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Author : Kenneth M Golden,Geoffrey R Grimmett,Richard D James
Publisher : Unknown
Page : 300 pages
File Size : 45,9 Mb
Release : 1998-06-26
Category : Electronic
ISBN : 1461217296
Author : Kenneth M. Golden,Geoffrey R. Grimmett,Richard D. James,Graeme W. Milton,Pabitra N. Sen
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461217282
The 1995-1996 program at the Institute for Mathematics and its Applications was devoted to mathematical methods in material science, and was attended by materials scientists, physicists, geologists, chemists engineers, and mathematicians. This volume contains chapters which emerged from four of the workshops, focusing on disordered materials; interfaces and thin films; mechanical response of materials from angstroms to meters; and phase transformation, composite materials and microstructure. The scales treated in these workshops ranged from the atomic to the macroscopic, the microstructures from ordered to random, and the treatments from "purely" theoretical to highly applied. Taken together, these results form a compelling and broad account of many aspects of the science of multi-scale materials, and will hopefully inspire research across the self-imposed barriers of twentieth century science.
Author : Weizhu Bao,Qiang Du
Publisher : World Scientific
Page : 285 pages
File Size : 40,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814360890
The Institute for Mathematical Sciences at the National University of Singapore hosted a two-month research program on "Mathematical Theory and Numerical Methods for Computational Materials Simulation and Design" from 1 July to 31 August 2009. As an important part of the program, tutorials and special lectures were given by leading experts in the fields for participating graduate students and junior researchers. This invaluable volume collects four expanded lecture notes with self-contained tutorials. They cover a number of aspects on multiscale modeling, analysis and simulations for problems arising from materials science including some critical components in computational prediction of materials properties such as the multiscale properties of complex materials, properties of defects, interfaces and material microstructures under different conditions, critical issues in developing efficient numerical methods and analytic frameworks for complex and multiscale materials models. This volume serves to inspire graduate students and researchers who choose to embark into original research work in these fields.
Author : Weinan E
Publisher : Cambridge University Press
Page : 485 pages
File Size : 50,9 Mb
Release : 2011-07-07
Category : Mathematics
ISBN : 9781107096547
A systematic discussion of the fundamental principles, written by a leading contributor to the field.
Author : Martin Oliver Steinhauser
Publisher : Springer
Page : 405 pages
File Size : 48,6 Mb
Release : 2016-11-29
Category : Science
ISBN : 9783662532249
The idea of the book is to provide a comprehensive overview of computational physics methods and techniques, that are used for materials modeling on different length and time scales. Each chapter first provides an overview of the basic physical principles which are the basis for the numerical and mathematical modeling on the respective length-scale. The book includes the micro-scale, the meso-scale and the macro-scale, and the chapters follow this classification. The book explains in detail many tricks of the trade of some of the most important methods and techniques that are used to simulate materials on the perspective levels of spatial and temporal resolution. Case studies are included to further illustrate some methods or theoretical considerations. Example applications for all techniques are provided, some of which are from the author’s own contributions to some of the research areas. The second edition has been expanded by new sections in computational models on meso/macroscopic scales for ocean and atmosphere dynamics. Numerous applications in environmental physics and geophysics had been added.
Author : Young Kwon,David H. Allen,Ramesh R. Talreja
Publisher : Springer Science & Business Media
Page : 634 pages
File Size : 46,9 Mb
Release : 2007-12-04
Category : Technology & Engineering
ISBN : 9780387363189
This book presents the state-of-the-art in multiscale modeling and simulation techniques for composite materials and structures. It focuses on the structural and functional properties of engineering composites and the sustainable high performance of components and structures. The multiscale techniques can be also applied to nanocomposites which are important application areas in nanotechnology. There are few books available on this topic.
Author : Alain Damlamian,Bernadette Miara,Tatsien Li
Publisher : World Scientific
Page : 316 pages
File Size : 52,5 Mb
Release : 2011-10-13
Category : Mathematics
ISBN : 9789814458122
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
Author : Tomasz Sadowski,Patrizia Trovalusci
Publisher : Springer
Page : 278 pages
File Size : 46,8 Mb
Release : 2014-10-14
Category : Science
ISBN : 9783709118122
The papers in this volume deal with materials science, theoretical mechanics and experimental and computational techniques at multiple scales, providing a sound base and a framework for many applications which are hitherto treated in a phenomenological sense. The basic principles are formulated of multiscale modeling strategies towards modern complex multiphase materials subjected to various types of mechanical, thermal loadings and environmental effects. The focus is on problems where mechanics is highly coupled with other concurrent physical phenomena. Attention is also focused on the historical origins of multiscale modeling and foundations of continuum mechanics currently adopted to model non-classical continua with substructure, for which internal length scales play a crucial role.
Author : Leonid Berlyand,Volodymyr Rybalko
Publisher : Springer
Page : 178 pages
File Size : 40,6 Mb
Release : 2018-11-22
Category : Computers
ISBN : 9783030017774
The objective of this book is to navigate beginning graduate students in mathematics and engineering through a mature field of multiscale problems in homogenization theory and to provide an idea of its broad scope. An overview of a wide spectrum of homogenization techniques ranging from classical two-scale asymptotic expansions to Gamma convergence and the rapidly developing field of stochastic homogenization is presented. The mathematical proofs and definitions are supplemented with intuitive explanations and figures to make them easier to follow. A blend of mathematics and examples from materials science and engineering is designed to teach a mixed audience of mathematical and non-mathematical students.
Author : Alexander Mielke
Publisher : Springer Science & Business Media
Page : 697 pages
File Size : 48,7 Mb
Release : 2006-10-14
Category : Mathematics
ISBN : 9783540356578
This book reports recent mathematical developments in the Programme "Analysis, Modeling and Simulation of Multiscale Problems", which started as a German research initiative in 2006. Multiscale problems occur in many fields of science, such as microstructures in materials, sharp-interface models, many-particle systems and motions on different spatial and temporal scales in quantum mechanics or in molecular dynamics. The book presents current mathematical foundations of modeling, and proposes efficient numerical treatment.
Author : Grigoris Pavliotis,Andrew Stuart
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 52,7 Mb
Release : 2008-01-18
Category : Mathematics
ISBN : 9780387738291
This introduction to multiscale methods gives you a broad overview of the methods’ many uses and applications. The book begins by setting the theoretical foundations of the methods and then moves on to develop models and prove theorems. Extensive use of examples shows how to apply multiscale methods to solving a variety of problems. Exercises then enable you to build your own skills and put them into practice. Extensions and generalizations of the results presented in the book, as well as references to the literature, are provided in the Discussion and Bibliography section at the end of each chapter.With the exception of Chapter One, all chapters are supplemented with exercises.
Author : Jacob Fish
Publisher : Oxford University Press on Demand
Page : 631 pages
File Size : 43,8 Mb
Release : 2010
Category : Mathematics
ISBN : 9780199233854
Small scale features and processes occurring at nanometer and femtosecond scales have a profound impact on what happens at a larger scale and over an extensive period of time. The primary objective of this volume is to reflect the state-of-the-art in multiscale mathematics, modeling, and simulations and to address the following barriers: What is the information that needs to be transferred from one model or scale to another and what physical principles must be satisfied during thetransfer of information? What are the optimal ways to achieve such transfer of information? How can variability of physical parameters at multiple scales be quantified and how can it be accounted for to ensure design robustness?The multiscale approaches in space and time presented in this volume are grouped into two main categories: information-passing and concurrent. In the concurrent approaches various scales are simultaneously resolved, whereas in the information-passing methods the fine scale is modeled and its gross response is infused into the continuum scale. The issue of reliability of multiscale modeling and simulation tools which focus on a hierarchy of multiscale models and an a posteriori model of errorestimation including uncertainty quantification, is discussed in several chapters. Component software that can be effectively combined to address a wide range of multiscale simulations is also described. Applications range from advanced materials to nanoelectromechanical systems (NEMS), biologicalsystems, and nanoporous catalysts where physical phenomena operates across 12 orders of magnitude in time scales and 10 orders of magnitude in spatial scales.This volume is a valuable reference book for scientists, engineers and graduate students practicing in traditional engineering and science disciplines as well as in emerging fields of nanotechnology, biotechnology, microelectronics and energy.
Author : Grigory Panasenko
Publisher : World Scientific
Page : 171 pages
File Size : 55,5 Mb
Release : 2022-06-29
Category : Mathematics
ISBN : 9781800612334
This book introduces the reader to multiscale mathematical modeling that starts by describing a physical process at the microscopic level, and is followed by the macroscopic description of that process. There are two preliminary chapters introducing the main equations of mathematical physics and serves as revision of all of the necessary mathematical notions needed to navigate the domain of multiscale research.The author gives a rigorous presentation of the tools of mathematical modeling, as well as an evaluation of the errors of the method. This allows readers to analyze the limitations and accuracy of the method.The book is accessible to a wide range of readers, from specialists in engineering to applied mathematicians working in the applications of materials science, biophysics and medicine.
Author : Pierre Deymier,Keith Runge,Krishna Muralidharan
Publisher : Springer
Page : 300 pages
File Size : 55,5 Mb
Release : 2015-11-25
Category : Science
ISBN : 9783319245294
This book presents cutting-edge concepts, paradigms, and research highlights in the field of computational materials science and engineering, and provides a fresh, up-to-date perspective on solving present and future materials challenges. The chapters are written by not only pioneers in the fields of computational materials chemistry and materials science, but also experts in multi-scale modeling and simulation as applied to materials engineering. Pedagogical introductions to the different topics and continuity between the chapters are provided to ensure the appeal to a broad audience and to address the applicability of integrated computational materials science and engineering for solving real-world problems.
Author : Ivan Giorgio,Luca Placidi,Emilio Barchiesi,Bilen Emek Abali,Holm Altenbach
Publisher : Springer Nature
Page : 739 pages
File Size : 55,8 Mb
Release : 2022-05-03
Category : Science
ISBN : 9783031045486
This book is devoted to the 60th birthday of the Prof. Francesco dell’Isola, who is known for his long-term contribution in the field of multiscale materials. It contains several contributions from researchers in the field, covering theoretical analyses, computational aspects and experiments.