Search results for "Monte Carlo method"
showing 10 items of 1234 documents
Non-reversible Monte Carlo simulations of spin models
2011
Abstract Monte Carlo simulations are used to study simple systems where the underlying Markov chain satisfies the necessary condition of global balance but does not obey the more restrictive condition of detailed balance. Here, we show that non-reversible Markov chains can be set up that generate correct stationary distributions, but reduce or eliminate the diffusive motion in phase space typical of the usual Monte Carlo dynamics. Our approach is based on splitting the dynamics into a set of replicas with each replica representing a biased movement in reaction-coordinate space. This introduction of an additional bias in a given replica is compensated for by choosing an appropriate dynamics …
On the adoption of the Monte Carlo method to solve one-dimensional steady state thermal diffusion problems for non-uniform solids
2013
Abstract The present paper is focussed on the investigation of the potential adoption of the Monte Carlo method to solve one-dimensional, steady state, thermal diffusion problems for continuous solids characterised by an isotropic, space-dependent conductivity tensor and subjected to non-uniform heat power deposition. To this purpose the steady state form of Fourier’s heat diffusion equation relevant to a continuous, heterogeneous and isotropic solid, undergoing a space-dependent heat power density has been solved in a closed analytical form for the general case of Cauchy’s boundary conditions. The thermal field obtained has been, then, put in a peculiar functional form, indicating that it …
Growth Kinetics of Wetting Layers at Surfaces
1990
Monte Carlo simulation of lattice gas models for the wetting transitions in systems with short range forces are described. A nearest-neighbor simple cubic lattice with nonconserved “Glauber dynamics” is used, applying a slab geometry (LxL cross section). It is shown that the growth proceeds in two stages: for short times t, the thickness of the wetting layer at an initially nonwet wall increases proportional to the logarithm of the time; for t » L2(lnL)2 the thickness increases proportional to t1/2/L. Generalizations to other systems are briefly discussed. Also two-dimensional growth of a wetting film at surface steps is considered, considering “terraces” of an LxM geometry with M»L as subs…
Fatigue crack initiation and subsequent crack growth in fillet welded steel joints
2019
Abstract The fatigue damage evolution in fillet welded steel joints where cracks are emanating from the weld toe is investigated. Based on existing experimental data for as-welded joints including crack depth measurements of the early crack growth it is proposed to make a distinction between the crack initiation phase and the subsequent crack growth phase. The welded detail in question is an F class detail with plate thickness 25 mm made of medium strength carbon steel. It is found that the crack initiation phase defined at a crack depth of 0.1 mm is close to 25% of the fatigue life even at a relatively high constant stress range of 150 MPa. At lower stress ranges it is concluded that the i…
Heterogeneous nucleation of a droplet pinned at a chemically inhomogeneous substrate: A simulation study of the two-dimensional Ising case
2018
Heterogeneous nucleation is studied by Monte Carlo simulations and phenomenological theory, using the two-dimensional lattice gas model with suitable boundary fields. A chemical inhomogeneity of length b at one boundary favors the liquid phase, while elsewhere the vapor is favored. Switching on the bulk field Hb favoring the liquid, nucleation and growth of the liquid phase starting from the region of the chemical inhomogeneity are analyzed. Three regimes occur: for small fields, Hb bcrit, the critical droplet radius is so large that a critical droplet having the contact angle θc required by Young's equation in the region of the chemical inhomogeneity does not yet "fit" there since the base…
On the Ground State Structure of Adsorbed Monolayers: Can One Find them by Monte Carlo Simulation?
2002
While the classical ground state structure of an atomic monolayer adsorbed at a noncorrugated perfectly flat substrate trivially is a triangular lattice, the spacing being the minimum of the interatomic potential, nontrivial structures occur on corrugated substrates. This problem is exemplified for the (100) face of a face-centered cubic crystal, varying both the density of the adsorbed monolayer and the strength of the potential due to the surface. Increasing the density beyond that of the commensurate c(2 x 2) structure, incommensurate patterns become stable with “heavy” walls (HW) oriented along the face diagonals [including the “crossing heavy walls” (CRHW) phase]. It is shown that slow…
EDA: EXAFS data-analysis software package
2021
The EXAFS data-analysis software package EDA consists of a suite of programs running under a Windows operating system environment that is designed to perform all steps of conventional EXAFS data analysis such as extraction of the XANES/EXAFS parts of the X-ray absorption coefficient, Fourier filtering and EXAFS fitting using the Gaussian and cumulant models. The package also includes two advanced approaches which allow the reconstruction of the radial distribution function (RDF) from EXAFS based on the regularization-like method and the calculation of configuration-averaged EXAFS using a set of atomic configurations obtained from molecular-dynamics or Monte Carlo simulations.---- / / / ----…
Capillary condensation in the two-dimensional lattice gas: A Monte Carlo test of fluctuation corrections to the Kelvin equation
1997
A two-dimensional lattice gas model with nearest-neighbour attractive interaction confined in a strip of width L between two parallel boundaries at which an attractive short-range force acts is studied by Monte Carlo simulations, for cases where the system is in the wet phase near the critical wetting transition line for . We study the shift of the chemical potential of the transition in the strip as a function of L by thermodynamic integration methods, , and also obtain the thickness of the wetting film at the chemical potential at which capillary condensation occurs. In the range the data are consistent with a variation according to the Kelvin equation, , as well as with a shifted Kelvin …
Structural properties ofSi1−xGexalloys: A Monte Carlo simulation with the Stillinger-Weber potential
1995
The structural properties of binary silicon-germanium alloys are investigated by means of large-scale constant-pressure Monte Carlo simulations of the Stillinger-Weber model. At low temperatures, the binary-mixture phase separates into Si-rich and Ge-rich phases. The two-phase coexistence region is terminated by a critical point that belongs to the mean-field universality class. We also studied the structural properties of pure Si and Ge as well as the binary mixture. In particular, we found that the linear thermal expansions for both Si and Ge are in agreement with experiments, and that V\'egard's law is valid at temperatures above the critical point. Finally, we compare the bond-length an…
Monte Carlo Simulations of Body Centered Cubic Alloys
1994
We illustrate the use of Monte Carlo simulations in the study of order-disorder phenomena in metallic alloys by presenting detailed work on a fairly realistic lattice model for iron aluminum. The model has been constructed based on recent measurements of effective interaction parameters and includes a description of the magnetism of iron within a Heisenberg Hamiltonian. We show that it reproduces the bulk phase diagram in a qualitatively correct way. Then internal antiphase boundaries and free surfaces in the (100)-direction are studied. An interfacial roughening transition is predicted as well as critical broadening of the profiles as the bulk approaches a second order transition. Nonstoec…