Multiscale Methods: Bridging the Scales in Science and Engineering

Hardcover | October 22, 2010

EditorJacob Fish

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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, andsimulations 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 the transfer of information? What are the optimal ways to achieve such transfer of information? How canvariability of physical parameters at multiple scales be quantified and how can it be accounted for to ensure design robustness?Various 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 itsgross response is infused into the continuum scale. The issue of reliability of multiscale modeling and simulation tools is discussed in several, which focus on hierarchy of multiscale models and a posterior model error estimation including uncertainty quantification. Component software that can beeffectively combined to address a wide range of multiscale simulations is described as well. Applications range from advanced materials, to nanoelectromechanical systems (NEMS), to biological systems, and nanoporous catalysts where physical phenomena operates across 12 orders of magnitude in timescales and 10 orders of magnitude in spatial scales. 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.

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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, andsimulations and to address the following barriers...

Dr Fish is The Rosalind and John J. Redfern Jr. '33 Chaired Professor in Engineering at the Renssalaer Polytechnic Institute and a Fellow of the American Academy of Mechanics, United States Association for Computational Mechanics, and the International Association for Computational Mechanics. He has written over 150 articles and book ...

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Format:HardcoverDimensions:456 pages, 9.21 × 6.14 × 0.98 inPublished:October 22, 2010Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199233853

ISBN - 13:9780199233854

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Table of Contents

Preface1. Information-Passing Multiscale Methods in Space1. J. E. Aarnes (SINTEF, Norway), Y. Efendiev (Texas AandM), T.Y. Hou (Caltech), L. Jiang (Texas AandM): Mixed multiscale finite element methods on adaptive unstructured grids using limited global information2. R.C. Picu and M.A. Soare: Formulations of Mechanics problems for materials with self-similar multiscale microstructure3. J. Fish and Z. Yuan (Rensselaer): N-scale Model Reduction Theory2. Concurrent Multiscale Methods in Space4. T. Belytschko, R. Gracie and M. Xu (Northwestern): Concurrent Coupling of Atomistic and Continuum Models5. R.E. Rudd (Lawrence Livermore National Laboratory): Coarse-grained molecular dynamics: Concurrent Multiscale Simulation at Finite Temperature6. M. Gunzburger (FSU), P. Bochev, R. Lehoucq (Sandia): Atomistic to continuum coupling3. Space-Time Scale Bridging Methods7. A. Brandt (Weizmann Institute and UCLA): Methods of Systematic Upscaling8. G. Samaey (Leuven, Belgium), A. J. Roberts (U. of Southern Queensland, Australia), and I. G. Kevrekidis (Princeton): Equation-free computation: an overview of patch dynamics9. P. Ladeveze, D. Neron, J.-C. Passieux (LMT-Cachan, France): On multiscale computational mechanics with time-space homogenization4. Adaptivity, Error Estimation and Uncertainty Quantification10. J. T. Oden, S. Prudhomme, P. Bauman, and L. Chamoin (U. of Texas): Estimation and Control of Modeling Error: A General Approach to Multiscale Modeling11. D. Estep (U. Colorado): Error Estimates for Multiscale Methods for Multiphysics Problems5. Multiscale Software12. M.S. Shephard, M.A. Nuggehally, B. Franz Dale, C.R. Picu and J. Fish (Rensselaer): Component Software for Multiscale Simulation6. Selected Multiscale Applications13. Z. Tang and N. R. Aluru (University of Illinois at Urbana-Champaign): Finite Temperature Multiscale Methods for Silicon NEMS14. Sidney Yip (MIT): Multiscale materials15. Tamar Schlick (NYU): From Macroscopic to Mesoscopic Models of Chromatin Folding16. Marc-Olivier Coppens (Rensselaer and Delft): Multiscale Nature Inspired Chemical Engineering