Search results for "Monte carlo method"
showing 10 items of 1234 documents
Finite-size scaling and the crossover to mean-field critical behavior in the two-dimensional Ising model with medium-ranged interactions.
1993
Critical amplitudes in finite-size scaling relations show a singular dependence on the range of the interactions, R. The respective power laws are predicted from phenomenological crossover scaling considerations. These predictions are tested by Monte Carlo simulations for medium-ranged Ising square lattices. It is speculated that some deviations between the simulation results and corresponding predictions may be due to logarithmic corrections.
Monte Carlo tests of theoretical predictions for critical phenomena: still a problem?
2000
Two Monte Carlo studies of critical behavior in ferromagnetic Ising models are described: the first one deals with the crossover from the Ising class to the mean field class, when the interaction range increases. The second study deals with the finite size behavior at dimensionalities above the marginal dimension where Landau theory applies. The numerical results are compared to pertinent theoretical predictions, and unsolved problems are briefly described.
Non-linear Systems Under Poisson White Noise Handled by Path Integral Solution
2008
An extension of the path integral to non-linear systems driven by a Poissonian white noise process is presented. It is shown that at the limit when the time increment becomes infinitesimal the Kolmogorov— Feller equation is fully restored. Applications to linear and non-linear systems with different distribution of the Dirac's deltas occurrences are performed and results are compared with analytical solutions (when available) and Monte Carlo simulation.
Stochastic dynamics of nonlinear systems driven by non-normal delta-correlated processes
1993
In this paper, nonlinear systems subjected to external and parametric non-normal delta-correlated stochastic excitations are treated. A new interpretation of the stochastic differential calculus allows first a full explanation of the presence of the Wong-Zakai or Stratonovich correction terms in the Itoˆ’s differential rule. Then this rule is extended to take into account the non-normality of the input. The validity of this formulation is confirmed by experimental results obtained by Monte Carlo simulations.
An Efficient Wiener Path Integral Technique Formulation for Stochastic Response Determination of Nonlinear MDOF Systems
2015
The recently developed approximate Wiener path integral (WPI) technique for determining the stochastic response of nonlinear/hysteretic multi-degree-of-freedom (MDOF) systems has proven to be reliable and significantly more efficient than a Monte Carlo simulation (MCS) treatment of the problem for low-dimensional systems. Nevertheless, the standard implementation of the WPI technique can be computationally cumbersome for relatively high-dimensional MDOF systems. In this paper, a novel WPI technique formulation/implementation is developed by combining the “localization” capabilities of the WPI solution framework with an appropriately chosen expansion for approximating the system response PDF…
Probabilistic characterization of nonlinear systems under Poisson white noise via complex fractional moments
2014
In this paper, the probabilistic characterization of a nonlinear system enforced by Poissonian white noise in terms of complex fractional moments (CFMs) is presented. The main advantage in using such quantities, instead of the integer moments, relies on the fact that, through the CFMs the probability density function (PDF) is restituted in the whole domain. In fact, the inverse Mellin transform returns the PDF by performing integration along the imaginary axis of the Mellin transform, while the real part remains fixed. This ensures that the PDF is restituted in the whole range with exception of the value in zero, in which singularities appear. It is shown that using Mellin transform theorem…
Sensitivity and uncertainty analysis of an integrated ASM2d MBR model for wastewater treatment
2018
Abstract An integrated membrane bioreactor (MBR) model was previously proposed and tested. The model provides a comprehensive and detailed description of the nitrogen biological removal processes with respect to up-to-date literature. This paper presents a sensitivity and uncertainty analysis aimed at identifying the key factors affecting the variability of the model predictions. The Standardized Regression Coefficients (SRC) method was adopted for the sensitivity analysis. The uncertainty analysis was employed by running Monte Carlo simulations by varying only the value of the key factors affecting the model outputs. The sensitivity analysis combined with the uncertainty analysis applied h…
Wetting of polymer liquids: Monte Carlo simulations and self-consistent field calculations
2003
Using Monte Carlo simulations and self-consistent field (SCF) theory we study the surface and interface properties of a coarse grained off-lattice model. In the simulations we employ the grand canonical ensemble together with a reweighting scheme in order to measure surface and interface free energies and discuss various methods for accurately locating the wetting transition. In the SCF theory, we use a partial enumeration scheme to incorporate single-chain properties on all length scales and use a weighted density functional for the excess free energy. The results of various forms of the density functional are compared quantitatively to the simulation results. For the theory to be accurate…
Atomistic theory of mesoscopic pattern formation induced by bimolecular surface reactions between oppositely charged molecules
2011
The kinetics of mesoscopic pattern formation is studied for a reversible A+B⇌0 reaction between mobile oppositely charged molecules at the interface. Using formalism of the joint correlation functions, non-equilibrium charge screening and reverse Monte Carlo methods, it is shown that labyrinth-like percolation structure induced by (even moderate-rate) reaction is principally non-steady-state one and is associated with permanently growing segregation of dissimilar reactants and aggregation of similar reactants into mesoscopic size domains. A role of short-range and long-range reactant interactions in pattern formation is discussed.
Simulation of Order-Disorder Phenomena and Diffusion in Metallic Alloys
1991
The application of the Monte Carlo method to lattice-statistics problems in metallurgy is reviewed. Examples are given for the prediction of phase diagrams from simple model assumptions for effective interatomic potentials and for the calculation of parameters describing long- and short-range order, ordering energy, etc., both for face-centered cubic (fcc) and body-centered cubic (bcc) lattices. Applications to real systems such as Cu—Au and Fe—Al alloys are discussed.