Bimodality in the transverse fluctuations of a grafted semiflexible polymer and the diffusion-convection analogue: An effective-medium approach

Recent Monte Carlo simulations of a grafted semiflexible polymer in
1+1 dimensions have revealed a pronounced bimodal structure in the
probability distribution of the transverse (bending) fluctuations
of the free end, when the total contour length is of the order of
the persistence length G. Lattanzi , Phys. Rev E 69, 021801
(2004)]. In this paper, we show that the emergence of bimodality is
related to a similar behavior observed when a random walker is
driven in the transverse direction by a certain type of shear flow.
We adapt an effective-medium argument, which was first introduced
in the context of the sheared random-walk problem E. Ben-Naim ,
Phys. Rev. A 45, 7207 (1992)], in order to obtain a simple analytic
approximation of the probability distribution of the free-end
fluctuations. We show that this approximation captures the
bimodality and most of the qualitative features of the free-end
fluctuations. We also predict that relaxing the local
inextensibility constraint of the wormlike chain could lead to the
disappearence of bimodality.