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Title: Finite Dimensional Approximations for Continuum Multiscale Problems

Abstract

The completed research project concerns the development of novel computational techniques for modeling nonlinear multiscale physical and biological phenomena. Specifically, it addresses the theoretical development and applications of the homogenization theory (coarse graining) approach to calculation of the effective properties of highly heterogenous biological and bio-inspired materials with many spatial scales and nonlinear behavior. This theory studies properties of strongly heterogeneous media in problems arising in materials science, geoscience, biology, etc. Modeling of such media raises fundamental mathematical questions, primarily in partial differential equations (PDEs) and calculus of variations, the subject of the PI’s research. The focus of completed research was on mathematical models of biological and bio-inspired materials with the common theme of multiscale analysis and coarse grain computational techniques. Biological and bio-inspired materials offer the unique ability to create environmentally clean functional materials used for energy conversion and storage. These materials are intrinsically complex, with hierarchical organization occurring on many nested length and time scales. The potential to rationally design and tailor the properties of these materials for broad energy applications has been hampered by the lack of computational techniques, which are able to bridge from the molecular to the macroscopic scale. The project addressed the challenge ofmore » computational treatments of such complex materials by the development of a synergistic approach that combines innovative multiscale modeling/analysis techniques with high performance computing.« less

Authors:
 [1]
  1. Pennsylvania State Univ., University Park, PA (United States)
Publication Date:
Research Org.:
Pennsylvania State Univ., University Park, PA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1340478
Report Number(s):
DOE-PSU-25862
DOE Contract Number:  
FG02-08ER25862
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; bio-mimetic; multiscale modeling; coarse-graining; computational complexity; high performance computing

Citation Formats

Berlyand, Leonid. Finite Dimensional Approximations for Continuum Multiscale Problems. United States: N. p., 2017. Web. doi:10.2172/1340478.
Berlyand, Leonid. Finite Dimensional Approximations for Continuum Multiscale Problems. United States. doi:10.2172/1340478.
Berlyand, Leonid. Tue . "Finite Dimensional Approximations for Continuum Multiscale Problems". United States. doi:10.2172/1340478. https://www.osti.gov/servlets/purl/1340478.
@article{osti_1340478,
title = {Finite Dimensional Approximations for Continuum Multiscale Problems},
author = {Berlyand, Leonid},
abstractNote = {The completed research project concerns the development of novel computational techniques for modeling nonlinear multiscale physical and biological phenomena. Specifically, it addresses the theoretical development and applications of the homogenization theory (coarse graining) approach to calculation of the effective properties of highly heterogenous biological and bio-inspired materials with many spatial scales and nonlinear behavior. This theory studies properties of strongly heterogeneous media in problems arising in materials science, geoscience, biology, etc. Modeling of such media raises fundamental mathematical questions, primarily in partial differential equations (PDEs) and calculus of variations, the subject of the PI’s research. The focus of completed research was on mathematical models of biological and bio-inspired materials with the common theme of multiscale analysis and coarse grain computational techniques. Biological and bio-inspired materials offer the unique ability to create environmentally clean functional materials used for energy conversion and storage. These materials are intrinsically complex, with hierarchical organization occurring on many nested length and time scales. The potential to rationally design and tailor the properties of these materials for broad energy applications has been hampered by the lack of computational techniques, which are able to bridge from the molecular to the macroscopic scale. The project addressed the challenge of computational treatments of such complex materials by the development of a synergistic approach that combines innovative multiscale modeling/analysis techniques with high performance computing.},
doi = {10.2172/1340478},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Tue Jan 24 00:00:00 EST 2017},
month = {Tue Jan 24 00:00:00 EST 2017}
}

Technical Report:

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