# Survey of roughness by stochastic oscillations

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1 SPCTS - Science des Procédés Céramiques et de Traitements de Surface

Abstract : In this paper, connections between surface roughness and directed polymers in random medium are studied, when the surface is considered as a directed line undergoing stochastic oscillations. This is performed by studying the influence of a stochastic elastic forcing term $-\kappa y+\etas$, on a particle moving along a rough surface. Two models are proposed and analysed in this way: the random-walk process RW in its discrete and continuous form, and a Markovian process via the Ornstein-Uhlenbeck O-U process. It is shown that the continuous RW leads to an oscillator equation, via an effective action obeying a KPZ equation which is solved analytically. The O-U process allows to obtain information on the profile of surface for a long size substrate. The analogy with the roughness is achieved by introducing a quantity suited to directed line formalism: the height velocity variation $\partial h-\partial s$.

Mots-clés : stochastic processes surface structure KPZ equation

Autor: Eric Moreau -

Fuente: https://hal.archives-ouvertes.fr/

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