## Multiscale Materials

*Sidney Yip*

### in Multiscale Methods: Bridging the Scales in Science and Engineering

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199233854
- eISBN:
- 9780191715532
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233854.003.0014
- Subject:
- Mathematics, Applied Mathematics

Modeling and simulation across different length and time scales enables atomic-level understanding of materials properties and behavior which manifest at the meso- and macro-scales. Case studies of ... More

## Numerical Simulation Of Microflows And Nanoflows

*Narayan R. Aluru and George Em Karniadakis*

### in Micro/Nano Technology Systems for Biomedical Applications: Microfluidics, Optics, and Surface Chemistry

- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199219698
- eISBN:
- 9780191594229
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199219698.003.0003
- Subject:
- Mathematics, Mathematical Biology

In this chapter we review recent advances in numerical simulation of micro and nanoflows. For coarse-grained simulation of microfuidics, we present an overview of Lattice Boltzmann, Brownian ... More

## Multiscale Sampling

*Thomas J. Stohlgren*

### in Measuring Plant Diversity: Lessons from the Field

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780195172331
- eISBN:
- 9780199790395
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195172331.003.0005
- Subject:
- Biology, Plant Sciences and Forestry

This chapter reveals that sampling plant diversity at multiple spatial scales may allow for a deeper understanding of relationships between species distributions and composition shifts relative to ... More

## Multiscale Methods: Bridging the Scales in Science and Engineering

*Jacob Fish (ed.)*

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199233854
- eISBN:
- 9780191715532
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233854.001.0001
- Subject:
- Mathematics, Applied Mathematics

Small scale features and processes occurring at nanometer and femtosecond scales have a profound impact on what happens at larger space and time scales. In view of the increasing need of ... More

## Error Estimates for Multiscale Operator Decomposition for Multiphysics Models

*D. Estep*

### in Multiscale Methods: Bridging the Scales in Science and Engineering

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199233854
- eISBN:
- 9780191715532
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233854.003.0011
- Subject:
- Mathematics, Applied Mathematics

Multiphysics, multiscale models present significant challenges in terms of computing accurate solutions and for estimating the error in information computed from numerical solutions. In this chapter, ... More

## Component Software for Multiscale Simulation

*M.S. Shephard, M.A. Nuggehally, B. FranzDale, C.R. Picu, J. Fish, O. Klaas, and M.W. Beall*

### in Multiscale Methods: Bridging the Scales in Science and Engineering

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199233854
- eISBN:
- 9780191715532
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233854.003.0012
- Subject:
- Mathematics, Applied Mathematics

Building on a general abstraction of the steps and transformations of a multiscale analysis, this chapter considers an approach to the development of multiscale simulation in which interoperable ... More

## Mixed Multiscale Finite Element Methods on Adaptive Unstructured Grids Using Limited Global Information

*J. E. Aarnes, Y. Efendiev, T.Y. Hou, and L. Jiang*

### in Multiscale Methods: Bridging the Scales in Science and Engineering

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199233854
- eISBN:
- 9780191715532
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233854.003.0001
- Subject:
- Mathematics, Applied Mathematics

We study mixed multiscale finite element methods (MsFEM) on unstructured coarse grids. Unstructured grids are often used when highly heterogeneous reservoirs are discretized via irregular anisotropic ... More

## Formulations of Mechanics Problems for Materials with Self-Similar Multiscale Microstructure

*R.C. Picu and M.A. Soare*

### in Multiscale Methods: Bridging the Scales in Science and Engineering

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199233854
- eISBN:
- 9780191715532
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233854.003.0002
- Subject:
- Mathematics, Applied Mathematics

A broad range of natural and man-made materials, such as the trabecular bone, aerogels have hierarchical microstructure. Performing efficient design of structures made from such materials requires ... More

## N-Scale Model Reduction Theory

*Jacob Fish and Zheng Yuan*

### in Multiscale Methods: Bridging the Scales in Science and Engineering

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199233854
- eISBN:
- 9780191715532
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233854.003.0003
- Subject:
- Mathematics, Applied Mathematics

A model reduction approach aimed at systematically reducing computational complexity of multiple scale homogenization for nonlinear history-dependent problems is developed. The so-called N-scale ... More

## Concurrent Coupling of Atomistic and Continuum Models

*Mei Xu*

### in Multiscale Methods: Bridging the Scales in Science and Engineering

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199233854
- eISBN:
- 9780191715532
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233854.003.0004
- Subject:
- Mathematics, Applied Mathematics

This chapter presents a review of concurrent multiscale methods for coupling continuum, molecular, and quantum mechanics with a particular emphasis on the Bridging Domain Method. An expanded taxonomy ... More

## Coarse-Grained Molecular Dynamics: Concurrent Multiscale Simulation at Finite Temperature Protect 1

*Robert E. Rudd*

### in Multiscale Methods: Bridging the Scales in Science and Engineering

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199233854
- eISBN:
- 9780191715532
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233854.003.0005
- Subject:
- Mathematics, Applied Mathematics

Coarse-grained molecular dynamics (CGMD) is a computer modeling technique that couples conventional molecular dynamics (MD) in some spatial regions of the simulation to a more coarse-grained ... More

## Blending Methods for Coupling Atomistic and Continuum Models

*P. Bochev, R. Lehoucq, M. Parks, S. Badia, and M. Gunzburger*

### in Multiscale Methods: Bridging the Scales in Science and Engineering

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199233854
- eISBN:
- 9780191715532
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233854.003.0006
- Subject:
- Mathematics, Applied Mathematics

We review some recent developments in the coupling of atomistic and continuum models based on the blending of the two models in an overlap, or bridge, subdomain. These coupling schemes resemble ... More

## Principles of systematic upscaling

*Achi Brandt*

### in Multiscale Methods: Bridging the Scales in Science and Engineering

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199233854
- eISBN:
- 9780191715532
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233854.003.0007
- Subject:
- Mathematics, Applied Mathematics

Building on the complementary advantages of Renormalization Group (RG) and multigrid (MG) methods, Systematic Upscaling (SU) comprises rigorous procedures for deriving suitable variables and ... More

## On Multiscale Computational Mechanics with Time-Space Homogenization

*P. Ladevèze, David Néron, and Jean-Charles Passieux*

### in Multiscale Methods: Bridging the Scales in Science and Engineering

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199233854
- eISBN:
- 9780191715532
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233854.003.0009
- Subject:
- Mathematics, Applied Mathematics

The chapter deals with multiple scales in both space and time. First, the state-of-the-art is presented. Then, we discuss a family of computational approaches using time-space homogenization. ... More

## MULTISCALE COMPUTER SIMULATION METHODS

*Nasr M. Ghoniem and Daniel D. Walgraef*

### in Instabilities and Self-Organization in Materials: Volume I: Fundamentals of Nanoscience, Volume II: Applications in Materials Design and Nanotechnology

- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780199298686
- eISBN:
- 9780191720222
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199298686.003.0010
- Subject:
- Physics, Condensed Matter Physics / Materials

Computational modelling of materials behaviour is becoming a reliable tool of scientific investigation, complementary to traditional theory and experimentation. The Multiscale Materials Modelling ... More

## The Bigger Picture: Integrated Multiscale Models

*Roger White, Guy Engelen, and Inge Uljee*

### in Modeling Cities and Regions As Complex Systems: From Theory to Planning Applications

- Published in print:
- 2015
- Published Online:
- May 2016
- ISBN:
- 9780262029568
- eISBN:
- 9780262331371
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262029568.003.0007
- Subject:
- Political Science, Environmental Politics

Spatial structure is the result of locational decisions reflecting criteria operating at a variety of scales. Thus the CA land use model is augmented with a regionalized, spatial interaction based ... More

## Dislocations, Mesoscale Simulations and Plastic Flow

*Ladislas Kubin*

- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780198525011
- eISBN:
- 9780191756238
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525011.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials

In the past twenty years, new experimental approaches, improved models and progress in simulation techniques have brought new insights into longstanding issues concerning dislocation-based plasticity ... More

## Atomistic Spin Dynamics: Foundations and Applications

*Olle Eriksson, Anders Bergman, Lars Bergqvist, and Johan Hellsvik*

- Published in print:
- 2017
- Published Online:
- May 2017
- ISBN:
- 9780198788669
- eISBN:
- 9780191830747
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198788669.001.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics

The purpose of this book is to provide a theoretical foundation and an understanding of atomistic spin-dynamics, and to give examples of where the atomistic Landau-Lifshitz-Gilbert equation can and ... More

## Multiscale organization

*Curtis Roads*

### in Composing Electronic Music: A New Aesthetic

- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780195373233
- eISBN:
- 9780190232900
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195373233.003.0009
- Subject:
- Music, Theory, Analysis, Composition

Chapter 9 is the core of the book, as it touches on the essence of composing: organizing sound. While other chapters examine different elements deployed in the game, this chapter addresses the game ... More

## Hybrid Simulation Modeling in Population Health

*Sally C. Brailsford, Dave C. Evenden, and Joe Viana*

### in Complex Systems and Population Health

- Published in print:
- 2020
- Published Online:
- July 2020
- ISBN:
- 9780190880743
- eISBN:
- 9780190880774
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190880743.003.0015
- Subject:
- Public Health and Epidemiology, Public Health, Epidemiology

Hybrid simulation is particularly useful in population health, since healthcare systems are characterized by both dynamic and stochastic complexity and the use of one single simulation approach may ... More