Related papers: Anomalous polymer collapse winding angle distribut…
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 collapse transition of an isolated polymer has been modelled by many different approaches, including lattice models based on self-avoiding walks and self-avoiding trails. In two dimensions, previous simulations of kinetic growth trails,…
Trails (bond-avoiding walks) provide an alternative lattice model of polymers to self-avoiding walks, and adding self-interaction at multiply visited sites gives a model of polymer collapse. Recently, a two-dimensional model (triangular…
The winding angle probability distribution of a planar self-avoiding walk has been known exactly since a long time: it has a gaussian shape with a variance growing as $<\theta^2>\sim \ln L$. For the three-dimensional case of a walk winding…
We have simulated four-dimensional interacting self-avoiding trails (ISAT) on the hyper-cubic lattice with standard interactions at a wide range of temperatures up to length 4096 and at some temperatures up to length 16384. The results…
The statistics of equally weighted random paths (ideal polymer) is studied in $2$ and $3$ dimensional percolating clusters. This is equivalent to diffusion in the presence of a trapping environment. The number of $N$ step walks follows a…
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…
We study winding angles of oriented polymers with orientation-dependent interaction in two dimensions. Using exact analytical calculations, computer simulations, and phenomenological arguments, we succeed in finding the variance of the…
We investigate polymers pulled away from an interacting surface, where the force is applied to the untethered endpoint and at an angle $\theta$ to the surface. We use the canonical self-avoiding walk model of polymers and obtain the phase…
We have investigated a polymer growth process on the triangular lattice where the configurations produced are self-avoiding trails. We show that the scaling behaviour of this process is similar to the analogous process on the square…
We study by computer simulation a recently introduced generalised model of self-interacting self-avoiding trails on the square lattice that distinguishes two topologically different types of self-interaction: namely crossings where the…
We consider a directed walk model of a homopolymer (in two dimensions) which is self-interacting and can undergo a collapse transition, subject to an applied tensile force. We review and interpret all the results already in the literature…
In earlier work we provided the first evidence that the collapse, or coil-globule, transition of an isolated polymer in solution can be seen in a four-dimensional model. Here we investigate, via Monte Carlo simulations, the canonical…
In this paper we present a new and flexible method to show that, in one dimension, various self-repellent random walks converge to self-repellent Brownian motion in the limit of weak interaction after appropriate space-time scaling. Our…
Extensive Monte Carlo data analysis gives clear evidence that collapsed linear polymers in two dimensions fall in the universality class of athermal, dense self-avoiding walks, as conjectured by B.Duplantier [Phys.Rev.Lett. 71, 4274…
There have been separate studies of the polymer collapse transition, where the collapse was induced by two different types of attraction. In each case, the configurations of the polymer were given by the same subset of random walks being…
Three-dimensional Monte Carlo simulations provide a striking confirmation to a recent theoretical prediction: the Brownian non-Gaussian diffusion of critical self-avoiding walks. Although the mean square displacement of the polymer center…
We consider the phase transition induced by compressing a self-avoiding walk in a slab where the walk is attached to both walls of the slab in two and three dimensions, and the resulting phase once the polymer is compressed. The process of…
We use complete enumeration and Monte Carlo techniques to study self--avoiding walks with random nearest--neighbor interactions described by $v_0q_iq_j$, where $q_i=\pm1$ is a quenched sequence of ``charges'' on the chain. For equal numbers…
Various subsets of self-avoiding walks naturally appear when investigating existing methods designed to predict the 3D conformation of a protein of interest. Two such subsets, namely the folded and the unfoldable self-avoiding walks, are…