Writhing Geometry at Finite Temperature: Random Walks and Geometric phases for Stiff Polymers
نویسنده
چکیده
We study the geometry of a semiflexible polymer at finite temperatures. The writhe can be calculated from the properties of Gaussian random walks on the sphere. We calculate static and dynamic writhe correlation functions. The writhe of a polymer is analogous to geometric or Berry phases studied in optics and wave mechanics. Our results can be applied to confocal microscopy studies of stiff filaments and to simulations of short DNA loops.
منابع مشابه
Writhing Geometry of Stiff Polymers and Scattered Light
The geometry of a smooth line is characterized locally by its curvature and torsion, or globally by its writhe. In many situations of physical interest the line is, however, not smooth so that the classical Frenet description of the geometry breaks down everywhere. One example is a thermalized stiff polymer such as DNA, where the shape of the molecule is the integral of a Brownian process. In s...
متن کاملOn Finite Geometric Random Walks and Probabilistic Combinatorics
In this paper we deene and analyze convergence of the geometric random walks. We show that the behavior of such walks is given by certain random matroid processes. In particular, the mixing time is given by the expected stopping time, and the cutoo is equivalent to a phase transition. We also discuss some random geometric random walks as well as some examples and symmetric cases.
متن کاملUnbinding of mutually avoiding random walks and two-dimensional quantum gravity.
We analyze the unbinding transition for a two-dimensional lattice polymer in which the constituent strands are mutually avoiding random walks. At low temperatures the strands are bound and form a single self-avoiding walk. We show that unbinding in this model is a strong first order transition. The entropic exponents associated with denaturated loops and end-segment distributions show sharp dif...
متن کاملBallistic Phase of Self-Interacting Random Walks
We explain a unified approach to a study of ballistic phase for a large family of self-interacting random walks with a drift and self-interacting polymers with an external stretching force. The approach is based on a recent version of the OrnsteinZernike theory developed in Campanino et al. (2003, 2004, 2007). It leads to local limit results for various observables (e.g., displacement of the en...
متن کاملHyperbolic and Parabolic Unimodular Random Maps Omer Angel Tom Hutchcroft Asaf Nachmias Gourab Ray
We show that for infinite planar unimodular random rooted maps, many global geometric and probabilistic properties are equivalent, and are determined by a natural, local notion of average curvature. This dichotomy includes properties relating to amenability, conformal geometry, random walks, uniform and minimal spanning forests, and Bernoulli bond percolation. We also prove that every simply co...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008