Related papers: Efficient method of finding scaling exponents from…
A new Monte Carlo method is proposed for fermion systems interacting with classical degrees of freedom. To obtain a weight for each Monte Carlo sample with a fixed configuration of classical variables, the moment expansion of the density of…
Extensive Monte-Carlo simulations were performed to study bond percolation on the simple cubic (s.c.), face-centered cubic (f.c.c.), and body-centered cubic (b.c.c.) lattices, using an epidemic kind of approach. These simulations provide…
Monte Carlo simulations alone could not clarify the corrections to scaling for the size-dependent p_c(L) above the upper critical dimension. Including the previous series estimate for the bulk threshold $p_c(\infty)$ gives preference for…
Large particle systems are often described by high-dimensional (linear) kinetic equations that are simulated using Monte Carlo methods for which the asymptotic convergence rate is independent of the dimensionality. Even though the…
In this paper, we aim to compute numerical approximation integral by using an adaptive Monte Carlo algorithm. We propose a stratified sampling algorithm based on an iterative method which splits the strata following some quantities called…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…
Importance sampling Monte-Carlo methods are widely used for the approximation of expectations with respect to partially known probability measures. In this paper we study a deterministic version of such an estimator based on quasi-Monte…
Scaling describes how a given quantity $Y$ that characterizes a system varies with its size $P$. For most complex systems it is of the form $Y\sim P^\beta$ with a nontrivial value of the exponent $\beta$, usually determined by regression…
We present a multilevel Monte Carlo simulation method for analysing multi-scale physical systems via a hierarchy of coarse-grained representations, to obtain numerically-exact results, at the most detailed level. We apply the method to a…
Monte Carlo simulations are one of the major tools in statistical physics, complex system science, and other fields, and an increasing number of these simulations is run on distributed systems like clusters or grids. This raises the issue…
This work demonstrates algorithms to accurately compute solutions to thermal radiation transport problems using a reduced floating-point precision implementation of the Implicit Monte Carlo method. Several techniques falling into the…
Machine learning has been successfully applied to identify phases and phase transitions in condensed matter systems. However, quantitative characterization of the critical fluctuations near phase transitions is lacking. In this study we…
In the present paper we consider the initial data, external force, viscosity coefficients, and heat conductivity coefficient as random data for the compressible Navier--Stokes--Fourier system. The Monte Carlo method, which is frequently…
We implement an adaptive step size method for the Hybrid Monte Carlo a lgorithm. The adaptive step size is given by solving a symmetric error equation. An integr ator with such an adaptive step size is reversible. Although we observe…
A new Monte Carlo algorithm is introduced for the simulation of supercooled liquids and glass formers, and tested in two model glasses. The algorithm is shown to thermalize well below the Mode Coupling temperature and to outperform other…
In the last decade, sequential Monte-Carlo methods (SMC) emerged as a key tool in computational statistics. These algorithms approximate a sequence of distributions by a sequence of weighted empirical measures associated to a weighted…
Exponential observables, formulated as $\log \langle e^{\hat{X}}\rangle$ where $\hat{X}$ is an extensive quantity, play a critical role in study of quantum many-body systems, examples of which include the free-energy and entanglement…
It is shown that superefficient Monte Carlo computations can be carried out by using chaotic dynamical systems as non-uniform random-number generators. Here superefficiency means that the expectation value of the square of the error…
Monte Carlo simulation has been performed in a two-dimensional modified XY-model first proposed by Domany et. al [E. Domany, M. Schick and R. H. Swendsen, Phys. Rev. Lett. 52, 1535 (1984)]. The cluster algorithm of Wolff has been used and…
In this work we have considered the Taylor series expansion of the dynamic scaling relation of the magnetization with respect to small initial magnetization values in order to study the dynamic scaling behaviour of 2- and 3-dimensional…