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The Periodic Unfolding Method

The Periodic Unfolding Method
Author: Doina Cioranescu
Publisher: Springer
Total Pages: 515
Release: 2018-11-03
Genre: Mathematics
ISBN: 9811330328

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This is the first book on the subject of the periodic unfolding method (originally called "éclatement périodique" in French), which was originally developed to clarify and simplify many questions arising in the homogenization of PDE's. It has since led to the solution of some open problems. Written by the three mathematicians who developed the method, the book presents both the theory as well as numerous examples of applications for partial differential problems with rapidly oscillating coefficients: in fixed domains (Part I), in periodically perforated domains (Part II), and in domains with small holes generating a strange term (Part IV). The method applies to the case of multiple microscopic scales (with finitely many distinct scales) which is connected to partial unfolding (also useful for evolution problems). This is discussed in the framework of oscillating boundaries (Part III). A detailed example of its application to linear elasticity is presented in the case of thin elastic plates (Part V). Lastly, a complete determination of correctors for the model problem in Part I is obtained (Part VI). This book can be used as a graduate textbook to introduce the theory of homogenization of partial differential problems, and is also a must for researchers interested in this field.


An Introduction to Homogenization

An Introduction to Homogenization
Author: Doïna Cioranescu
Publisher: Oxford University Press on Demand
Total Pages: 262
Release: 1999
Genre: Mathematics
ISBN: 9780198565543

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Composite materials are widely used in industry: well-known examples of this are the superconducting multi-filamentary composites which are used in the composition of optical fibres. Such materials are complicated to model, as different points in the material will have different properties. The mathematical theory of homogenization is designed to deal with this problem, and hence is used to model the behaviour of these important materials. This book provides a self-contained and authoritative introduction to the subject for graduates and researchers in the field.


Multiscale Problems

Multiscale Problems
Author: Alain Damlamian
Publisher: World Scientific
Total Pages: 316
Release: 2011-10-13
Genre: Mathematics
ISBN: 9814458120

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The focus of this is on the latest developments related to the analysis of problems in which several scales are presented. After a theoretical presentation of the theory of homogenization in the periodic case, the other contributions address a wide range of applications in the fields of elasticity (asymptotic behavior of nonlinear elastic thin structures, modeling of junction of a periodic family of rods with a plate) and fluid mechanics (stationary Navier–Stokes equations in porous media). Other applications concern the modeling of new composites (electromagnetic and piezoelectric materials) and imperfect transmission problems. A detailed approach of numerical finite element methods is also investigated. Contents:An Introduction to Periodic Homogenization (Alain Damlamian)The Periodic Unfolding Method in Homogenization (Alain Damlamian)Deterministic Homogenization of Stationary Navier–Stokes Type Equations (Gabriel Nguetseng & Lazarus Signing)Homogenization of a Class of Imperfect Transmission Problems (Patricia Donato)Decompositions of Displacements of Thin Structures (Georges Griso)Decomposition of Rods Deformations. Asymptotic Behavior of Nonlinear Elastic Rods (Georges Griso)Junction of a Periodic Family of Rods with a Plate in Elasticity (Dominique Blanchard)Multi-scale Modelling of New Composites: Theory and Numerical Simulation (Bernadette Miara)A Priori and a Posteriori Error Analysis for Numerical Homogenization: A Unified Framework (Assyr Abdulle) Readership: PhD students and researchers in applied mathematics, mechanics, physics and engineering. Keywords:Multiscale Problem;Homogenization;Asymptotic Behavior;Approximation


Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics

Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics
Author: G. F. Roach
Publisher: Princeton University Press
Total Pages: 400
Release: 2012-03-04
Genre: Mathematics
ISBN: 1400842654

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Electromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature. Because of their wide range of important applications, these materials have been intensely studied over the past twenty-five years, mainly from the perspectives of physics and engineering. But a body of rigorous mathematical theory has also gradually developed, and this is the first book to present that theory. Designed for researchers and advanced graduate students in applied mathematics, electrical engineering, and physics, this book introduces the electromagnetics of complex media through a systematic, state-of-the-art account of their mathematical theory. The book combines the study of well posedness, homogenization, and controllability of Maxwell equations complemented with constitutive relations describing complex media. The book treats deterministic and stochastic problems both in the frequency and time domains. It also covers computational aspects and scattering problems, among other important topics. Detailed appendices make the book self-contained in terms of mathematical prerequisites, and accessible to engineers and physicists as well as mathematicians.


Classical and Quantum Dynamics in Condensed Phase Simulations

Classical and Quantum Dynamics in Condensed Phase Simulations
Author: Bruce J Berne
Publisher: World Scientific
Total Pages: 880
Release: 1998-06-17
Genre: Science
ISBN: 9814496057

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The school held at Villa Marigola, Lerici, Italy, in July 1997 was very much an educational experiment aimed not just at teaching a new generation of students the latest developments in computer simulation methods and theory, but also at bringing together researchers from the condensed matter computer simulation community, the biophysical chemistry community and the quantum dynamics community to confront the shared problem: the development of methods to treat the dynamics of quantum condensed phase systems. This volume collects the lectures delivered there. Due to the focus of the school, the contributions divide along natural lines into two broad groups: (1) the most sophisticated forms of the art of computer simulation, including biased phase space sampling schemes, methods which address the multiplicity of time scales in condensed phase problems, and static equilibrium methods for treating quantum systems; (2) the contributions on quantum dynamics, including methods for mixing quantum and classical dynamics in condensed phase simulations and methods capable of treating all degrees of freedom quantum-mechanically. Contents:Barrier Crossing: Classical Theory of Rare but Important Events (D Chandler)Monte Carlo Simulations (D Frenkel)Molecular Dynamics Methods for the Enhanced Sampling of Phase Space (B J Berne)Constrained and Nonequilibrium Molecular Dynamics (G Ciccotti & M Ferrario)From Erying to Kramers: Computation of Diffusive Barrier Crossing Rates (M J Ruiz-Montero)Monte Carlo Methods for Sampling of Rare Event States (W Janke)Proton Transfer in Ice (D Marx)Nudged Elastic Band Method for Finding Minimum Energy Paths of Transitions (H Jónsson et al.)RAW Quantum Transition State Theory (G Mills et al.)Dynamics of Peptide Folding (R Elber et al.)Theoretical Studies of Activated Processes in Biological Ion Channels (B Roux & S Crouzy)The Semiclassical Initial Value Representation for Including Quantum Effects in Molecular Dynamics Simulations (W H Miller)Tunneling in the Condensed Phase: Barrier Crossing and Dynamical Control (N Makri)Feynman Path Centroid Methods for Condensed Phase Quantum Dynamics (G A Voth)Quantum Molecular Dynamics Using Wigner Representation (V S Filinov et al.)Nonadiabatic Molecular Dynamics Methods for Diffusion (D Laria et al.)and other papers Readership: Computational and statistical physicists. Keywords:Quantum;Molecular Dynamics;DynamicsReviews: “… this volume is a useful introduction to currently popular, and widely-used techniques in chemical and statistical physics. The authors are well-respected researchers in the field and the level is appropriate to graduate students and researchers.” Journal of Statistical Physics


Elements of Applied Bifurcation Theory

Elements of Applied Bifurcation Theory
Author: Yuri Kuznetsov
Publisher: Springer Science & Business Media
Total Pages: 648
Release: 2013-03-09
Genre: Mathematics
ISBN: 1475739788

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Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.


Some Topics in Industrial and Applied Mathematics

Some Topics in Industrial and Applied Mathematics
Author: Rolf Jeltsch
Publisher: Dr. Vuong Quan Hoang
Total Pages: 24
Release: 2007
Genre: Applied mathematics
ISBN: 7040219034

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The Shanghai Forum on Industrial and Applied Mathematics was organized in May 2006 on the occasion that many famous industrial and applied mathematicians gathered in Shanghai from different countries to participate in the Officers' Meeting and the Board Meeting of the ICIAM (International Council for Industrial and Applied Mathematics). This volume collects the material covered by the majority of the lectures of which reflects panoramically recent results and trends in industrial and applied mathematics. This book will be very useful for graduate students and researchers in industrial and applied mathematics.


The Mathematical Theory of Communication

The Mathematical Theory of Communication
Author: Claude E Shannon
Publisher: University of Illinois Press
Total Pages: 141
Release: 1998-09-01
Genre: Language Arts & Disciplines
ISBN: 025209803X

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Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.


Emerging Problems in the Homogenization of Partial Differential Equations

Emerging Problems in the Homogenization of Partial Differential Equations
Author: Patrizia Donato
Publisher: Springer Nature
Total Pages: 122
Release: 2021-02-01
Genre: Mathematics
ISBN: 3030620301

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This book contains some of the results presented at the mini-symposium titled Emerging Problems in the Homogenization of Partial Differential Equations, held during the ICIAM2019 conference in Valencia in July 2019. The papers cover a large range of topics, problems with weak regularity data involving renormalized solutions, eigenvalue problems for complicated shapes of the domain, homogenization of partial differential problems with strongly alternating boundary conditions of Robin type with large parameters, multiscale analysis of the potential action along a neuron with a myelinated axon, and multi-scale model of magnetorheological suspensions. The volume is addressed to scientists who deal with complex systems that presents several elements (characteristics, constituents...) of very different scales, very heterogeneous, and search for homogenized models providing an effective (macroscopic) description of their behaviors.


Mystery of the Periodic Table

Mystery of the Periodic Table
Author: Benjamin D Wiker
Publisher: Bethlehem Books
Total Pages: 145
Release: 2003-04-18
Genre: Juvenile Fiction
ISBN: 188393771X

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Leads the reader on a delightful and absorbing journey through the ages, on the trail of the elements of the Periodic Table as we know them today. He introduces the young reader to people like Von Helmont, Boyle, Stahl, Priestly, Cavendish, Lavoisier, and many others, all incredibly diverse in personality and approach, who have laid the groundwork for a search that is still unfolding to this day. The first part of Wiker's witty and solidly instructive presentation is most suitable to middle school age, while the later chapters are designed for ages 12-13 and up, with a final chapter somewhat more advanced. Illustrated by Jeanne Bendick and Ted Schluenderfritz.