Stochastic curvature of enclosed semiflexible polymers

Pavel Castro-Villarreal; J. E. Ramírez

doi:10.1103/PhysRevE.100.012503

paper

Stochastic curvature of enclosed semiflexible polymers

arXiv:1812.03281 · doi:10.1103/PhysRevE.100.012503

Abstract

The conformational states of a semiflexible polymer enclosed in a compact domain of typical size $a$ are studied as stochastic realizations of paths defined by the Frenet equations under the assumption that stochastic "curvature" satisfies a white noise fluctuation theorem. This approach allows us to derive the Hermans-Ullman equation, where we exploit a multipolar decomposition that allows us to show that the positional probability density function is well described by a Telegrapher's equation whenever $2 a / ℓ_{p} > 1$ , where $ℓ_{p}$ is the persistence length. We also develop a Monte Carlo algorithm for use in computer simulations in order to study the conformational states in a compact domain. In addition, the case of a semiflexible polymer enclosed in a square domain of side $a$ is presented as an explicit example of the formulated theory and algorithm. In this case, we show the existence of a polymer shape transition similar to the one found by Spakowitz and Wang [Phys. Rev. Lett. {\bf 91}, 2 (2003)] where in this case the critical persistence length is $ℓ_{p}^{*} ≃ a /8$ such that the mean-square end-to-end distance exhibits an oscillating behavior for values $ℓ_{p} > ℓ_{p}^{*}$ , whereas for $ℓ_{p} < ℓ_{p}^{*}$ it behaves monotonically increasing.

arXiv comment32 pages, 10 figures

Stochastic curvature of enclosed semiflexible polymers

Abstract

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