Related papers: Geometric properties of two-dimensional O(n) loop …
A brief introduction to the technique of Monte Carlo simulations in statistical physics is presented. The topics covered include statistical ensembles random and pseudo random numbers, random sampling techniques, importance sampling, Markov…
This paper presents a tool for addressing a key component in many algorithms for planning robot trajectories under uncertainty: evaluation of the safety of a robot whose actions are governed by a closed-loop feedback policy near a nominal…
We consider a two-dimensional bi-layered loop model with a certain interlayer coupling and study its spectrum on a torus. Each layer consists of an $O(n)$ model on a honeycomb lattice with periodic boundary conditions; these layers are…
Neutron transport along guides is governed by the Liouville theorem and the technology involved has advanced in recent decades. Computer simulations have proven to be useful tools in the design and conception of neutron guide systems in…
Diagrammatic Monte Carlo methods provide robust routines for accurate computations of correlated electronic systems in the thermodynamical limit. Recently, its versatility was extended to SU(N) Hubbard model, where the core is a novel…
Conventional Monte Carlo simulations are stochastic in the sense that the acceptance of a trial move is decided by comparing a computed acceptance probability with a random number, uniformly distributed between 0 and 1. Here we consider the…
Due to the complex characteristics of bottle-brush polymers, it became a challenge to develop an efficient algorithm for studying such macromolecules under various solvent conditions or some constraints in the space by using computer…
We study $N$-cluster correlation functions in four- and five-dimensional (4D, 5D) bond percolation by extensive Monte Carlo simulation. We reformulate the transfer Monte Carlo algorithm for percolation [Phys. Rev. E {\bf 72}, 016126 (2005)]…
World-line quantum Monte Carlo methods are reviewed with an emphasis on breakthroughs made in recent years. In particular, three algorithms -- the loop algorithm, the worm algorithm, and the directed-loop algorithm -- for updating…
Markov Chain Monte Carlo methods have revolutionised mathematical computation and enabled statistical inference within many previously intractable models. In this context, Hamiltonian dynamics have been proposed as an efficient way of…
We develop numerical tools for Diagrammatic Monte-Carlo simulations of non-Abelian lattice field theories in the t'Hooft large-N limit based on the weak-coupling expansion. First we note that the path integral measure of such theories…
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…
We consider a class of finite time horizon nonlinear stochastic optimal control problem, where the control acts additively on the dynamics and the control cost is quadratic. This framework is flexible and has found applications in many…
We determine the scaling properties of geometric operators such as lengths, areas, and volumes in models of higher derivative quantum gravity by renormalizing appropriate composite operators. We use these results to deduce the fractal…
Identification of nonlinear systems is a challenging problem. Physical knowledge of the system can be used in the identification process to significantly improve the predictive performance by restricting the space of possible mappings from…
Variational minimization of tensor network states enables the exploration of low energy states of lattice gauge theories. However, the exact numerical evaluation of high-dimensional tensor network states remains challenging in general. In…
We describe a novel switching algorithm based on a ``reverse'' Monte Carlo method, in which the potential is stochastically modified before the system configuration is moved. This new algorithm facilitates a generalized formulation of…
One of the most demanding calculations is to generate random samples from a specified probability distribution (usually with an unknown normalizing prefactor) in a high-dimensional configuration space. One often has to resort to using a…
The fractal structure of directed percolation clusters, grown at the percolation threshold inside parabolic-like systems, is studied in two dimensions via Monte Carlo simulations. With a free surface at y=\pm Cx^k and a dynamical exponent…
The thermal resistivity and its scaling function in quasi-2D $^4$He systems are studied by Monte Carlo and spin-dynamics simulation. We use the classical 3D XY model on $L\times L\times H$ lattices with $L\gg H$, applying open boundary…