Asymptotic behavior of self-affine processes in semi-infinite domains

Abstract

We propose to model the stochastic dynamics of a polymer passing through a pore (translocation) by means of a fractional Brownian motion, and study its behavior in presence of an absorbing boundary. Based on scaling arguments and numerical simulations, we present a conjecture that provides a link between the persistence exponent $\theta$ and the Hurst exponent $H$ of the process, thus sheding light on the spatial and temporal features of translocation. Furthermore, we show that this conjecture applies more generally to a broad class of self affine processes undergoing anomalous diffusion in bounded domains, and we discuss some significant examples.

arXiv comment4 pages, 3 figures; to be published in Phys. Rev. Lett

References in corpus (10)

• Fast DNA translocation through a solid-state nanopore
• Driven Polymer Translocation Through a Narrow Pore
• Anomalous Dynamics of Translocation
• Anomalous Dynamics of Forced Translocation
• Fractional Laplacian in Bounded Domains
• Persistence exponents for fluctuating interfaces
• Persistence in Nonequilibrium Systems
• How long does it take to pull an ideal polymer into a small hole?
• Anomalous Diffusion with Absorbing Boundary
• Probability distributions for polymer translocation

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