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Thermalization of rate-independent processes by entropic regularization

Sullivan, T. J. and Koslowski, M. and Theil, F. and Ortiz, Michael (2013) Thermalization of rate-independent processes by entropic regularization. Discrete and Continuous Dynamical Systems Series S, 6 (1). pp. 215-233. ISSN 1937-1632. http://resolver.caltech.edu/CaltechAUTHORS:20171117-150903971

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Abstract

We consider the effective behaviour of a rate-independent process when it is placed in contact with a heat bath. The method used to ``thermalize'' the process is an interior-point entropic regularization of the Moreau--Yosida incremental formulation of the unperturbed process. It is shown that the heat bath destroys the rate independence in a controlled and deterministic way, and that the effective dynamics are those of a non-linear gradient descent in the original energetic potential with respect to a different and non-trivial effective dissipation potential.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.3934/dcdss.2013.6.215DOIArticle
http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=7785PublisherArticle
https://arxiv.org/abs/1209.3619arXivDiscussion Paper
Additional Information:© 2013 American Institute of Mathematical Sciences Received: May 2011; Revised: July 2011; Available Online: October 2012. The first author acknowledges portions of this work supported by the Engineering and Physical Sciences Research Council (http://www.epsrc.ac.uk/).
Group:GALCIT
Funders:
Funding AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
Subject Keywords:Gradient descent, non-linear evolution equations, thermodynamics
Classification Code:Mathematics Subject Classification: Primary: 47J35, 82C35
Record Number:CaltechAUTHORS:20171117-150903971
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20171117-150903971
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83306
Collection:CaltechAUTHORS
Deposited By: Lydia Suarez
Deposited On:20 Nov 2017 23:03
Last Modified:20 Nov 2017 23:14

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