Dynamic weighting in simulations of spin systems

We establish the invariance property of a dynamically weighted Monte Carlo process and apply the method to the simulation of spin glasses and Ising models. For the two-dimensional Edwards-Anderson model, we obtain an ergodicity time of O(L^2.44), where L is the linear dimension of the lattice. The results suggest that dynamic weighting is a highly promising new tool for Monte Carlo simulation.     

Determining the stability of genetic switches: explicitly accounting for mRNA noise

Cells use genetic switches to shift between alternate gene-expression states, e.g., to adapt to new environments or to follow a developmental pathway. Here, we study the dynamics of switching in a generic-feedback on-off switch. Unlike protein-only models, we explicitly account for stochastic fluctuations of mRNA, which have a dramatic impact on switch dynamics. Employing the WKB theory to treat the underlying chemical master equations, we obtain accurate results for the quasistationary distributions of mRNA and protein copy numbers and for the mean switching time, starting from either state. Our analytical results agree well with Monte Carlo simulations. Importantly, one can use the approach to study the effect of varying biological parameters on switch stability.     

Green function simulation of Hamiltonian lattice models with stochastic reconfiguration

We apply a recently proposed Green function Monte Carlo procedure to the study of Hamiltonian lattice gauge theories. This class of algorithms computes quantum vacuum expectation values by averaging over a set of suitable weighted random walkers. By means of a procedure called stochastic reconfiguration the long standing problem of keeping fixed the walker population without a priori knowledge of the ground state is completely solved. In the model, which we choose as our theoretical laboratory, we evaluate the mean plaquette and the vacuum energy per plaquette. We find good agreement with previous works using model-dependent guiding functions for the random walkers. Received: 23 November 1999 / Published online: 25 February 2000     

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.     

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.     

Numerical Analysis on Enhanced Backscatterings of Light Based on Rayleigh-Debye Scattering Theory

Enhanced backscatterings from the disordered dense media are investigated by means of the Monte Carlo simulation. On the basis of the Rayleigh-Debye scattering theory, numerical simulations demonstrate the dependences of the peak, width and spatial anisotropy of enhanced intensity distributions on the size of scattering particles. Discussions are made by decomposing the backscattering intensity to the contributions with different scattering orders. As a result, it is shown that the particle-size dependence of the peak and width is described by the probability density function of the scattering order and the mean free pathlength. It is also shown that the spatial anisotropy of the intensity peak is described by the depolarization at each scattering event and the extinction in propagation within the random media.     

航天器表面环境散射返回流TPMC模拟

介绍试验粒子Monte Carlo(test particle Monte Carlo,TPMC)方法,并采用该方法对4种航天器表面出气分子形成的环境散射返回流进行数值模拟.其中,圆球出气表面的计算结果与已有的DSMC(direct simulation Monte Carlo)结果一致,验证了方法的正确性.此外,对不同出气和来流条件下圆形平板、凸半球和凹半球3种航天器简化表面出气分子形成的环境散射返回流进行计算,结果表明:出气表面外形是影响返回通量比的一个重要因素;圆形平板和凹半球出气表面的返回通量比远大于凸半球表面的;凹半球表面的出气分子会直接和出气表面碰撞形成直接流污染,且其量级远大于返回流污染.因此,在航天器设计中尽可能使用凸形表面作为敏感的出气表面可以有效降低出气分子污染.     

Monte Carlo techniques for real-time quantum dynamics

The stochastic-gauge representation is a method of mapping the equation of motion for the quantum mechanical density operator onto a set of equivalent stochastic differential equations. One of the stochastic variables is termed the “weight”, and its magnitude is related to the importance of the stochastic trajectory. We investigate the use of Monte Carlo algorithms to improve the sampling of the weighted trajectories and thus reduce sampling error in a simulation of quantum dynamics. The method can be applied to calculations in real time, as well as imaginary time for which Monte Carlo algorithms are more-commonly used. The Monte-Carlo algorithms are applicable when the weight is guaranteed to be real, and we demonstrate how to ensure this is the case. Examples are given for the anharmonic oscillator, where large improvements over stochastic sampling are observed.     

Diffusion and aggregation of adatoms on faceted Pd/Mo(111) surface

Diffusion of Pd adatoms on faceted Pd/Mo(111) surface with hill and valley structure is studied by kinetic Monte Carlo method. The surface consists of {211} channeled facets separated by concave and convex edges. It is shown that diffusion on the faceted surface is significantly reduced with comparison to diffusion on (112) surface by the presence of concave edges. A simple formula for the diffusion coefficient is proposed. The growth of linear structures, studied at low coverage θ = 0.1, depends on the cross-channel diffusion, although the cross-channel diffusion coefficient is by 6–8 orders of magnitude smaller than the in-channel diffusion coefficient. We observed that most of atomic structures grow in valleys and the average size of the structure increases with increase of facet size.     

Two-stage ordering of spins in dipolar spin ice on the kagome lattice

Spin ice, a peculiar thermal state of a frustrated ferromagnet on the pyrochlore lattice, has a finite entropy density and excitations carrying magnetic charge. By combining analytical arguments and Monte Carlo simulations, we show that spin ice on the two-dimensional kagome lattice orders in two stages. The intermediate phase has ordered magnetic charges and is separated from the paramagnetic phase by an Ising transition. The transition to the low-temperature phase is of the three-state Potts or Kosterlitz-Thouless type, depending on the presence of defects in the charge order.     

On the inclusion of collisional correlations in quantum dynamics

We present a formalism to describe collisional correlations responsible for thermalization effects in finite quantum systems. The approach consists in a stochastic extension of time dependent mean field theory. Correlations are treated in time dependent perturbation theory and loss of coherence is assumed at some time intervals allowing a stochastic reduction of the correlated dynamics in terms of a stochastic ensemble of time dependent mean-fields. This theory was formulated long ago in terms of density matrices but never applied in practical cases because of its complexity. We propose here a reformulation of the theory in terms of wave functions and use a simplified 1D model of cluster and molecules allowing to test the theory in a schematic but realistic manner. We illustrate the performance in terms of several observables, in particular global moments of the density matrix and single particle entropy built on occupation numbers. The occupation numbers remain fixed in time dependent mean-field propagation and change when evaluating the correlations, then taking fractional values. They converge asymptotically towards Fermi distributions which is a clear indication of thermalization.     

Accelerated Monte Carlo for Optimal Estimation of Time Series

Asbstract By casting stochastic optimal estimation of time series in path integral form, one can apply analytical and computational techniques of equilibrium statistical mechanics. In particular, one can use standard or accelerated Monte Carlo methods for smoothing, filtering and/or prediction. Here we demonstrate the applicability and efficiency of generalized (nonlocal) hybrid Monte Carlo and multigrid methods applied to optimal estimation, specifically smoothing. We test these methods on a stochastic diffusion dynamics in a bistable potential. This particular problem has been chosen to illustrate the speedup due to the nonlocal sampling technique, and because there is an available optimal solution which can be used to validate the solution via the hybrid Monte Carlo strategy. In addition to showing that the nonlocal hybrid Monte Carlo is statistically accurate, we demonstrate a significant speedup compared with other strategies, thus making it a practical alternative to smoothing/filtering and data assimilation on problems with state vectors of fairly large dimensions, as well as a large total number of time steps.     

Order by disorder from nonmagnetic impurities in a two-dimensional quantum spin liquid

We consider doping of nonmagnetic impurities in the spin-1/2, 1/5-depleted square lattice. This structure, whose undoped phase diagram offers both magnetically ordered and spin-liquid ground states, is realized physically in CaV4O9. Doping into the ordered phase results in a progressive loss of order, which becomes complete at the percolation threshold. By contrast, doping into the spin liquids creates a phase of weak but long-ranged antiferromagnetic order, a true order-by-disorder phenomenon. We study the phase diagram of the doped system by computing the static susceptibility and staggered magnetization using a stochastic series-expansion quantum Monte Carlo technique.     

Bayesian and Frequentist Inferences on a Type I Half-Logistic Odd Weibull Generator with Applications in Engineering

In this article, we have proposed a new generalization of the odd Weibull-G family by consolidating two notable families of distributions. We have derived various mathematical properties of the proposed family, including quantile function, skewness, kurtosis, moments, incomplete moments, mean deviation, Bonferroni and Lorenz curves, probability weighted moments, moments of (reversed) residual lifetime, entropy and order statistics. After producing the general class, two of the corresponding parametric statistical models are outlined. The hazard rate function of the sub-models can take a variety of shapes such as increasing, decreasing, unimodal, and Bathtub shaped, for different values of the parameters. Furthermore, the sub-models of the introduced family are also capable of modelling symmetric and skewed data. The parameter estimation of the special models are discussed by numerous methods, namely, the maximum likelihood, simple least squares, weighted least squares, Cramér-von Mises, and Bayesian estimation. Under the Bayesian framework, we have used informative and non-informative priors to obtain Bayes estimates of unknown parameters with the squared error and generalized entropy loss functions. An extensive Monte Carlo simulation is conducted to assess the effectiveness of these estimation techniques. The applicability of two sub-models of the proposed family is illustrated by means of two real data sets.     

An improved wavelength selection scheme for Monte Carlo solvers applied to hypersonic plasmas

A new databasing scheme is developed for Monte Carlo Ray Tracing methods applied to hypersonic planetary entry. In this scheme, the complex relationships for the emission wavelength selection of atomic and molecular species in nonequilibrium flows are simplified by developing random number relationships for individual transitions, as opposed to using relationships for the spectral emission coefficient of a given species. These new techniques speed up wavelength selection by about 2 orders of magnitude, and offer flexibility for use in weighted or part-spectrum Monte Carlo solvers.     

Energy diffusion controlled reaction rate in dissipative Hamiltonian systems

In this paper the energy diffusion controlled reaction rate in dissipative Hamiltonian systems is investigated by using the stochastic averaging method for quasi Hamiltonian systems. The boundary value problem of mean first-passage time (MFPT) of averaged system is formulated and the energy diffusion controlled reaction rate is obtained as the inverse of MFPT. The energy diffusion controlled reaction rate in the classical Kramers bistable potential and in a two-dimensional bistable potential with a heat bath are obtained by using the proposed approach respectively. The obtained results are then compared with those from Monte Carlo simulation of original systems and from the classical Kramers theory. It is shown that the reaction rate obtained by using the proposed approach agrees well with that from Monte Carlo simulation and is more accurate than the classical Kramers rate.     

雷电电磁场峰值的概率分布

获得雷电电磁场的随机特性,是研究雷电电磁场对电子系统有害耦合效应评估的基础。基于雷电流的统计特性,在具有一般性的概率框架下讨论雷电电磁场,导出电磁场峰值的概率分布函数及密度函数,采用多重积分法计算出不同位置处电场强度和磁场强度峰值的概率分布图和累积概率分布图,计算结果与蒙特卡洛模拟结果吻合。     

An Analysis of Polynomial Chaos Approximations for Modeling Single-Fluid-Phase Flow in Porous Medium Systems

We examine a variety of polynomial-chaos-motivated approximations to a stochastic form of a steady state groundwater flow model. We consider approaches for truncating the infinite dimensional problem and producing decoupled systems. We discuss conditions under which such decoupling is possible and show that to generalize the known decoupling by numerical cubature, it would be necessary to find new multivariate cubature rules. Finally, we use the acceleration of Monte Carlo to compare the quality of polynomial models obtained for all approaches and find that in general the methods considered are more efficient than Monte Carlo for the relatively small domains considered in this work. A curse of dimensionality in the series expansion of the log-normal stochastic random field used to represent hydraulic conductivity provides a significant impediment to efficient approximations for large domains for all methods considered in this work, other than the Monte Carlo method.     

二维正方晶格Compass-XY模型的方向序和拓扑序

采用Monte Carlo方法研究二维正方晶格Compass-XY模型,通过调节过渡参量α,计算了降低交换相互作用的阻挫对方向序和拓扑序的影响.结果表明,方向序和拓扑序之间的转变是一个逐渐过渡的过程,并不存在明显的界限.在某一范围内,这两种序是相互重叠的,难以区分.阻挫的降低,易于形成拓扑序,同时会抑制方向序.当阻挫变得足够弱时,方向序被破坏.     

微米量级表面结构形貌特性对二次电子发射抑制的优化

抑制二次电子倍增效应是提高空间大功率微波器件和粒子加速器等设备性能的重要课题,而使用表面处理降低材料的二次电子发射系数是抑制二次电子倍增的有效手段.为优化寻找抑制效果最好的表面形貌,本文采用蒙特卡罗方法模拟了各种微米量级不同表面形貌的二次电子发射特性,研究占空比、深宽比、结构形状及排列方式等的影响.模拟结果表明,正方形、圆形、三角形凸起和凹陷结构的二次电子发射系数随占空比和深宽比的增大而减小,但存在饱和值;凸起结构的排列方式对二次电子发射系数的影响不大,但是凸起结构形状却对二次电子发射系数的影响较大,其中三角形的抑制效果最佳.对凹陷结构而言,不同形状的抑制效果差别不大;同时,占空比和深宽比相同时,凸起结构较凹陷结构抑制效果更佳.究其原因,核心在于垂直侧壁的“遮挡效应”,凹陷结构遮挡效应的大小与“陷阱”垂直高度有关,而凸起结构遮挡效应的大小和凸起部分的斜方向投影大小有关.