Interface Instability under Forced Displacements

De Masi, Anna, Dirr, Nicolas P. ORCID: https://orcid.org/0000-0003-3634-7367 and Presutti, Errico 2006. Interface Instability under Forced Displacements. Annales Henri Poincaré 7 (3) , pp. 471-511. 10.1007/s00023-005-0257-1

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Abstract

By applying linear response theory and the Onsager principle, the power (per unit area) needed to make a planar interface move with velocity V is found to be equal to V2/ μ, μ a mobility coefficient. To verify such a law, we study a one dimensional model where the interface is the stationary solution of a non local evolution equation, called an instanton. We then assign a penalty functional to orbits which deviate from solutions of the evolution equation and study the optimal way to displace the instanton. We find that the minimal penalty has the expression V2/ μ only when V is small enough. Past a critical speed, there appear nucleations of the other phase ahead of the front, their number and location are identified in terms of the imposed speed.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Springer
ISSN:	1424-0637
Last Modified:	18 Oct 2022 13:13
URI:	https://orca.cardiff.ac.uk/id/eprint/13078

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