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Instability of interface under forced displacements
Anna De Masi, Nicolas Dirr and Errico Presutti
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 $V^2/\mu$, $\mu$ 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 $V^2/\mu$ 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.