Abstract
In this paper, we investigate the potential for a class of non‐Gaussian processes so‐called generalized grey Brownian motion. We obtain a closed analytic form for the potential as an integral of the M‐Wright functions and the Green function. In particular, we recover the special cases of Brownian motion and fractional Brownian motion. In addition, we give the connection to a fractional partial differential equation and its the fundamental solution.
Highlights
Polymers are consisting of small chemical units that act on each other via different forces
A continuum limit of those models, that is, where the polymers are modeled by Brownian motion (Bm) paths, led to a deeper understanding in the asymptotic scaling behavior of the chains
Fractional Brownian motion paths have been suggested as a heuristic model,[6] without yet including the “excluded volume effect” a more proper model would be based on self-avoiding fractional random walks
Summary
Polymers are consisting of small chemical units that act on each other via different forces. The drawback of Bm or random walk models is that they can not reflect long-range forces along the chain without introducing a further potential. Fractional Brownian motion (fBm) paths have been suggested as a heuristic model,[6] without yet including the “excluded volume effect” a more proper model would be based on self-avoiding fractional random walks. The interaction potentials are long-range along the chain but can give rise to multiparticle nonlinear forces between the constituents. The class of underlying random processes is that of generalized grey Brownian motion (ggBm) that will give rise to chain models with nonlinear forces between the constituents and nonergodic dynamics as shown in Molina-Garcí.[9] There occur higher order interactions; in particular, we give an explicit form for.
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