Weighted Monte Carlo Method Research Articles

Prediction Model for Coformer Screening of Energetic Eutectics Based on Flory‐Huggins Interaction Parameter

AbstractBased on intermolecular interactions, Flory‐Huggins interaction parameter χAB>0 was presented as a prediction model to screen the coformer of energetic eutectics. To evaluate the predictive accuracy of this model, 80 energetic eutectics were collected from literatures. The molecular structures were optimized by computationally cheap molecular mechanics and high precision dispersion‐corrected density functional, respectively. Then the weighted Monte Carlo method was used to calculate the mixing energy ΔEmix of the binary system and thus derive the dimensionless χAB. The results show that the prediction accuracy is up to 85% based on M06‐2X‐D3/6‐311+G (d, p) optimization geometry and RESP charge, much greater than 45% of molecular mechanics method. Furthermore, size/shape mismatch between eutectic molecules was considered by shape index and molecular volume to enrich the prediction model. Based on this prediction model, a new energetic eutectic MTNP‐TNT was discovered, whose χAB value is 3.376 obtained by M06‐2X‐D3/6‐311+G (d, p) method. Experimentally, the classical “V” phase diagram drawn from the differential scanning calorimetry (DSC) data also suggests the MTNP‐TNT eutectic with eutectic temperature of 54.41°C at the molar ratio of 51.50: 48.50. Theoretical and experimental results successfully validate the χAB>0 prediction model for screening the coformers of energetic eutectics. This work opens a way for the crystal engineering of energetic eutectic solid forms with attractive physicochemical properties using a computational approach.

Water position sampling on protein structures based on a 3D distribution function using a weighted Monte Carlo method

Abstract To gain a detailed understanding of protein structure, function, and interaction, water molecules around proteins are important. Therefore, computational methods for predicting water positions are required. When a hydration water distribution such as a 3D distribution function is available, methods to predict water positions explicitly from the water distribution are useful. In this paper, we introduce DroPred, a method for predicting water positions based on a 3D distribution function of water oxygen atoms using a weighted Monte Carlo method. The probability density derived from the 3D distribution function is used as weight in the weighted Monte Carlo method. DroPred generates multiple samples from a single 3D distribution function. We evaluated the performance of DroPred by predicting water positions at protein–protein interface structures. By adjusting the weight using an exponential parameter, prediction performance of DroPred in water position sampling was improved. This method will be helpful for understanding protein structure, function, and interaction.

A Generalized Weighted Monte Carlo Calibration Method for Derivative Pricing

The weighted Monte Carlo method is an elegant technique to calibrate asset pricing models to market prices. Unfortunately, the accuracy can drop quite quickly for out-of-sample options as one moves away from the strike range and maturity range of the benchmark options. To improve the accuracy, we propose a generalized version of the weighted Monte Carlo calibration method with two distinguishing features. First, we use a probability distortion scheme to produce a non-uniform prior distribution for the simulated paths. Second, we assign multiple weights per path to fit with the different maturities present in the set of benchmark options. Our tests on S&P500 options data show that the new calibration method proposed here produces a significantly better out-of-sample fit than the original method for two commonly used asset pricing models.

Differentially weighted operator splitting Monte Carlo method for simulating complex aerosol dynamic processes

A differentially weighted operator splitting Monte Carlo (DWOSMC) method is developed to solve complex aerosol dynamic processes by coupling the differentially weighted Monte Carlo method and the operator splitting technique. This method is validated by analytical solutions and a sectional method in different aerosol dynamic processes. It is first validated in coagulation and condensation processes, and nucleation and coagulation processes, and then validated through simultaneous nucleation, coagulation, and condensation processes. The results show that the DWOSMC method is a computationally efficient and quantitatively accurate method for simulating complex aerosol dynamic processes.

Bidirectionally weighted Monte Carlo method for radiation transfer in the participating media

ABSTRACTA bidirectionally weighted Monte Carlo method has been developed for radiation transfer in participating media. For every two elementary cells, the radiation exchange is expressed as the weighted combination of those obtained from the forward and reverse Monte Carlo methods. And the weight is derived, so that the standard deviation of the radiation exchange is minimized, in contrast to the forward and reverse methods for the same computing cost. Moreover, this method can be applied to complex systems such as that containing highly spectral media. In benchmark solutions, the method was validated and results in less statistical errors than other types of Monte Carlo methods.

Weighted Monte Carlo estimators for angular distributions of the solar radiation reflected from a cloud layer

AbstractThe paper is focused on development of weighted Monte Carlo methods allowing one to estimate simultaneously the characteristics of the radiation field reflected from the medium based on a single Markov chain and in a sufficiently wide range of wavelengths. Such Markov chain is constructed with the use of a special ‘artificial’ scattering phase function whose choice is approximately optimized according to the criterion of minimum of the spectral maximum of the variance of estimates. The efficiency of the considered weighted method is studied on a model problem related to scattering of solar radiation by a cloud layer. The weighted method developed in the present article is aimed to supercomputer simulation.

Bayesian Estimation for Linear Functions of Poisson Rates

The probability matching prior for linear functions of Poisson parameters is derived. A comparison is made between the confidence intervals obtained by Stamey and Hamilton (2006), and the intervals derived by us when using the Jeffreys’ and probability matching priors. The intervals obtained from the Jeffreys’ prior are in some cases fiducial intervals (Krishnamoorthy and Lee, 2010). A weighted Monte Carlo method is used for the probability matching prior. The power and size of the test, using Bayesian methods, is compared to tests used by Krishnamoorthy and Thomson (2004). The Jeffreys’, probability matching and two other priors are used.

Population Balance-Monte Carlo Simulation for Gas-to-Particle Synthesis of Nanoparticles

The process simulation of nanoparticle synthesis via the gas-phase method is essential to understanding the detailed dynamic evolution of nanoparticles within a very short time period under high temperature. The task is, however, very challengeable up to now as the conversion of the gaseous precursor to the end-use nanoparticle is a complex physicochemical process involving nucleation of the particulate phase, agglomeration between particles and sintering under industrial production conditions. In this article, we extended the differentially weighted Monte Carlo method for population balance to simulate the dynamic evolution of titania (TiO2) nanoparticles synthesized by gas-to-particle conversion in a single aerosol reactor, considering simultaneous nucleation, agglomeration, and sintering. The simulated size distribution of TiO2 agglomerate and primary particles produced by the thermal decomposition of titanium tetraisoproxide agreed well with the experimental data. In the simulation, the fast population balance-Monte Carlo method was utilized to accelerate the process simulation on a desktop PC. Results were obtained up to 178 times faster than that of a normal Monte Carlo method. The inhomogeneous internal structure of primary particles was considered through solving population balance of polydisperse primary particles within agglomerate. It was found the polydisperse model could predict the primary particle size distribution better. Simulation results revealed a complex competition relation among nucleation, agglomeration and sintering. Copyright 2013 American Association for Aerosol Research

A Monte Carlo method for coagulation of charged particles

A simple, straightforward Monte Carlo method for handling coagulation of charged particles has been presented in this note, which is essentially by extending a differentially weighted Monte Carlo method. Then the Monte Carlo scheme is applied to a case study of coagulation of bipolarly charged particles. It is shown that the Monte Carlo method proposed can achieve satisfactory results with a very straightforward algorithm and greatly minimized programming efforts.

Improving Langley calibrations by reducing diurnal variations of aerosol Ångström parameters

Abstract. Errors in the sun photometer calibration constant lead to artificial diurnal variations, symmetric around solar noon, of the retrieved aerosol optical depth (AOD) and the associated Ångström exponent α and its curvature γ. We show in simulations that within the uncertainty of state-of-the-art Langley calibrations, these diurnal variations of α and γ can be significant in low AOD conditions, while those of AOD are negligible. We implement a weighted Monte Carlo method of finding an improved calibration constant by minimizing the diurnal variations in α and γ and apply the method to sun photometer data of a clear day in Innsbruck, Austria. The results show that our method can be used to improve the calibrations in two of the four wavelength channels by up to a factor of 3.6.

Engineering More Effective Weighted Monte Carlo Option Pricing Models

The Weighted Monte Carlo (WMC) method (Avellaneda (1998) and Avellaneda et al. (2001)) is a practical and robust method for calibrating a contingent claim pricing model that is consistent with the prices of liquid market instruments. We discuss new, tractable instances of the WMC method that make use of underlying asset prices that evolve with Student t (rather than, for example, Gaussian) innovations, relative U-entropy (rather than Kullback-Leibler relative entropy), and constraints that force model prices to lie within the bid-ask bands together with penalties on the discrepancies from the mid-market prices. We demonstrate the effectiveness of these WMC instances via benchmarking exercises on SPX option and LIBOR swaption data. In particular, we find that our WMC instances can be successfully calibrated to more liquid options (in our benchmarking exercises, our WMC instances reduced calibration failure rates – SPX options and LIBOR swaptions priced outside the bid-ask band – by a factors of over 2,000 and 38, respectively), and are more accurate on “out-of-sample” options than previously described WMC instances, particularly short-dated options and highly out-of-the-money options, where our instances are less prone to underpricing.

Phase Transition Determinated by Weighted Monte Carlo Simulations

We study the weighted Monte Carlo method, which was proposed by Milchev, Heermann and Binder. First, we describe our method and the Monte Carlo procedure. Second, we apply the procedure to study the phase transitions of and Sine-Gordon models, respectively. The critical values of the parameters allow us to determine the phase diagram of the models.

Weighted modification of the majorizing frequency method as applied to solving nonlinear kinetic equations

A special two-parameter weighted Monte Carlo method is constructed that is, on the one hand, as fast as the well-known majorizing frequency method and, on the other hand, applies to pair collisions of unbounded frequency. The variances of the collision and absorption estimates are proved to be bounded for the method.

Two-component Brownian coagulation: Monte Carlo simulation and process characterization

The compositional distribution within aggregates of a given size is essential to the functionality of composite aggregates that are usually enlarged by rapid Brownian coagulation. There is no analytical solution for the process of such two-component systems. Monte Carlo method is an effective numerical approach for two-component coagulation. In this paper, the differentially weighted Monte Carlo method is used to investigate two-component Brownian coagulation, respectively, in the continuum regime, the free-molecular regime and the transition regime. It is found that (1) for Brownian coagulation in the continuum regime and in the free-molecular regime, the mono-variate compositional distribution, i.e., the number density distribution function of one component amount (in the form of volume of the component in aggregates) satisfies self-preserving form the same as particle size distribution in mono-component Brownian coagulation; (2) however, for Brownian coagulation in the transition regime the mono-variate compositional distribution cannot reach self-similarity; and (3) the bivariate compositional distribution, i.e., the combined number density distribution function of two component amounts in the three regimes satisfies a semi self-preserving form. Moreover, other new features inherent to aggregative mixing are also demonstrated; e.g., the degree of mixing between components, which is largely controlled by the initial compositional mass fraction, improves as aggregate size increases.

Application of statistical methods for the study of kinetic model of traffic flow with separated accelerations

The problem of numerical estimation of the functionals of the solutions to a Boltzmann type nonlinear equation in the kinetic model of a vehicle traffic flow with separated acceleration is considered. The authors construct a second-kind integral equation for the original probabilistic model of a vehicle traffic flow, which is related to a linear N-particle model of the vehicle system evolution. Weighted Monte Carlo methods are proposed for the estimation of the functionals of the solution to the obtained equation. The practical suitability of this approach to the solution of traffic problems is demonstrated by numerical experiments. It should be noted that, in contrast to the previous papers, the authors do not use an artificial time step not included in the original traffic flow model.

A differentially weighted Monte Carlo method for two-component coagulation

The direct simulation Monte Carlo (DSMC) method for population balance modeling is capable of retaining the history of each simulation particle and is thus able to deal with multivariate properties in a simple and straightforward manner. As opposed to conventional DSMC approaches that track equally weighted simulation particles, a differentially weighted Monte Carlo method is extended to simulate two-component coagulation processes and is thereby able to simulate the micromixing of the components. A new feature of the method for this bivariate population balance modeling is that it is possible to specify how the simulation particles are distributed over the compositional axis. This allows us to obtain information about particles in those regions of the size and composition distribution functions where the non-weighted MC methods place insufficient simulation particles to obtain an inaccurate solution. The new feature results in lower statistical noise for simulating two-component coagulation, which is validated by using two-component coagulation cases for which analytical solutions exist (a discrete process with sum kernel for initial monodisperse populations and a process with constant kernel for initial polydisperse populations).

Transfer matrices and solution of the heat-mass transfer problem for aerosol clusters in a rarefied gas medium by the Monte Carlo method

The form of the decomposition of summands in Neumann series and the general solution to a linear integral equation based on separation of variables are considered under some assumptions on the properties of the integral transform. It is shown that one can reduce the order of the problem. Special transfer matrices are proposed for estimation of functionals. Based on weighted Monte Carlo methods and the use of transfer matrices, an algorithm for the calculation of molecular heat-mass transfer in an aerosol cluster is constructed in the approximation of free molecular gas kinetics. The cluster exists in a rarefied gas medium and, in the general case, absorbs radiation in the visible and infrared wave ranges. The algorithm allows one to compute the molecular heat transfer, photophoretic forces and their momenta, the four tensors describing the viscous forces and their momenta, and also the relationship between the translatory and rotatory motion of the cluster under an approximation linear with respect to the translatory and rotatory velocities of the system. The results of the application of the developed algorithms to the analysis of the influence of gravito-photophoresis on aerosol stratification in the stratosphere and mesosphere of the Earth are discussed as well.

Recurrent partial averaging in the theory of weighted Monte Carlo methods

Recurrent partial averaging in the theory of weighted Monte Carlo methods

Weighted Monte Carlo method for an approximate solution of the nonlinear coagulation equation

New weighted modifications of direct statistical simulation methods designed for the approximate solution of the nonlinear Smoluchowski equation are developed on the basis of stratification of the interaction distribution in a multiparticle system according to the index of a pair of interacting particles. The weighted algorithms are validated for a model problem with a known solution. It is shown that they effectively estimate variations in the functionals with varying parameters, in particular, with the initial number N0 of particles in the simulating ensemble. The computations performed for the problem with a known solution confirm the semiheuristic hypothesis that the model error is O(N0−1). Estimates are derived for the derivatives of the approximate solution with respect to the coagulation coefficient.

Conservative method for the reduction of the number of particles in the Monte Carlo simulation method for kinetic equations

A method for the reduction of the number of particles in the weighted Monte Carlo method for kinetic equations is described. The method randomly redistributes statistical weights over the particle ensemble in such a way that the weight of some particles becomes 0, i.e., the particles are cancelled, while all physically relevant macroscopic moments (e.g., mass, energy, momentum) of the ensemble do not change. The method has been applied to the spatially uniform relaxation of a gas of hard spheres.