2006/10/27 by Eric Moreau, Éric Moreau, Moreau, Eric
Engineering · Materials Science · Physics and Astronomy · #Adhesion, Friction, and Surface Interactions #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Textile materials and evaluations #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0610775
8 pages, 4 figures
openalex publication_date 2006/10/27 · arxiv created 2007/01/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 -κy+η(s), 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 ∂ h/∂ s.