The Library
Gradient flows as a selection procedure for equilibria of nonconvex energies
Tools
Ortner, Christoph (2006) Gradient flows as a selection procedure for equilibria of nonconvex energies. SIAM Journal on Mathematical Analysis, Volume 38 (Number 4). pp. 1214-1234. doi:10.1137/050643982 ISSN 0036-1410.
|
PDF
WRAP_Ortner_2006-SIMA-GFlow.pdf - Published Version - Requires a PDF viewer. Download (459Kb) | Preview |
Official URL: http://dx.doi.org/10.1137/050643982
Abstract
For atomistic material models, global minimization gives the wrong qualitative behavior; a theory of equilibrium solutions needs to be defined in different terms. In this paper, a concept based on gradient flow evolutions, to describe local minimization for simple atomistic models based on the Lennard–Jones potential, is presented. As an application of this technique, it is shown that an atomistic gradient flow evolution converges to a gradient flow of a continuum energy as the spacing between the atoms tends to zero. In addition, the convergence of the resulting equilibria is investigated in the case of elastic deformation and a simple damaged state.
Item Type: | Journal Article | ||||||||
---|---|---|---|---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Multiscale modeling, Continuum mechanics | ||||||||
Journal or Publication Title: | SIAM Journal on Mathematical Analysis | ||||||||
Publisher: | Society for Industrial and Applied Mathematics | ||||||||
ISSN: | 0036-1410 | ||||||||
Official Date: | 15 December 2006 | ||||||||
Dates: |
|
||||||||
Volume: | Volume 38 | ||||||||
Number: | Number 4 | ||||||||
Page Range: | pp. 1214-1234 | ||||||||
DOI: | 10.1137/050643982 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 27 December 2015 | ||||||||
Date of first compliant Open Access: | 27 December 2015 |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year