A roadmap is presented to transition seamlessly from an image to a predictive computational model for granular materials. So far, constitutive modelling in granular materials has been based on macroscopic experimental observations. Here, the point of departure is the basic granular scale where kinematics, contact forces and fabric control the macroscopic mechanical behaviour of the material. Ne...

In this paper, a multiscale virtual particle based elastic network model (MVP-ENM) is proposed for biomolecular normal mode analysis. The multiscale virtual particle model is proposed for the discretization of biomolecular density data in different scales. Essentially, the model works as the coarse-graining of the biomolecular structure, so that a delicate balance between biomolecular geometric...

Molecular dynamics (MD) methods are opening new opportunities for simulating the fundamental processes of material behavior at the atomistic level. However, current analysis is limited to small domains and increasing the size of the MD domain quickly presents intractable computational demands. A preferred approach to surmount this computational limitation has been to combine continuum mechanics...

A convenient setting for studying multiscale techniques in various areas of applications is usually based on a sequence of nested closed subspaces of some function space F which is often referred to as multiresolution analysis. The concept of wavelets is a prominent example where the practical use of such a mul-tiresolution analysis relies on explicit representations of the orthogonal diierence...

An alternative example of the method of multiple scales is presented. This example arises in the study of the classical heat equation with a slowly varying flux imposed at one end. The module presents introductory ideas about dimensionless variables, multiple-scale expansions, and scaling of the dependent variable. The necessarily obfuscating algebraic computation is less than that for more fam...

Recent work of the authors and colleagues on the turbulent mixing of compressible fluids is developed and extended with an emphasis on the multiscale aspects of this work. Specifically, we study an interplay between micro and macro aspects of mixing. 2008 Elsevier B.V. All rights reserved.

The context of this work is the design of a software, called MEMSALab, dedicated to the automatic derivation of multiscale models of arrays of microand nanosystems. In this domain a model is a partial differential equation. Multiscale methods approximate it by another partial differential equation which can be numerically simulated in a reasonable time. The challenge consists in taking into acc...

In this paper, we develop a new multiscale modeling framework for characterizing positive-valued data with long-range-dependent correlations. Using the Haar wavelet transform and a special multiplicative structure on the wavelet coeecients to ensure non-negative results, the model provides a rapid O(N) algorithm for synthesizing N-point data sets. We study the second-order and mul-tifractal pro...

We investigate the fast-reaction asymptotics for a one-dimensional reaction-diffusion system describing the penetration of the carbonation reaction in concrete. The technique of matchedasymptotics is used to show that the reaction-diffusion system leads to two distinct classes of sharpinterface models. These correspond to different scalings of a small parameter representing the fast-reaction an...

This paper introduces an framework for adaptivity for a class of heterogeneous multiscale finite element methods for elliptic problems, which is suitable for a posteriori error estimation with separated quantification of the model error as well as the macroscopic and microscopic discretization errors. The method is derived within a general framework for “goal-oriented” adaptivity, the so-called...