Writhing Geometry at Finite Temperature: Random Walks and Geometric phases for Stiff Polymers

We perform simulations to numerically study the writhe distribution of a stiff polymer. We compare with analytic results of Bouchiat and Mezard (PRL 80 1556- (1998); cond-mat/9706050).

When double stranded DNA is turned in experiments it undergoes a transition. We use an interacting self-avoiding walk on a three-dimensional fcc lattice weighted by writhe to relate to these experiments and treat this problem via simulations. We provide evidence for the existence of a thermodynamic phase transition induced by writhe and examine related phase diagrams taking solvent quality and stretching into account.

We consider a simple lattice model of a topological phase transition in open polymers. To be precise, we study a model of self-avoiding walks on the simple cubic lattice tethered to a surface and weighted by an appropriately defined writhe. We also consider the effect of pulling the untethered end of the polymer from the surface. Regardless of the force we find a first-order phase transition which we argue is a consequence of increased knotting in the lattice polymer, rathe...

We provide numerical support for a long-standing prediction of universal scaling of winding angle distributions. Simulations of interacting self-avoiding walks show that the winding angle distribution for $N$-step walks is compatible with the theoretical prediction of a Gaussian with a variance growing asymptotically as $C\log N$, with $C=2$ in the swollen phase (previously verified), and $C=24/7$ at the $\theta$-point. At low temperatures weaker evidence demonstrates compati...

We map the problem of self-avoiding random walks in a Theta solvent with a chemical potential for writhe to the three-dimensional symmetric U(N)-Chern-Simons theory as N goes to 0. We find a new scaling regime of topologically constrained polymers, with critical exponents that depend on the chemical potential for writhe, which gives way to a fluctuation-induced first-order transition.

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 Tel...

In this work we present the general phase behavior of short tubelike flexible polymers. The geometric thickness constraint is implemented through the concept of the global radius of curvature. We use sophisticated Monte Carlo sampling methods to simulate small bead-stick polymer models with Lennard-Jones interaction among non-bonded monomers. We analyze energetic fluctuations and structural quantities to classify conformational pseudophases. We find that the tube thickness in...

We study analytically and numerically the winding of directed polymers of length $t$ around each other or around a rod. Unconfined polymers in pure media have exponentially decaying winding angle distributions, the decay constant depending on whether the interaction is repulsive or neutral, but not on microscopic details. In the presence of a chiral asymmetry, the exponential tails become non universal. In all these cases the mean winding angle is proportional to $\ln t$. Whe...

We map self-avoiding random walks with a chemical potential for writhe to the three-dimensional complex O(N) Chern-Simons theory as N -> 0. We argue that at the Wilson-Fisher fixed point which characterizes normal self-avoiding walks (with radius of gyration exponent nu = 0.588) a small chemical potential for writhe is irrelevant and the Chern-Simons field does not modify the monomer- monomer correlation function. For a large chemical potential the polymer collapses.

The conformational states of a semiflexible polymer enclosed in a volume $V:=\ell^{3}$ are studied as stochastic realizations of paths using the stochastic curvature approach developed in [Rev. E 100, 012503 (2019)], in the regime whenever $3\ell/\ell_ {p}> 1$, where $\ell_{p}$ is the persistence length. The cases of a semiflexible polymer enclosed in a cube and sphere are considered. In these cases, we explore the Spakowitz-Wang type polymer shape transition, where the criti...