Español
Publisher : Springer Nature
ISBN 13 : 3031044967
Total Pages : 514 pages
Book Rating : 4.60/5 ( download)

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Download or read book Research in Mathematics of Materials Science written by Malena I. Español and published by Springer Nature. This book was released on 2022-09-27 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume highlights contributions of women mathematicians in the study of complex materials and includes both original research papers and reviews. The featured topics and methods draw on the fields of Calculus of Variations, Partial Differential Equations, Functional Analysis, Differential Geometry and Topology, as well as Numerical Analysis and Mathematical Modelling. Areas of applications include foams, fluid-solid interactions, liquid crystals, shape-memory alloys, magnetic suspensions, failure in solids, plasticity, viscoelasticity, homogenization, crystallization, grain growth, and phase-field models.

Author : J. Eggers
Publisher : Cambridge University Press
ISBN 13 : 1107098416
Total Pages : 471 pages
Book Rating : 4.11/5 ( download)

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Download or read book Singularities: Formation, Structure and Propagation written by J. Eggers and published by Cambridge University Press. This book was released on 2015-09-10 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores a wide range of singular phenomena, providing mathematical tools for understanding them and highlighting their common features.

Author : Alfredo Bermúdez de Castro
Publisher : Springer Science & Business Media
ISBN 13 : 3540342885
Total Pages : 1202 pages
Book Rating : 4.85/5 ( download)

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Download or read book Numerical Mathematics and Advanced Applications written by Alfredo Bermúdez de Castro and published by Springer Science & Business Media. This book was released on 2007-10-08 with total page 1202 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings collect lectures given at ENUMATH 2005, the 6th European Conference on Numerical Mathematics and Advanced Applications held in Santiago de Compostela, Spain in July, 2005. Topics include applications such as fluid dynamics, electromagnetism, structural mechanics, interface problems, waves, finance, heat transfer, unbounded domains, numerical linear algebra, convection-diffusion, as well as methodologies such as a posteriori error estimates, discontinuous Galerkin methods, multiscale methods, optimization, and more.

Author : Wolfgang Alt
Publisher : Birkhäuser
ISBN 13 : 303488043X
Total Pages : 308 pages
Book Rating : 4.35/5 ( download)

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Download or read book Polymer and Cell Dynamics written by Wolfgang Alt and published by Birkhäuser. This book was released on 2012-12-06 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Martin Grötschel
Publisher : Springer Science & Business Media
ISBN 13 : 364211248X
Total Pages : 405 pages
Book Rating : 4.85/5 ( download)

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Download or read book Production Factor Mathematics written by Martin Grötschel and published by Springer Science & Business Media. This book was released on 2010-08-05 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics as a production factor or driving force for innovation? Those, who want to know and understand why mathematics is deeply involved in the design of products, the layout of production processes and supply chains will find this book an indispensable and rich source. Describing the interplay between mathematical and engineering sciences the book focusses on questions like How can mathematics improve to the improvement of technological processes and products? What is happening already? Where are the deficits? What can we expect for the future? 19 articles written by mixed teams of authors of engineering, industry and mathematics offer a fascinating insight of the interaction between mathematics and engineering.

Author : Malte Henkel
Publisher : Springer Science & Business Media
ISBN 13 : 3662039370
Total Pages : 433 pages
Book Rating : 4.73/5 ( download)

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Download or read book Conformal Invariance and Critical Phenomena written by Malte Henkel and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Critical phenomena arise in a wide variety of physical systems. Classi cal examples are the liquid-vapour critical point or the paramagnetic ferromagnetic transition. Further examples include multicomponent fluids and alloys, superfluids, superconductors, polymers and fully developed tur bulence and may even extend to the quark-gluon plasma and the early uni verse as a whole. Early theoretical investigators tried to reduce the problem to a very small number of degrees of freedom, such as the van der Waals equation and mean field approximations, culminating in Landau's general theory of critical phenomena. Nowadays, it is understood that the common ground for all these phenomena lies in the presence of strong fluctuations of infinitely many coupled variables. This was made explicit first through the exact solution of the two-dimensional Ising model by Onsager. Systematic subsequent developments have been leading to the scaling theories of critical phenomena and the renormalization group which allow a precise description of the close neighborhood of the critical point, often in good agreement with experiments. In contrast to the general understanding a century ago, the presence of fluctuations on all length scales at a critical point is emphasized today. This can be briefly summarized by saying that at a critical point a system is scale invariant. In addition, conformal invaTiance permits also a non-uniform, local rescal ing, provided only that angles remain unchanged.

Author : Nicola Gigli
Publisher : American Mathematical Soc.
ISBN 13 : 1470427656
Total Pages : 161 pages
Book Rating : 4.58/5 ( download)

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Download or read book Nonsmooth Differential Geometry–An Approach Tailored for Spaces with Ricci Curvature Bounded from Below written by Nicola Gigli and published by American Mathematical Soc.. This book was released on 2018-02-23 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author discusses in which sense general metric measure spaces possess a first order differential structure. Building on this, spaces with Ricci curvature bounded from below a second order calculus can be developed, permitting the author to define Hessian, covariant/exterior derivatives and Ricci curvature.

Author :
Publisher : Elsevier
ISBN 13 : 0444640045
Total Pages : 710 pages
Book Rating : 4.48/5 ( download)

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Download or read book Geometric Partial Differential Equations - Part I written by and published by Elsevier. This book was released on 2020-01-14 with total page 710 pages. Available in PDF, EPUB and Kindle. Book excerpt: Besides their intrinsic mathematical interest, geometric partial differential equations (PDEs) are ubiquitous in many scientific, engineering and industrial applications. They represent an intellectual challenge and have received a great deal of attention recently. The purpose of this volume is to provide a missing reference consisting of self-contained and comprehensive presentations. It includes basic ideas, analysis and applications of state-of-the-art fundamental algorithms for the approximation of geometric PDEs together with their impacts in a variety of fields within mathematics, science, and engineering. About every aspect of computational geometric PDEs is discussed in this and a companion volume. Topics in this volume include stationary and time-dependent surface PDEs for geometric flows, large deformations of nonlinearly geometric plates and rods, level set and phase field methods and applications, free boundary problems, discrete Riemannian calculus and morphing, fully nonlinear PDEs including Monge-Ampere equations, and PDE constrained optimization Each chapter is a complete essay at the research level but accessible to junior researchers and students. The intent is to provide a comprehensive description of algorithms and their analysis for a specific geometric PDE class, starting from basic concepts and concluding with interesting applications. Each chapter is thus useful as an introduction to a research area as well as a teaching resource, and provides numerous pointers to the literature for further reading The authors of each chapter are world leaders in their field of expertise and skillful writers. This book is thus meant to provide an invaluable, readable and enjoyable account of computational geometric PDEs