# Interface instability under forced displacements

### Reference:

De Masi, A., Dirr, N. and Presutti, E., 2006. Interface instability under forced displacements. *Annales Henri Poincare*, 7 (3), pp. 471-511.

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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 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.

### Details

Item Type | Articles |

Creators | De Masi, A., Dirr, N. and Presutti, E. |

DOI | 10.1007/s00023-005-0257-1 |

Departments | Faculty of Science > Mathematical Sciences |

Refereed | Yes |

Status | Published |

ID Code | 7079 |

Additional Information | ID number: ISI:000237323100004 |

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