Small scale features and processes occurring at a nanometer and femtoseconds scales have a profound impact on what happens at a larger scale and over extensive period of time. This text reflects the state-of-art in multiscale mathematics, modelling and simulations and addresses current challenges through a series of edited chapters written by leading experts in the field. The volume is intended as a 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.
Preface 1. Information-Passing Multiscale Methods in Space 1: J. E. Aarnes (SINTEF, Norway), Y. Efendiev (Texas A&M), T.Y. Hou (Caltech), L. Jiang (Texas A&M): Mixed multiscale finite element methods on adaptive unstructured grids using limited global information 2: R.C. Picu and M.A. Soare: Formulations of Mechanics problems for materials with self-similar multiscale microstructure 3: J. Fish and Z. Yuan (Rensselaer): N-scale Model Reduction Theory 2. Concurrent Multiscale Methods in Space 4: T. Belytschko, R. Gracie and M. Xu (Northwestern): Concurrent Coupling of Atomistic and Continuum Models 5: R.E. Rudd (Lawrence Livermore National Laboratory): Coarse-grained molecular dynamics: Concurrent Multiscale Simulation at Finite Temperature 6: M. Gunzburger (FSU), P. Bochev, R. Lehoucq (Sandia): Atomistic to continuum coupling 3. Space-Time Scale Bridging Methods 7: A. Brandt (Weizmann Institute and UCLA): Methods of Systematic Upscaling 8: G. Samaey (Leuven, Belgium), A. J. Roberts (U. of Southern Queensland, Australia), and I. G. Kevrekidis (Princeton): Equation-free computation: an overview of patch dynamics 9: P. Ladeveze, D. Neron, J.-C. Passieux (LMT-Cachan, France): On multiscale computational mechanics with time-space homogenization 4. Adaptivity, Error Estimation and Uncertainty Quantification 10: J. T. Oden, S. Prudhomme, P. Bauman, and L. Chamoin (U. of Texas): Estimation and Control of Modeling Error: A General Approach to Multiscale Modeling 11: D. Estep (U. Colorado): Error Estimates for Multiscale Methods for Multiphysics Problems 5. Multiscale Software 12: M.S. Shephard, M.A. Nuggehally, B. Franz Dale, C.R. Picu and J. Fish (Rensselaer): Component Software for Multiscale Simulation 6. Selected Multiscale Applications 13: Z. Tang and N. R. Aluru (University of Illinois at Urbana-Champaign): Finite Temperature Multiscale Methods for Silicon NEMS 14: Sidney Yip (MIT): Multiscale materials 15: Tamar Schlick (NYU): From Macroscopic to Mesoscopic Models of Chromatin Folding 16: Marc-Olivier Coppens (Rensselaer and Delft): Multiscale Nature Inspired Chemical Engineering
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 chapters on the subject of multiscale computational science. Dr. Fish received numerous NSF awards including Young Investigator Award, NASA Langley research grant related to High Speed Civil Transport (HSCT), contracts from Lockheed Missiles & Space Company, Sikorski, ALCOA, Northrop-Grumman, GE, Rolls-Royce, Allison Engines, GM, Chrysler and Ford on various aspects of structural integrity; NSF, AFOSR, ONR, SANDIA and DARPA grants for development of multiscale computational techniques. He is currently directing the National Science Foundation Nanoscale Interdisciplinary Research Teams (NIRT) program at Rensselaer.