Asymptotic behavior of self-affine processes in semi-infinite domains.
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 the 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 shedding 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.
Zoia
Andrea
A
CEA/Saclay, DEN/DM2S/SFME/LSET, Bâtiment 454, 91191 Gif-sur-Yvette Cedex, France. andrea.zoia@cea.fr
Rosso
Alberto
A
Majumdar
Satya N
SN
D008956:Models, Chemical; D008958:Models, Molecular; D011108:Polymers / Q000737:chemistry*; D013269:Stochastic Processes
D011108:Polymers