Self-Repelling Fractional Brownian Motion - A Generalized Edwards Model for Chain Polymers

Abstract

We present an extension of the Edwards model for conformations of individual chain molecules in solvents in terms of fractional Brownian motion, and discuss the excluded volume effect on the end-to-end length of such trajectories or molecules.

Scaling Properties of Weakly Self-Avoiding Fractional Brownian Motion in One Dimension

“…These models might be considered unphysical. However, as in the Brownian case, there exists a recursion formula [KF78], which would predict the Flory index in higher dimensional cases from the one-dimensional one, [BOS11].…”

Self-avoiding Fractional Brownian Motion—The Edwards Model

“…the reviews [vdHK01], [PV02] and references therein. A tentative to extend these to fractional Brownian motion has recently been undertaken in [BOS11].…”

Persistence probabilities of mixed FBM and other mixed processes

“…For example, diffusions with short-range properties are observed in the motion of charge carriers with certain semiconductors [45,51], in the spreading of tracer molecules in subsurfaces [50], on random site percolation clusters [28], whereas diffusions with long-range properties are observed in active motion within biological cells [16], spreading in layered velocity fields [34] and in mediated surface exchange [57], see also [55] for further references and applications in physics. Additional mentionable applications in which FBM naturally arises are the modelling of polymers, see [13,27], where such models appear under the name Edwards model, and the modelling of fluctuating interfaces, where FBM turned out to be an equivalent for the Edwards-Wilkinson model in the case of an initial condition with fully-developed steady-state roughness, see [30].…”