A generalized optimization of Monte Carlo particle transport schemes

Formulations and algorithms for optimizing biased random walk problems in radiation transport are described. A matrix-integral equation is constructed by coupling the second moment and its derivative with respect to the biasing parameter. The optimization is based on estimation of the second moment around the score and the Monte Carlo perturbation algorithm to treat the variation in the biasing parameter.     

Condensed history Monte Carlo methods for photon transport problems

We study methods for accelerating Monte Carlo simulations that retain most of the accuracy of conventional Monte Carlo algorithms. These methods - called Condensed History (CH) methods - have been very successfully used to model the transport of ionizing radiation in turbid systems. Our primary objective is to determine whether or not such methods might apply equally well to the transport of photons in biological tissue. In an attempt to unify the derivations, we invoke results obtained first by Lewis, Goudsmit and Saunderson and later improved by Larsen and Tolar. We outline how two of the most promising of the CH models - one based on satisfying certain similarity relations and the second making use of a scattering phase function that permits only discrete directional changes - can be developed using these approaches. The main idea is to exploit the connection between the space-angle moments of the radiance and the angular moments of the scattering phase function. We compare the results obtained when the two CH models studied are used to simulate an idealized tissue transport problem. The numerical results support our findings based on the theoretical derivations and suggest that CH models should play a useful role in modeling light-tissue interactions.     

蒙特卡罗粒子输运软件JMCT抽样工具库设计

为通用型蒙特卡罗粒子输运程序JMCT设计了抽样工具库,通过两种技术途径提供各分布的抽样。一是针对各种常见分布提供特定抽样子程序;二是提供一个通用型的抽样子程序,可以实现任意离散分布和任意一维有限区间上连续分布的自动抽样。在设计任意一维有限区间上连续分布的自动抽样工具时利用了部分开源代码,利用其功能提供给用户最大的方便性。对抽样工具库的检验表明,其可以正确、方便地实现各种输运模拟中常见分布的抽样。     

输运问题蒙特卡罗模拟方法回顾及展望北大核心CSCD

蒙特卡罗(MC)方法具有复杂几何处理能力强,方法通用灵活,核数据完备,模拟忠实于物理过程等特点,成为中子学数值模拟的首选方法之一。在核能领域,MC方法得益于计算机的快速发展,在辐射屏蔽、反应堆堆芯临界安全分析、乏燃料后处理、放射性废物处置、核设施退役、核事故应急、放射性石油测井、核医学等领域均有广泛应用。对MC方法及软件输运计算做简要回顾,并对未来发展进行展望。     

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.     

Time-dependent integral equations of neutron transport for calculating the kinetics of nuclear reactors by the Monte Carlo method

Integral equations for the shape functions in the adiabatic, quasi-static, and improved quasi-static approximations are presented. The approach to solving these equations by the Monte Carlo method is described.     

A hybrid (Monte Carlo/deterministic) approach for multi-dimensional radiation transport

A novel hybrid Monte Carlo transport scheme is demonstrated in a scene with solar illumination, scattering and absorbing 2D atmosphere, a textured reflecting mountain, and a small detector located in the sky (mounted on a satellite or a airplane). It uses a deterministic approximation of an adjoint transport solution to reduce variance, computed quickly by ignoring atmospheric interactions. This allows significant variance and computational cost reductions when the atmospheric scattering and absorption coefficient are small. When combined with an atmospheric photon-redirection scheme, significant variance reduction (equivalently acceleration) is achieved in the presence of atmospheric interactions.     

纤锌矿相GaN空穴输运特性的Monte Carlo模拟研究

用全带多粒子Monte Carlo方法模拟纤锌矿相(Wurtzite)GaN空穴输运特性的结果. 用经验赝势法计算得到能带结构数据. 模拟包含了声学声子散射，光学声子散射，极性光学声子散射，压电散射，电离杂质散射及带间散射等散射机理. 计算得到了空穴沿3个主要对称方向上的空穴平均漂移速度和平均能量与电场强度的关系曲线，室温下漂移速度呈现饱和特性. 在所研究的电场范围内，最大平均漂移速度约为6×10⁶cm s^-1，最大空穴平均能量约为0.12eV, 这些值均比电子的相应参数低很多. 还给出了空穴的扩散迁移率与杂质浓度关系的模拟结果. 关键词： 蒙特卡罗 氮化镓 输运特性 能带结构     

Hermite-DG methods for pdf equations modelling particle transport and deposition in turbulent boundary layers

A novel methodology is presented for the numerical treatment of multi-dimensional pdf (probability density function) models used to study particle transport in turbulent boundary layers. A system of coupled Fokker–Planck type equations is constructed to describe the transport of phase-space conditioned moments of particle and fluid velocities, both streamwise and wall-normal. This system, unlike conventional moment-based transport equations, allows for an exact treatment of particle deposition at the flow boundary and provides an efficient way to handle the 5-dimensional phase-space domain. Moreover, the equations in the system are linear and can be solved in a sequential fashion; there is no closure problem to address.A hybrid Hermite-Discontinuous Galerkin scheme is developed to treat the system. The choice of Hermite basis functions in combination with an iterative scaling approach permits the efficient computation of solutions to high accuracy. Results demonstrate the effectiveness of the methodology in resolving the extreme gradients characteristic of distributions near an absorbing boundary.     

Monte Carlo methods for the study of phase transitions and phase equilibria

Monte Carlo methods can predict macroscopic properties of N-body systems from the (classical) Hamiltonian describing the interactions between the particles and hence can serve as a basic tool of equilibrium statistical mechanics, avoiding uncontrolled approximations. However, a necessary ingredientis the control of finite size effects. For this purpose, the finite size scaling analysis of suitable distribution functions is a powerful tool. The basic ideas of this approach will be discussed, including extensions to critical phenomena where the hyperscaling relation between critical exponents is violated (colloid-polymer mixtures in random media as a realization of the random field Ising model, phase transitions caused by competition of interfacial and surface effects, etc.) Finite size effects on two-phase coexistence cause the existence of a van-der-Waals-like loop, but it has a completely different origin, the “spinodal” reflecting the “droplet evaporation/condensation” transition. Also the possibility to extract interface free energies is discussed.     

Critical exponent for the loop erased self-avoiding walk by Monte Carlo methods

A Monte Carlo simulation was performed for loop-erased self-avoiding walks (LESAW) to ascertain the exponentv for the Z² and Z³ lattices. The estimated values were 2v=1.600±0.006 in two dimensions and 2v=1.232±0.008 in three dimensions, leading to the conjecturev=4/5 for the two-dimensional LESAW. These results add to existing evidence that the loop-erased self-avoiding walks are not in the same universality class as self-avoiding walks.     

Hybrid MC/RISM technique for simulation of polymer solutions: Monte Carlo+ RISM integral equations

A new (hybrid) method is reported for modelling complex macromolecular systems. The approach combines the traditional atomistic Monte Carlo (MC) computer simulation of flexible polymer chains with the numerical solution of the site-site Ornstein-Zernike-like (RISM) integral equations. The method is used for calculating properties of a linear polymer in dilute solution. Since the condensed-phase environment of a flexible macromolecule affects the equilibrium configuration probability distribution of the macromolecule, the site-site intramolecular correlation function and the intramolecular potential field are treated in a self-consistent manner. Briefly, the MC method is applied to generate the configurations of a single chain molecule. Using the coordinates of chain beads, the averaged intrapolymer correlation function is obtained. Then, solving the coupled RISM equations for a given density of solvent particles, we find the polymer-solvent correlation functions. This yields the medium-induced intrapolymer potential and the corresponding effective intramolecular energies, which are used in the standard Metropolis MC procedure. The structural properties of the polymer chain are computed by averaging over the statistically representative set of configurations. As a result of many such iterations, the intramolecular structure is determined self-consistently. Using the hybrid MC/RISM method, extensive studies have been made of static properties of flexible polymer chains surrounded by LJ particles with purely repulsive interactions between the particles and chain beads. Also, direct molecular dynamics simulations have been carried out and have demonstrated that the hybrid MC/RISM approach gives a quite accurate prediction for condensed-phase effects.     

Guidelines for choosing the transition matrix in Monte Carlo methods using Markov chains

The sampling method proposed by Metropolis et al. (J. Chem. Phys. 21 (1953), 1087) requires the simulation of a Markov chain with a specified π as its stationary distribution. Hastings (Biometrika 57 (1970). 97) outlined a general procedure for constructing and simulating such a Markov chain. The matrix P = {p_ij} of transition probabilities is constructed using a defined symmetric function s and an arbitrary transition matrix Q. With respect to asymptotic variance reduction, Peskun (Biometrika 60 (1973), 607) determined, for a given Q, the optimum choice for s_ij. Here, guidelines are given for choosing Q so that the resulting Markov chain sampling method is as precise as is practically possible. Examples illustrating the use of the guidelines, including potential applications to problems in statistical mechanics and to the problem of estimating the probability of an simple event by “hit-ormiss” Monte Carlo in conjunction with Markov chain sampling, are discussed.     

Monte Carlo simulations of magnetic particle suspensions with a simple assessment method for the particle overlap between magnetic spheroids

We have developed a simple assessment method for the overlap between spheroidal particles, which neither requires the complex manipulation of vectors and matrices that is indispensable in the ordinary methods, nor is based on a model potential. Moreover, we have developed an evaluation method for the interaction energy arising from the overlap of the steric layer coating spheroidal particles. This is based on a sphere-connected particle model, but some modifications are introduced in order to express an appropriate repulsive interaction energy at the deepest overlapping position. We have investigated the phase change in a magnetic spheroidal particle suspension for a two-dimensional system by means of Monte Carlo simulations. In the case of no external magnetic field, if the magnetic particle-particle interaction is sufficiently strong to favour cluster formation, long raft-like clusters tend to be formed in a dilute situation. With decreasing values of area fraction, a chain-like structure in a dense situation transforms into a raft-like structure within a narrow range of the particle area fraction. Similarly, the raft-like clusters are preferred in a weak applied magnetic field, but an increase in the field strength induces a phase change from a raft-like into a chain-like structure.

Highlights of the present paper:

1. A simple assessment method has been proposed for the overlap between two spheroidal particles.

2. The particle overlap assessment is free from a complex mathematical manipulation regarding vectors and matrices.

3. A modified sphere-connected model has been proposed in order to more accurately evaluate a repulsive interaction due to the overlap of the steric layers coating spheroidal particles.

4. 2D Monte Carlo simulations have been performed to elucidate the phenomenon of a phase change by magnetic spheroidal particles on a material plane surface.

5. A phase change between a raft-like and a chain-like aggregate structure is able to be controlled by the area fraction of particles and an external magnetic field.

     

Modification of the individual collision technique for simulating electron transport using the Monte Carlo method

A new software version of the computing complex BRAND used for modeling the electron trans-port process is considered. Our modification differs in the use of nonanalog simulation of the azimuthal angle of particle scattering. The results of simulating electron transport problems are presented.     

Comparing the efficiency of Metropolis Monte Carlo and molecular-dynamics methods for configuration space sampling

Summary Computer methods for sampling statistical ensembles generate chains of configurations in which subsequent members differ only slightly. Statistical errors are determined by the number of independent configurations contained in the sample. A quantitative treatment of the persistence of correlation shows how the first two moments of the autocorrelation function of a variablef along the chain are connected with the expected variance of its mean. The variance of the potential energy in the canonical ensemble is shown be to larger than that in the microcanonical one by a factor which is the ratio of the system heat capacity to that of an ideal gas. A comparison has been made of the efficiency of Metropolis Monte Carlo (MC), the usual microcanonical molecular dynamic (MDM) and a modification of molecular dynamics for canonical ensemble sampling (MDC). The analysis is focused on three aspects: the mean square displacement of a representative point in configuration space, the persistence of correlation in the potential energyV and also in a function of interest in free-energy-difference calculations. In MDM simulations of crystalline solids, it was found thatV behaves as an ?oscillatory? variable and that the variance of its mean is reduced by antithetic variations of its values. Work performed under the auspices of the United State Department of Energy, Istituto per la Ricerca Scientifica e Tecnologica, Trento, and Gruppo Nazionale di Struttura della Materia del C.N.R., Italy.     

Monte Carlo simulation of in-plane spin-polarized transport in GaAs/GaAlAs quantum well in the three-subband approximation

We develop a Monte Carlo (MC) tool incorporated with the three-subband approximation model to investigate the in-plane spin-polarized transport in GaAs/GaAlAs quantum well. Using the tool, the effects of the electron occupation of higher subbands and the intersubband scattering on the spin dephasing have been studied. Compared with the corresponding results of the simple one-subband approximation model, the spin dephasing length is reduced four times under 0.125\,kV/cm of driving electric field at 300K by the MC tool incorporated with the three-subband approximation model, indicating that the three-subband approximation model predicts significantly shorter spin dephasing length with temperature increasing. Our simulation results suggest that the effects of the electron occupation of higher subbands and the intersubband scattering on the spin-dependent transport of GaAs 2-dimensional electron gas need to be considered when the driving electric field exceeds the moderate value and the lattice temperature is above 100K. The simulation by using the MC tool incorporated with the three-subband approximation model also indicates that, under a certain driving electric field and lattice temperature, larger channel widths cause spins to be depolarized faster. Ranges of the three components of the spins are different for three different injected spin polarizations due to the anisotropy of spin--orbit interaction.     

Application of the Monte Carlo methods and variational procedure for optimizing time-of-flight neutron diffractometer characteristics

Based on variational calculus, a procedure for the optimal approximation of detector surface of the time-of-flight neutron diffractometer has been suggested. The exact solution for a point sample and zero thickness detector has been obtained. Using the shape of the detector surface, an optimized Monte Carlo simulation has been performed for the parameters of the spectrometer depending on the sample size and detector thickness, its azimuthal and Bragg’s angular dimensions, and taking into account the neutron absorption in the sample and detector.