Related papers: Cut-and-permute algorithm for self-avoiding walks …
The pivot algorithm for self-avoiding walks has been implemented in a manner which is dramatically faster than previous implementations, enabling extremely long walks to be efficiently simulated. We explicitly describe the data structures…
We present a Monte Carlo method that allows efficient and unbiased sampling of Hamiltonian walks on a cubic lattice. Such walks are self-avoiding and visit each lattice site exactly once. They are often used as simple models of globular…
We study self-avoiding walks on the four-dimensional hypercubic lattice via Monte Carlo simulations of walks with up to one billion steps. We study the expected logarithmic corrections to scaling, and find convincing evidence in support the…
The pivot algorithm is a Markov Chain Monte Carlo algorithm for simulating the self-avoiding walk. At each iteration a pivot which produces a global change in the walk is proposed. If the resulting walk is self-avoiding, the new walk is…
We introduce a fast implementation of the pivot algorithm for self-avoiding walks, which we use to obtain large samples of walks on the cubic lattice of up to $33 \times 10^6$ steps. Consequently the critical exponent $\nu$ for…
Surface hopping algorithms are popular tools to study dynamics of the quantum-classical mixed systems. In this paper, we propose a surface hopping algorithm in diabatic representations, based on time dependent perturbation theory and…
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…
The pivot algorithm is the most efficient known method for sampling polymer configurations for self-avoiding walks and related models. Here we introduce two recent improvements to an efficient binary tree implementation of the pivot…
We present a hybrid Brownian dynamics / Monte Carlo algorithm for simulating solutions of highly entangled semiflexible polymers or filaments. The algorithm combines a Brownian dynamics time-stepping approach with an efficient scheme for…
We introduce an efficient nonreversible Markov chain Monte Carlo algorithm to generate self-avoiding walks with a variable endpoint. In two dimensions, the new algorithm slightly outperforms the two-move nonreversible Berretti-Sokal…
We recently demonstrated that standard fixed-time lattice random-walk models cannot be modified to properly represent biased diffusion processes in more than two dimensions. The origin of this fundamental limitation appears to be the fact…
The pivot algorithm -- we also call it the pivot chain -- is an algorithm for approximately uniform sampling from $\Omega _{N},$ the set of $N$-step self-avoiding walks on $\mathbb{Z}^{d}$ ($N,$ $d\geq 1$). Based on this algorithm and the…
We introduce a `virtual-move' Monte Carlo (VMMC) algorithm for systems of pairwise-interacting particles. This algorithm facilitates the simulation of particles possessing attractions of short range and arbitrary strength and geometry, an…
We propose an algorithm based on local growth rules for kinetically generating self avoiding walk configurations at any given temperature. This algorithm, called the Interacting Growth Walk (IGW) algorithm, does not suffer from attrition on…
Current digital computers are about to hit basic physical boundaries with respect to integration density, clock frequencies, and particularly energy consumption. This requires the application of new computing paradigms, such as quantum and…
Bridging algorithms are global Monte Carlo moves which allow for an efficient sampling of single polymer chains. In this manuscript we discuss the adaptation of three bridging algorithms from lattice to continuum models, and give details on…
We describe collective-move Monte Carlo algorithms designed to approximate the overdamped dynamics of self-assembling nanoscale components equipped with strong, short-ranged and anisotropic interactions. Conventional Monte Carlo simulations…
We show how a Monte Carlo method for generating self-avoiding walks on lattice geometries which employs a binary-tree data structure can be adapted for hard-sphere polymers with continuous degrees of freedom. Data suggests that the time per…
This article is a pedagogical review of Monte Carlo methods for the self-avoiding walk, with emphasis on the extraordinarily efficient algorithms developed over the past decade. Many more details can be found in hep-lat/9405016.
Quantum walks are promising tools based on classical random walks, with plenty of applications such as many variants of optimization. Here we introduce the semiclassical walks in discrete time, which are algorithms that combines classical…