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

摘要

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