title: Bimodality in the transverse fluctuations of a grafted semiflexible polymer and the diffusion-convection analogue: an effective-medium approach.
abstract: 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 disappearance of bimodality.
authors.affiliation: Hahn-Meitner-Institut, Abteilung Theoretische Physik, Glienicker Strasse 100, D-14109 Berlin, Germany.
authors.forename: P
authors.initials: P
authors.lastname: Benetatos
authors.forename: T
authors.initials: T
authors.lastname: Munk
authors.forename: E
authors.initials: E
authors.lastname: Frey