Related papers: A new monte carlo algorithm for growing compact Se…
We find the generating function of self-avoiding walks and trails on a semi-regular lattice called the $3.12^2$ lattice in terms of the generating functions of simple graphs, such as self-avoiding walks, polygons and tadpole graphs on the…
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…
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…
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 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 introduce several bilocal algorithms for lattice self-avoiding walks that provide reasonable models for the physical kinetics of polymers in the absence of hydrodynamic effects. We discuss their ergodicity in different confined…
A linear polymer grafted to a hard wall and underneath an AFM tip can be modelled in a lattice as a grafted lattice polymer (or self-avoiding walk) compressed underneath a piston approaching the wall. As the piston approaches the wall the…
Polymer chains with hard-core interaction on a two-dimensional lattice are modeled by directed random walks. Two models, one with intersecting walks (IW) and another with non-intersecting walks (NIW) are presented, solved and compared. The…
We describe a class of growth algorithms for finding low energy states of heteropolymers. These polymers form toy models for proteins, and the hope is that similar methods will ultimately be useful for finding native states of real proteins…
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…
The self-avoiding walk on the square site-diluted correlated percolation lattice is considered. The Ising model is employed to realize the spatial correlations of the metric space. As a well-accepted result, the (generalized) Flory's mean…
The present paper is dedicated to the 2-dimensional Interacting Partially Directed Self Avoiding Walk constrained to remain in the upper-half plan and interacting with the horizontal axis. The model has been introduced in \cite{F90} to…
We review some recent results obtained in the framework of the 2-dimensional Interacting Self-Avoiding Walk (ISAW). After a brief presentation of the rigorous results that have been obtained so far for ISAW we focus on the Interacting…
We show that Wang-Landau sampling, combined with suitable Monte Carlo trial moves, provides a powerful method for both the ground state search and the determination of the density of states for the hydrophobic-polar (HP) protein model and…
The phase diagram for a two-dimensional self-avoiding walk model on the square lattice incorporating attractive short-ranged interactions between parallel sections of walk is derived using numerical transfer matrix techniques. The model…
The connections between (convex) optimization and (logconcave) sampling have been considerably enriched in the past decade with many conceptual and mathematical analogies. For instance, the Langevin algorithm can be viewed as a sampling…
A growing self-avoiding walk (GSAW) is a walk on a graph that is directed, does not visit the same vertex twice, and has a trapped endpoint. We show that the generating function enumerating GSAWs on a half-infinite strip of finite height is…
We show that the classical Rosenbluth method for sampling self-avoiding walks can be extended to a general algorithm for sampling many families of objects, including self-avoiding polygons. The implementation relies on an elementary move…
Oriented self-avoiding walks (OSAWs) on a square lattice are studied, with binding energies between steps that are oriented parallel across a face of the lattice. By means of exact enumeration and Monte Carlo simulation, we reconstruct the…
In this work, we present a simple and efficient generator of polymeric linear chains, based on a random self-avoiding walk process. The chains are generated using a discrete process of growth, in cubic networks and in a finite time, without…