Interface Instability under Forced Displacements |
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Authors: | Anna De Masi Nicolas Dirr Errico Presutti |
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Institution: | (1) Dipartimento di Matematica Pura ed Applicata, Universitá di L’Aquila, I-67100 L’Aquila, Italy;(2) Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, D-04103 Leipzig, Germany;(3) Dipartimento di Matematica, Universitá di Roma “Tor Vergata”, I-00133 Roma, Italy |
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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.
submitted 31/01/05, accepted 26/10/05 |
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Keywords: | |
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