An efficient,robust, domain-decomposition algorithm for particle Monte Carlo

A previously described algorithm [T.A. Brunner, T.J. Urbatsch, T.M. Evans, N.A. Gentile, Comparison of four parallel algorithms for domain decomposed implicit Monte Carlo, Journal of Computational Physics 212 (2) (2006) 527–539] for doing domain decomposed particle Monte Carlo calculations in the context of thermal radiation transport has been improved. It has been extended to support cases where the number of particles in a time step are unknown at the beginning of the time step. This situation arises when various physical processes, such as neutron transport, can generate additional particles during the time step, or when particle splitting is used for variance reduction. Additionally, several race conditions that existed in the previous algorithm and could cause code hangs have been fixed. This new algorithm is believed to be robust against all race conditions. The parallel scalability of the new algorithm remains excellent.     

A benchmark comparison of Monte Carlo particle transport algorithms for binary stochastic mixtures

We numerically investigate the accuracy of two Monte Carlo algorithms originally proposed by Zimmerman [1] and Zimmerman and Adams [2] for particle transport through binary stochastic mixtures. We assess the accuracy of these algorithms using a standard suite of planar geometry incident angular flux benchmark problems and a new suite of interior source benchmark problems. In addition to comparisons of the ensemble-averaged leakage values, we compare the ensemble-averaged material scalar flux distributions. Both Monte Carlo transport algorithms robustly produce physically realistic scalar flux distributions for the benchmark transport problems examined. The base Monte Carlo algorithm reproduces the standard Levermore-Pomraning model [3] and [4] results. The improved Monte Carlo algorithm generally produces significantly more accurate leakage values and also significantly more accurate material scalar flux distributions. We also present deterministic atomic mix solutions of the benchmark problems for comparison with the benchmark and the Monte Carlo solutions. Both Monte Carlo algorithms are generally significantly more accurate than the atomic mix approximation for the benchmark suites examined.     

Comparison between fixed and Gaussian steplength in Monte Carlo simulations for diffusion processes

We analyze the different degrees of accuracy of two Monte Carlo methods for the simulation of one-dimensional diffusion processes with homogeneous or spatial dependent diffusion coefficient that we assume correctly described by a differential equation. The methods analyzed correspond to fixed and Gaussian steplengths. For a homogeneous diffusion coefficient it is known that the Gaussian steplength generates exact results at fixed time steps Δt. For spatial dependent diffusion coefficients the symmetric character of the Gaussian distribution introduces an error that increases with time. As an example, we consider a diffusion coefficient with constant gradient and show that the error is not present for fixed steplength with appropriate asymmetric jump probabilities.     

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采用蒙特卡罗模型对氮空心阴极放电等离子体鞘层离子(N2 、N )的输运过程进行了模拟研究,计算了阴极鞘层中氮离子(N2 、N )的能量及角分布的空间变化和粒子密度及平均能量随放电参数的变化规律。研究结果表明:空心阴极放电产生的氮离子,在鞘层输运过程中,N2 是密度几乎不变的低能粒子;N 是密度逐渐减少的高能粒子。随着电压增加,N 密度减小,平均能量增加;N2 密度和平均能量变化不明显。能量及入射角的相对分布规律与平板电极氮直流辉光放电基本类似,但圆筒空心阴极放电更有利于氮离子的产生。     

An adaptive emission model for Monte Carlo simulations in highly inhomogeneous media represented by stochastic particle fields

Traditional Monte Carlo ray-tracing (MCRT) methods for continuous participating media are not applicable in media represented by point masses (or stochastic particles) frequently encountered in combustion modeling. In the authors’ previous work several ray models and particle models have been proposed for radiation simulations in such media. In the present paper an efficient emission scheme is developed for MCRT in highly inhomogeneous media represented by particle fields. Ray energies are limited to a narrow range to reduce statistical error, by having particles emit numbers of photons proportional to their emissive power (including combination of weak particles). A method to evaluate the radiative heat source, required by the overall energy equation, is also developed. A particle field representing the highly inhomogeneous medium in a turbulent jet flame is employed to test the proposed methods.     

Study on photon migration path of ultrashort light pulse in turbid media by Monte Carlo method

The photon density and the photon weight density are obtained by a Monte Carlo method. Based on these two concepts the Gaussian peak value photon paths and the weight mean photon paths of ultrashort light pulse in turbid media are defined and studied. The width of the Gaussian peak value photon path is also given. The influence of the exit angle and time on the photon path and its width are discussed. The relative probability of the photon path is given by the sum of the photon weight densities along the photon path, which could be used to calculate the normalized diffusive intensity approximately. The diffusive reflective intensities will arrive at the maximum at some instant at the place where the photon path reaches on the entrance surface at the same instant. The absorption coefficient has small effect on the photon path and its width in the case of the photon weight density.     

A Monte Carlo model for determination of binary diffusion coefficients in gases

A Monte Carlo method has been developed for the calculation of binary diffusion coefficients in gas mixtures. The method is based on the stochastic solution of the linear Boltzmann equation obtained for the transport of one component in a thermal bath of the second one. Anisotropic scattering is included by calculating the classical deflection angle in binary collisions under isotropic potential. Model results are compared to accurate solutions of the Chapman–Enskog equation in the first and higher orders. We have selected two different cases, H₂ in H₂ and O in O₂, assuming rigid spheres or using a model phenomenological potential. Diffusion coefficients, calculated in the proposed approach, are found in close agreement with Chapman–Enskog results in all the cases considered, the deviations being reduced using higher order approximations.     

A Monte Carlo algorithm for lattice ribbons

A lattice ribbon is a connected sequence of plaquettes subject to certain selfavoidance conditions. The ribbon can be closed to form an object which is topologically either a cylinder or a Möbius band, depending on whether its surface is orientable or nonorientable. We describe a grand canonical Monte Carlo algorithm for generating a sample of these ribbons, prove that the associated Markov chain is ergodic, and present and discuss numerical results about the dimensions and entanglement complexity of the ribbons.     

热辐射输运问题的高效蒙特卡罗模拟方法

惯性约束聚变研究中,热辐射光子在介质中的输运以及热辐射光子与介质的相互作用是重要研究课题,蒙特卡罗方法是该类问题的重要研究手段之一.隐式蒙特卡罗方法虽然能正确地模拟热辐射在介质中的输运过程,但当模拟重介质(材料的吸收系数大)问题时,该方法花费的计算时间将变得很长,导致模拟效率很低.本文以离散扩散蒙特卡罗方法为基础,开发了"离散扩散蒙特卡罗方法辐射输运模拟程序",可以较好地解决重介质区的计算效率问题,但是离散扩散蒙卡罗方法在模拟轻介质区时精度不够高.辐射输运问题中通常既有轻介质也有重介质,为了能同时解决蒙特卡罗方法模拟的效率和精度问题,本文研究了离散扩散蒙特卡罗方法与隐式蒙特卡罗方法相结合的模拟方法,并提出了新的扩散区与输运区界面处理方法,研制了混合蒙特卡罗方法的辐射输运模拟程序.典型辐射输运问题模拟显示:在模拟重介质问题时,该程序能大幅缩短模拟时间,且能取得与隐式蒙特卡罗方法一致的结果;在模拟轻重介质均存在的问题时,与隐式蒙特卡罗方法相比,混合蒙特卡罗方法的模拟精度与其相当且计算效率同样能够得到显著提升.     

Quiet Monte Carlo radiation transport

We model radiation transport by advancing computational photons through phase space with solutions to a set of stochastic differential equations of motion. Random numbers that appear in the equations of motion are sampled with deterministically chosen Gaussian quadrature weights and abscissas. In this way, the advantages of particle Monte Carlo are realized without generating statistical noise. We demonstrate this technique by performing one- and two-dimensional test problems in which gray radiation is energetically coupled to stationary material. Scattering is accomplished with a Fokker-Planck scattering operator. Free streaming, diffusion and Marshak waves are recovered in appropriate limits.     

Guaranteeing total balance in Metropolis algorithm Monte Carlo simulations

The condition of detailed balance has long been used as a proxy for the more difficult-to-prove condition of total balance, which along with ergodicity is required to guarantee convergence of a Markov Chain Monte Carlo (MCMC) simulation to the correct probability distribution. However, some simple-to-program update schemes such as the sequential and checkerboard Metropolis algorithms are known not to satisfy detailed balance for such common systems as the Ising model.     

Exact Monte Carlo for few-fermion systems

We have reconsidered the fundamental difficulties of fermion Monte Carlo as applied to few-body systems. We conclude that necessary ingredients of successful algorithms include the following: There must be equal populations of random walkers that carry positive and negative weights. The positions of positive walkers should be selected from a distribution that uses Green's functions to couple all walkers. The positions of negative walkers should be generated from those of positive walkers by means of odd permutations. The correct importance functions that take into account the global interactions of the populations are different for positive and negative walkers. Use of such importance functions breaks the symmetry that otherwise would exist between configurations (of the entire population) and configurations derived by interchanging positive and negative walkers. Based upon these observations, we have constructed a stable and accurate algorithm that solves a fully-polarized, three-dimensional, three-body model problem.     

A unified Monte Carlo treatment of the transport of electromagnetic energy, electrons, and phonons in absorbing and scattering media

The scalar Boltzmann transport equation (BTE) is often applicable to radiative energy transfer, electron-beam propagation, as well as thermal conduction by electrons and phonons provided that the characteristic length of the system is much larger than the wavelength of energy carriers and that certain interference phenomena and the polarization nature of carriers are ignored. It is generally difficult to solve the BTE analytically unless a series of assumptions are introduced for the particle distribution function and scattering terms. Yet, the BTE can be solved using statistical approaches such as Monte Carlo (MC) methods without simplifying the underlying physics significantly. Derivations of the MC methods are relatively straightforward and their implementation can be achieved with little effort; they are also quite powerful in accounting for complicated physical situations and geometries. MC simulations in radiative transfer, electron-beam propagation, and thermal conduction by electrons and phonons have similar simulation procedures; however, there are important differences in implementing the algorithms and scattering properties between these simulations. The objective of this review article is to present these simulation procedures in detail and to show that it is possible to adapt an existing MC computer code, for instance, in radiative transfer, to account for physics in electron-beam transport or phonon (or electronic thermal) conduction by sorting out the differences and implementing the correct corresponding steps. Several simulation results are presented and some of the difficulties associated with different applications are explained.     

Finite-size effects at critical points with anisotropic correlations: Phenomenological scaling theory and Monte Carlo simulations

Various thermal equilibrium and nonequilibrium phase transitions exist where the correlation lengths in different lattice directions diverge with different exponentsv ,v : uniaxial Lifshitz points, the Kawasaki spin exchange model driven by an electric field, etc. An extension of finite-size scaling concepts to such anisotropic situations is proposed, including a discussion of (generalized) rectangular geometries, with linear dimensionL in the special direction and linear dimensionsL in all other directions. The related shape effects forL L but isotropic critical points are also discussed. Particular attention is paid to the case where the generalized hyperscaling relationv +(d–1)v =+2 does not hold. As a test of these ideas, a Monte Carlo simulation study for shape effects at isotropic critical point in the two-dimensional Ising model is presented, considering subsystems of a 1024x1024 square lattice at criticality.Visiting Supercomputer Senior Scientist at Rutgers University.     

混浊介质多光子激发荧光显微成像的蒙特卡罗模拟

将蒙特卡罗方法与几何光线追踪技术相结合用于研究样品混浊特性对多光子激发蒌光显微成像的影响。推导了模拟多层样品显微成像的数学模型,给出了用程序框图表示的基本仿真系统骨架,对传统蒙特卡罗方法的改进有效地增强了对聚焦光束的模拟能力,初步的模拟结果说明了混浊介质散射特性对显微成像的显著影响。     

A boundary-based net-exchange Monte Carlo method for absorbing and scattering thick media

A boundary-based net-exchange Monte Carlo method was introduced (JQSRT 74 (2001) 563) that allows to bypass the difficulties encountered by standard Monte Carlo algorithms in the limit of optically thick absorption (and/or for quasi-isothermal configurations). With the present paper, this method is extended to scattering media. Developments are fully 3D, but illustrations are presented for plane parallel configuration. Compared to standard Monte Carlo algorithms, convergence qualities have been improved over a wide range of absorption and scattering optical thicknesses. The proposed algorithm still encounters a convergence difficulty in the case of optically thick, highly scattering media.     

A Monte Carlo implementation to solve radiation heat transfer in non-uniform media with spectrally dependent properties

This paper presents the application of the Monte Carlo method to solve the radiative heat exchange in non-homogeneous, non-isothermal gases with spectrally dependent properties. Among others models, the absorption-line blackbody (ALB) distribution function, originally defined and derived for the spectral line-based weighted-sum-of-gray-gases (SLW) model, allows an immediate, simple implementation of the Monte Carlo method to account the spectral dependence of the radiative properties. This work shows how the Monte Carlo method can be combined to the ALB distribution function, and provides results for heat transfer in a mixture of water vapor, carbon dioxide and nitrogen that have satisfactory agreement with the SLW method and with line-by-line integration. Finally, the solution technique is employed to solve two examples aiming at demonstrating the effect of the absorbing species concentration on the thermal radiative exchanges. The method is of great interest for the computation of radiative transfer in combustion systems where the chemical species concentration and the temperature are not uniform.     

Monte Carlo method and sensitivity estimations

It is shown that, starting from any existing Monte Carlo algorithm for estimation of a physical quantity A, it is possible to implement a simple additional procedure that simultaneously estimates the sensitivity of A to any problem parameter. The corresponding supplementary cost is very low as no additional random sampling is required. The principle is presented on a formal basis and simple radiative transfer examples are used for illustration.