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.     

MLIMCL：基于机器学习的隐式溶剂蒙特卡罗方法

对于分子结构的优化和预测,蒙特卡罗(MC)是很重要的计算工具. 当溶剂效应被显式的考虑时,由于水分子和电离子的自由度很大,蒙特卡罗方法变得非常昂贵. 相对而言,基于隐式溶剂的蒙特卡罗方法可以通过对溶剂效应平均场的近似来大大降低计算成本,同时还能保持目标分子在原子水平上的细节. 目前两种最流行的隐式溶剂模型是泊松-波兹曼模型和通用化波恩模型. 通用化波恩模型是泊松-波兹曼模型的近似,但在模拟计算时间上要快得多. 本文通过结合两种隐式溶剂模型在准确性和效率方面的优势,开发了一种基于机器学习的隐式溶剂蒙特卡罗方法. 具体而言,蒙特卡罗方法通过机器学习既保留了泊松-波兹曼模型的精度,又达到了通用化波恩模型的速度,从而能快速准确地获取模拟计算中每一步的静电溶解自由能. 本文采用苯-水系统和蛋白质-水系统来验证我们的蒙特卡罗方法. 实验证明蒙特卡罗方法在分子结构优化和预测的速度和准确性方面具有很大优势.     

Two-sided bounds on the free energy from local states in Monte Carlo simulations

We show that a precise assessment of free energy estimates in Monte Carlo simulations of lattice models is possible by using cluster variation approximations in conjunction with the local states approximations proposed by Meirovitch. The local states method (LSM) utilizes entropy expressions which recently have been shown to correspond to a converging sequence of upper bounds on the thermodynamic limit entropy density (i.e., entropy per lattice site), whereas the cluster variation method (CVM) supplies formulas that in some cases have been proven to be, and in other cases are believed to be, lower bounds. We have investigated CVM-LSM combinations numerically in Monte Carlo simulations of the two-dimensional Ising model and the two-dimensional five-states ferromagnetic Potts model. Even in the critical region the combination of upper and lower bounds enables an accurate and reliable estimation of the free energy from data of a single run. CVM entropy approximations are therefore useful in Monte Carlo simulation studies and in establishing the reliability of results from local states methods.     

Free energy change of crystallisation in single copolymers

ABSTRACT

We performed dynamic Monte Carlo simulations to calculate the free energy change of crystallisation in single linear and ring polymers containing one or more non-crystallisable sequence defects (comonomers) along the chain. We found that, similar to chain ends, the numbers of comonomers bring only a thermodynamic effect to the free energy barrier and shift down the melting points of single copolymers by following Flory’s thermodynamic equation. Furthermore, there exists a critical comonomer number (or sequence length) for the success of crystallisation, which explains the segregation of sequence lengths upon crystallisation in statistical copolymers. Our observations shed light onto the kinetic suppression of crystallinity for polymers containing various chemical, geometrical or stereo-optical sequence defects, as well as for protein molecules containing specific sequences.     

Solving quantum rotor model with different Monte Carlo techniques

We systematically test the performance of several Monte Carlo update schemes for the (2+1)d XY phase transition of quantum rotor model. By comparing the local Metropolis (LM), LM plus over-relaxation (OR), Wolff-cluster (WC), hybrid Monte Carlo (HM), hybrid Monte Carlo with Fourier acceleration (FA) schemes, it is clear that among the five different update schemes, at the quantum critical point, the WC and FA schemes acquire the smallest autocorrelation time and cost the least amount of CPU hours in achieving the same level of relative error, and FA enjoys a further advantage of easily implementable for more complicated interactions such as the long-range ones. These results bestow one with the necessary knowledge of extending the quantum rotor model, which plays the role of ferromagnetic/antiferromagnetic critical bosons or Z₂ topological order, to more realistic and yet challenging models such as Fermi surface Yukawa-coupled to quantum rotor models.     

用蒙特-卡罗模型模拟金等离子体光谱

 在局部热动平衡条件下,用Monte-Carlo模型计算Au等离子体中的复杂光谱。阐述了两种耦合（中间耦合和L-S耦合）条件下的Monte-Carlo理论模型,并给出了类钇金、类锆金的光谱。     

Monte Carlo方法在B样条函数分频理论中的应用

针对弹道参数的B样条表示问题,运用Monte Carlo方法对B样条函数分频理论进行仿真论证,得到B样条延拓节点的补充方法,并验证B样条函数逼近空间相容性定理的正确性.比较Monte Carlo方法和B样条分频算法的计算结果,说明分频算法合理.将该算法应用于外弹道跟踪测量数据的处理中,可以确定出表示弹道所需要的样条节点个数及样条节点序列的排布,有效减少待估参数个数.     

微细尺度对流体饱和性质影响的MonteCarlo模拟定

本文采用ＭｏｎｔｅＣａｒｌｏ方法研究了纳米石墨管中流体氩的热力学性质。模拟表明在纳米石墨管中,流体的饱和性质与大尺度条件下相比可以有很大差别,同时空间尺度、固体壁面势能和流体密度的大小都对流体的饱和性质有明显的影响．本文的研究结果对微尺度条件下流体相交换热现象的研究有重要意义．     

Monte Carlo Simulation of the Concentration Dependence of Segregation at Vicinal Grain Boundaries

Using the Metropolis algorithm Monte Carlo technique solute-atom segregation is studied at two vicinal grain boundaries (GBs)—the = 5/(002)/ = 36.89° symmetrical twist and the = 5/(310)/ = 53.13° symmetrical tilt—at 850 K on the Ni-rich side of the Ni-Pt phase diagram, over the concentration range 0–10 at.% Pt. Unlike the Pt-rich side of the phase diagram the structures of both GBs remain stable in this concentration range. The dilute limit behavior for most GB sites extends to at least 0.1 at. %. At higher concentrations the effective segregation energies steadily decrease with increasing solute concentrations, due to solute-solute interactions between segregated atoms, until saturation occurs. It is argued that simple statistical mechanical models, e.g., the Fowler-Guggenheim model do not work well, even in the case of simple vicinal GBs.     

The Convergence of Markov Chain Monte Carlo Methods: From the Metropolis Method to Hamiltonian Monte Carlo

From its inception in the 1950s to the modern frontiers of applied statistics, Markov chain Monte Carlo has been one of the most ubiquitous and successful methods in statistical computing. The development of the method in that time has been fueled by not only increasingly difficult problems but also novel techniques adopted from physics. Here, the history of Markov chain Monte Carlo is reviewed from its inception with the Metropolis method to the contemporary state‐of‐the‐art in Hamiltonian Monte Carlo, focusing on the evolving interplay between the statistical and physical perspectives of the method.     

Mesoscopic Modeling for Continuous Spin Lattice Systems: Model Problems and Micromagnetics Applications

In this paper we derive deterministic mesoscopic theories for model continuous spin lattice systems both at equilibrium and non-equilibrium in the presence of thermal fluctuations. The full magnetic Hamiltonian that includes singular integral (dipolar) interactions is also considered at equilibrium. The non-equilibrium microscopic models we consider are relaxation-type dynamics arising in kinetic Monte Carlo or Langevin-type simulations of lattice systems. In this context we also employ the derived mesoscopic models to study the relaxation of such algorithms to equilibrium     

Wetting and structural transition induced by segregation at grain boundaries: a monte carlo study.

Wetting of the Sigma = 5 (310) <001> symmetrical tilt grain boundary (GB) close to the solubility limit in the Cu(Ag) solid solution has been observed by means of Monte Carlo simulations at T = 600 K. More precisely, a finite thickness film almost pure in Ag, separating the two initial Cu(Ag) grains, can be obtained from a critical intergranular germ induced by the strong segregation of Ag in the GB. As this film is actually a single crystal, this implies a complete rearrangement of the GB core structure. Thus the initial GB is replaced by two Cu(Ag)/Ag(Cu) interfaces. Evidence is presented for the increase of the film thickness when approaching the solubility limit, as expected in wetting phenomena.     

R32热力学性质的蒙特卡罗模拟

建立在统计热力学和分子力学理论基础上的分子模拟方法逐渐运用于计算制冷剂的热力学性质。文中首先在NVT系综条件下,采用吉布斯蒙特卡罗模拟方法(GEMC),模拟了R32的气液相平衡的密度、饱和蒸汽压及蒸发焓;其次在NPT系综条件下,采用蒙特卡罗模拟方法(MC),模拟了R32在4MPa条件下的过冷液态密度。模拟结果同美国国家标准研究所(NIST)的Refprop 8.0相比,有很好的一致性。结果表明,运用该方法预测单一制冷剂的热力学性质是可行的。     

Partial auxeticity induced by nanoslits in the Yukawa crystal

Monte Carlo simulations in the isobaric–isothermal ensemble with variable shape of the periodic box were used to investigate Poisson's ratios of the hard‐core repulsive Yukawa crystals with periodically distributed nanoslits. Each nanoslit, oriented perpendicularly to the crystallographic direction [010], was filled by a monolayer of hard spheres. It is shown that presence of the nanoslits leads to negative Poisson's ratio, as low as –0.57(2), in the [100][001]‐direction. This direction is not auxetic in the pure Yukawa crystal, i.e. shows positive Poisson's ratio, equal to 0.43(1).     

Stability analysis and time-step limits for a Monte Carlo Compton-scattering method

A Monte Carlo method for simulating Compton scattering in high energy density applications has been presented that models the photon–electron collision kinematics exactly [E. Canfield, W.M. Howard, E.P. Liang, Inverse Comptonization by one-dimensional relativistic electrons, Astrophys. J. 323 (1987) 565]. However, implementing this technique typically requires an explicit evaluation of the material temperature, which can lead to unstable and oscillatory solutions. In this paper, we perform a stability analysis of this Monte Carlo method and develop two time-step limits that avoid undesirable behavior. The first time-step limit prevents instabilities, while the second, more restrictive time-step limit avoids both instabilities and nonphysical oscillations. With a set of numerical examples, we demonstrate the efficacy of these time-step limits.     

电子回旋共振放电电离特性的PIC/MCC模拟

A theoretical and computational model is presented to study the ionization of the argon electron cyclotron resonance(ECR)microwave discharge using a quasi-three-dimensional electromagnetic particle-in- cell plus Monte Carlo collision method.The interaction between the charged particles and microwave fields are described by the electromagnetic mode of particle-in-cell method.The collision processes are treated with Monte Carlo method.The simulation code is the original work.The results of the particle simulation for the ECR discharge of argon gas which include the microscopic features of charged particles and the electromagnetic characteristics of the ECR discharge plasma,and also the transient phenomena have been presented.     

Information Loss in Coarse-Graining of Stochastic Particle Dynamics

Recently a new class of approximating coarse-grained stochastic processes and associated Monte Carlo algorithms were derived directly from microscopic stochastic lattice models for the adsorption/desorption and diffusion of interacting particles^(12,13,15). The resulting hierarchy of stochastic processes is ordered by the level of coarsening in the space/time dimensions and describes mesoscopic scales while retaining a significant amount of microscopic detail on intermolecular forces and particle fluctuations. Here we rigorously compute in terms of specific relative entropy the information loss between non-equilibrium exact and approximating coarse-grained adsorption/desorption lattice dynamics. Our result is an error estimate analogous to rigorous error estimates for finite element/finite difference approximations of Partial Differential Equations. We prove this error to be small as long as the level of coarsening is small compared to the range of interaction of the microscopic model. This result gives a first mathematical reasoning for the parameter regimes for which approximating coarse-grained Monte Carlo algorithms are expected to give errors within a given tolerance. MSC (2000) subject classifications: 82C80; 60J22; 94A17     

Solute-atom segregation/structure relations at high-angle (002) twist boundaries in dilute Ni−Pt alloys

Monte Carlo simulations, utilizing embedded atom method (EAM) potentials, are employed to investigate in detail solute-atom segregation behavior at high-angle symmetrical (002) twist boundaries, at T=850 K, in Pt-3 at.% Ni and Ni-3 at.% Pt alloys. Solute enhancement in those alloys occurs on both sides of the phase diagram, although it is considerably higher on the Ni-rich side. The distributions of solute concentrations within the first and the second planes are very inhomogeneous, with the sites highly enhanced in solute being in the minority. The remaining sites exhibit little or no enhancement. The highest level of solute concentrations at individual sites continues to increase with the value of the rotations angle, , until saturation occurs at about the =5 misorientation. The large differences in concentrations between different types of sites suggest the possibility of an ordered grain-boundary phase. The correlation between the structure and solute species concentrations in most cases follows the trends observed for low-angle boundaries: Pt as a solute prefers the structural units of the perfect crystal type, while Ni as a solute tends to segregate at the filler units associated with the cores of the primary grain boundary dislocations. A strong correlation is observed between the position of a site in the first or second (002) plane and the plane of the interface. Rigid-body translations are detected for two boundaries on the Pt-rich side of the phase diagram. Roughening and possible structural multiplicity occur in the =5 boundary on the Ni-rich side. The same boundary on the Pt-rich side of the phase diagram exhibits a considerable amount of structural and chemical disorder.     

Thermodynamics of the uniform electron gas: Fermionic path integral Monte Carlo simulations in the restricted grand canonical ensemble

The uniform electron gas (UEG) is one of the key models for the understanding of warm dense matter—an exotic, highly compressed state of matter between solid and plasma phases. The difficulty in modelling the UEG arises from the need to simultaneously account for Coulomb correlations, quantum effects, and exchange effects, as well as finite temperature. The most accurate results so far were obtained from quantum Monte Carlo (QMC) simulations with a variety of representations. However, QMC for electrons is hampered by the fermion sign problem. Here, we present results from a novel fermionic propagator path integral Monte Carlo in the restricted grand canonical ensemble. The ab initio simulation results for the spin-resolved pair distribution functions and static structure factor are reported for two isotherms (T in the units of the Fermi temperature). Furthermore, we combine the results from the linear response theory in the Singwi-Tosi-Land-Sjölander scheme with the QMC data to remove finite-size errors in the interaction energy. We present a new corrected parametrization for the interaction energy and the exchange–correlation free energy in the thermodynamic limit, and benchmark our results against the restricted path integral Monte Carlo by Brown et al. [Phys. Rev. Lett. 110 , 146405 (2013)] and configuration path integral Monte Carlo/permutation-blocking path integral Monte Carlo by Dornheim et al. [Phys. Rev. Lett. 117 , 115701 (2016)].