CaltechAUTHORS
  A Caltech Library Service

Effective behavior of an interface propagating through a periodic elastic medium

Dondl, Patrick W. and Bhattacharya, Kaushik (2016) Effective behavior of an interface propagating through a periodic elastic medium. Interfaces and Free Boundaries, 18 (1). pp. 91-113. ISSN 1463-9963. http://resolver.caltech.edu/CaltechAUTHORS:20160701-103557323

[img] PDF - Submitted Version
See Usage Policy.

1429Kb

Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:20160701-103557323

Abstract

We consider a moving interface that is coupled to an elliptic equation in a heterogeneous medium. The problem is motivated by the study of displacive solid-solid phase transformations. We show that a nearly flat interface is given by the graph of the function g which evolves according to the equation g_t(x)=−(−Δ)^(1/2)g(x)+φ(x,g(x))+F. This equation also arises in the study of dislocations and fracture. We show in the periodic setting that such interfaces exhibit a stick-slip behavior associated with pinning and depinning. Further, we present some numerical evidence that the effective velocity of the phase boundary scales as the square-root of the excess macroscopic force above the depinning transition.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.4171/IFB/358 DOIArticle
http://www.ems-ph.org/journals/show_abstract.php?issn=1463-9963&vol=18&iss=1&rank=4PublisherArticle
https://arxiv.org/abs/1206.2578arXivDiscussion Paper
ORCID:
AuthorORCID
Bhattacharya, Kaushik0000-0003-2908-5469
Additional Information:© 2016 EMS Publishing House. This work draws from the doctoral thesis of Patrick Dondl at the California Institute of Technology. It is a pleasure to acknowledge discussions with Bogdan Craciun, Nicolas Dirr and Aaron Yip. We gratefully acknowledge the financial support of the National Science Foundation (ACI-0204932, DMS-0311788).
Funders:
Funding AgencyGrant Number
NSFACI-0204932
NSFDMS-0311788
Subject Keywords:Fractional Laplacian, interfaces, heterogeneous media, effective properties, homogenization, periodic media, free boundary problems, pinning
Record Number:CaltechAUTHORS:20160701-103557323
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20160701-103557323
Official Citation:Dondl Patrick, Bhattacharya Kaushik: Effective behavior of an interface propagating through a periodic elastic medium. Interfaces Free Bound. 18 (2016), 91-113. doi: 10.4171/IFB/358
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:68807
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:05 Jul 2016 17:35
Last Modified:05 Jul 2016 17:35

Repository Staff Only: item control page