Depinning of a polymer in a multi-interface medium

2009/01/19 by Francesco Caravenna, Caravenna, Francesco, Nicolas Pétrélis +1
Engineering · Mathematics · #60F05 #60K35 #82B41 #Acoustic Wave Phenomena Research #FOS: Mathematics #Heat Transfer and Optimization #Microfluidic and Bio-sensing Technologies #Probability (math.PR) #math.PR #msc:60F05 #msc:60K35 #msc:82B41

paper · pdf · doi:10.48550/arxiv.0901.2902

27 pages, 2 figures

arxiv created 2009/01/19 · openalex publication_date 2009/01/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider a model which describes a polymer chain interacting with an infinity of equi-spaced linear interfaces. The distance between two consecutive interfaces is denoted by T = T_N and is allowed to grow with the size N of the polymer. When the polymer receives a positive reward for touching the interfaces, its asymptotic behavior has been derived in a previous paper, showing that a transition occurs when T_N ≈ log(N). In the present paper, we deal with the so-called depinning case, i.e., the polymer is repelled rather than attracted by the interfaces. Using techniques from renewal theory, we determine the scaling behavior of the model for large N as a function of T_N, showing that two transitions occur, when T_N ≈ N^1/3 and when T_N ≈ N^1/2 respectively.

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