Analytical results are obtained by using Galerkin′s and multi-scale methods.
Using these terms, three different kinds of multi-scale methods are discussed.
This approach differs from previous multi-scale methods, where place recognition is performed through a non-optimized distance metric in a fixed and pre-determined scale space.
This paper investigates two critical issues, namely propagation of multi-scale uncertainty, and selection of failure criteria, related to reliability analysis of composites by using multi-scale methods.
A comprehensive overview of multi-scale methods is presented with a focus on the ways in which information is communicated between scales.
We demonstrate the efficiency of our proposed multi-scale methods through several numerical examples including a multi-scale coefficient problem, a high-contrast interface problem, and a convection-dominated diffusion problem.
We believe the key to achieving the required level of modeling lies within the computational approach, and we separate the approaches into top down (continuum-methods) vs. bottom up (multi-scale methods).
Previous modeling work on water transport in PEMFC involves developing rule-based and first-principle-based models, and first-principle-based models involve multi-scale methods from atomistic to full cell levels.
The application of the software-tool to the production of biodiesel is presented, highlighting the main features of the computer-aided, multi-stage, multi-scale methods that are able to determine more sustainable designs.
This book presents detailed reviews concerning the development of various techniques, including ab initio molecular dynamics, density functional theory, combined QM/MM methods, solvation models, force field methods, and free-energy estimation techniques, as well as successful applications of multi-scale methods in the biocatalysis systems including several protein enzymes and ribozymes.
Based on the multi- scale coupling method which field model and network model are combined, the smoke spread in the underground unidirectional tunnel was studied.
