Inhomogeneous Relaxation in Vibrated Granular Media: Consolidation Waves

We investigate the spatial dependence of the density of vibrated granular beds, using simulations based on a hybrid Monte Carlo algorithm. We find that the initial consolidation is typically inhomogeneous, both in the presence of a constant shaking intensity and when the granular bed is subjected to "annealed shaking". We also present a theoretical model which explains such inhomogeneous relaxation in terms of a "consolidation wave", in good qualitative agreement with our simulations. Our results are also in qualitative agreement with recent experiments.     

A hybrid transport-diffusion Monte Carlo method for frequency-dependent radiative-transfer simulations

Discrete Diffusion Monte Carlo (DDMC) is a technique for increasing the efficiency of Implicit Monte Carlo radiative-transfer simulations in optically thick media. In DDMC, particles take discrete steps between spatial cells according to a discretized diffusion equation. Each discrete step replaces many smaller Monte Carlo steps, thus improving the efficiency of the simulation. In this paper, we present an extension of DDMC for frequency-dependent radiative transfer. We base our new DDMC method on a frequency-integrated diffusion equation for frequencies below a specified threshold, as optical thickness is typically a decreasing function of frequency. Above this threshold we employ standard Monte Carlo, which results in a hybrid transport-diffusion scheme. With a set of frequency-dependent test problems, we confirm the accuracy and increased efficiency of our new DDMC method.     

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.     

Hamiltonian evolution for the hybrid Monte Carlo algorithm

We discuss a class of reversible, discrete approximations to Hamilton's equations for use in the hybrid Monte Carlo algorithm and derive an asymptotic formula for the step-size-dependent errors arising from this family of approximations. For lattice QCD with Wilson fermions, we construct several different updates in which the effect of fermion vacuum polarization is given a longer time step than the gauge field's self-interaction. On a 4⁴ lattice, one of these algorithms with an optimal choice of step size is 30% to 40% faster than the standard leapfrog update with an optimal step size.     

Investigation of nucleation and grain growth in 2-dimensional systems by using generalized Monte Carlo simulations

In this study, nucleation and grain growth was studied by using 2-dimensional generalized Monte Carlo simulations and experiments. As an attempt to improve the JMAK model, we proposed a new differential equation to be able to model nucleation and growth phenomena using nonextensive thermostatistics. One of the reasons that we would like to perform generalized Monte Carlo simulations in studying of nucleation and grain growth phenomena is that the generalized Monte Carlo algorithm was shown to be more effective than the standard Monte Carlo algorithm and also than the standard Molecular Dynamic algorithm in locating the minimum energy configuration. Therefore, for a given temperature, the fact that a configuration of the system with lower energy could be obtained by using the generalized Monte Carlo simulation means that a different textural configuration of grain growth could be also expected. In this respect, it is possible to say that the nonextensive statistics might be an appropriate tool in studying of nucleation and growth phenomena.     

Simulated Annealing Using Hybrid Monte Carlo

We propose a variant of the simulated annealing method for optimization in the multivariate analysis of differentiable functions. The method uses global actualizations via the hybrid Monte Carlo algorithm in their generalized version for the proposal of new configurations. We show how this choice can improve upon the performance of simulated annealing methods (mainly when the number of variables is large) by allowing a more effective searching scheme and a faster annealing schedule.     

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.     

Quantative measure of efficiency of Monte Carlo simulations

An easily applied, physically motivated algorithm for determining the efficiency of Monte Carlo simulations is introduced. The theoretical basis for the algorithm is developed. As an illustration we apply the method to the Lennard-Jones liquid near the triple point. We show that an acceptance ratio of 0.2 is twice as efficient for the purpose of generating a satisfactory sample as is an acceptance ratio of 0.5. There is a strong correlation between the efficiency measure and the diffusion rate of liquid particles during the simulation. We argue that the optimal value of the acceptance ratio is calculable from short Monte Carlo simulations. The method is very general and is applicable to Monte Carlo simulations involving arbitrary potentials.     

Advanced multicanonical Monte Carlo methods for efficient simulations of nucleation processes of polymers

The investigation of freezing transitions of single polymers is computationally demanding, since surface effects dominate the nucleation process. In recent studies we have systematically shown that the freezing properties of flexible, elastic polymers depend on the precise chain length. Performing multicanonical Monte Carlo simulations, we faced several computational challenges in connection with liquid–solid and solid–solid transitions. For this reason, we developed novel methods and update strategies to overcome the arising problems. We introduce novel Monte Carlo moves and two extensions to the multicanonical method.     

First-passage Monte Carlo algorithm: diffusion without all the hops

We present a novel Monte Carlo algorithm for N diffusing finite particles that react on collisions. Using the theory of first-passage processes and time dependent Green's functions, we break the difficult N-body problem into independent single- and two-body propagations circumventing numerous diffusion hops used in standard Monte Carlo simulations. The new algorithm is exact, extremely efficient, and applicable to many important physical situations in arbitrary integer dimensions.     

A Markov-property Monte Carlo method: One-dimensional Ising model

In this paper we introduce a new Monte Carlo procedure based on the Markov property. This procedure is particularly well suited to massively parallel computation. We illustrate the method on the critical phenomena of the well known one-dimensional Ising model. In the course of this work we found that the autocorrelation time for the Metropolis Monte Carlo algorithm is closely given by the square of the correlation length. We find speedup factors of the order of 1 million for the method as implemented on the CM2 relative to a serial machine. Our procedure gives error estimates which are quite consistent with the observed deviations from the analytically known exact results.     

Monte Carlo simulations in the isothermal—isobaric ensemble: the requirement of a ‘shell’ molecule and simulations of small systems

A modification of the widely used Monte Carlo method for determining thermophysical properties in the isothermal-isobaric ensemble is presented. The new Monte Carlo method, now consistent with recent derivations describing the proper statistical mechanical formulation of the constant pressure ensemble for small systems, requires a ‘shell’ molecule to uniquely identify the volume of the system, thereby avoiding the redundant counting of configurations. Ensemble averages obtained with the new algorithm differ from averages calculated with the old Monte Carlo method, particularly for small system sizes, although both sets of averages become equal in the thermodynamic limit. Monte Carlo simulations in the constant pressure ensemble applied to the Lennard-Jones fluid demonstrate these differences for small systems. Peculiarities of small systems are also discussed, revealing that ‘shape’ is an important thermodynamic variable. Finally, an extension of the Monte Carlo method to mixtures is presented.     

Full-band CA/Monte Carlo modeling of ultrasmall FETs

The modeling of ultra-small MOSFETs is presented using a newly developed full-band, hybrid ensemble Monte Carlo (EMC)-cellular automata (CA) device simulator. In this hybrid approach charge transport is simulated using the CA in regions of momentum space where most scattering events occur and the EMC elsewhere, thus optimizing the trade-off between the fast, but memory-consuming CA method and the slower EMC method. In order to efficiently model 3D ultra-small FETs, the hybrid algorithm is coupled self-consistently with a 2D and 3D multi-grid Poisson solver.     

Particle filtering with path sampling and an application to a bimodal ocean current model

This paper introduces a recursive particle filtering algorithm designed to filter high dimensional systems with complicated non-linear and non-Gaussian effects. The method incorporates a parallel marginalization (PMMC) step in conjunction with the hybrid Monte Carlo (HMC) scheme to improve samples generated by standard particle filters. Parallel marginalization is an efficient Markov chain Monte Carlo (MCMC) strategy that uses lower dimensional approximate marginal distributions of the target distribution to accelerate equilibration. As a validation the algorithm is tested on a 2516 dimensional, bimodal, stochastic model motivated by the Kuroshio current that runs along the Japanese coast. The results of this test indicate that the method is an attractive alternative for problems that require the generality of a particle filter but have been inaccessible due to the limitations of standard particle filtering strategies.     

Antiholons in one-dimensional t-J models

Using a newly developed hybrid Monte Carlo algorithm for the nearest-neighbor (nn) t-J model, we show that antiholons identified in the supersymmetric inverse squared (IS) t-J model are clearly visible in the electron-addition spectrum of the nn t-J model at J=2t and also for J=0.5t, a value of experimental relevance.     

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.     

Study on the efficiency of Eb/No algorithm for BER estimation over 112-Gb/s PDM CO-OFDM system with QPSK mapping

We research an efficient BER estimation method for 112-Gb/s polarization division multiplexing coherent optical OFDM (PDM CO-OFDM) with QPSK mapping over 800 km SSMF based on Eb/No algorithm in this paper. We first lay out the related formulas’ derivation to set up the theoretical basis for the feasibility of Eb/No algorithm and then we implement a series of simulations to illustrate the relationship of BER (and Q factor) versus OSNR, launch power of transmitter, chromatic dispersion and nonlinearity in optical fiber link via both Eb/No algorithm and Monte Carlo algorithm. The simulations demonstrate that BER estimated by Eb/No algorithm can achieve a precision up to 10⁻¹⁶ just with 10⁵ bits while Monte Carlo algorithm needs at least 10¹⁸ bits to get the same level. Therefore, Eb/No allows a quick and reliable method for BER estimation instead of the time consuming Monte Carlo method, which can be used to support simulations with various conditions.     

Monte Carlo simulation of quantum statistical lattice models

In this article we review recent developments in computational methods for quantum statistical lattice problems. We begin by giving the necessary mathematical basis, the generalized Trotter formula, and discuss the computational tools, exact summations and Monte Carlo simulation, that will be used to examine explicit examples. To illustrate the general strategy, the method is applied to an analytically solvable, non-trivial, model: the one-dimensional Ising model in a transverse field. Next it is shown how to generalized Trotter formula most naturally leads to different path-integral representations of the partition function by considering one-dimensional fermion lattice models. We show how to analyze the different representations and discuss Monte Carlo simulation results for one-dimensional fermions. Then Monte Carlo work on one- and two-dimensional spin-$\text{1}\text{2}$ models based upon the Trotter formula approach is reviewed and the more dedicated Handscomb Monte Carlo method is discussed. We consider electron-phonon models and discuss Monte Carlo simulation data on the Molecular Crystal Model in one, two and three dimensions and related one-dimensional polaron models. Exact numerical results are presented for free fermions and free bosons in the canonical ensemble. We address the main problem of Monte Carlo simulations of fermions in more than one dimension: the cancellation of large contributions. Free bosons on a lattice are compared with bosons in a box and the effects of finite size on Bose-Einstein condensation are discussed.     

碳气凝胶储氢性能的理论研究

采用基于Metropolis蒙特卡罗和Reverse蒙特卡罗的杂化逆向蒙特卡罗方法,构建碳气凝胶的微孔结构模型,根据碳气凝胶的介孔尺寸构建介孔模型.设计不同形状、不同孔径的介孔模型,使用巨正则蒙特卡罗方法详细模拟在298 K和77 K下的储氢量.结果显示,在77 K时,所设计的碳气凝胶的储氢量几乎是室温下的4倍.在77 K,100 bar时,储氢量最高可达到11.12 wt%和45.68 g·L^-1.     

Computational complexity of impact size estimation for spreading processes on networks

Spreading processes on networks are often analyzed to understand how the outcome of the process (e.g. the number of affected nodes) depends on structural properties of the underlying network. Most available results are ensemble averages over certain interesting graph classes such as random graphs or graphs with a particular degree distributions. In this paper, we focus instead on determining the expected spreading size and the probability of large spreadings for a single (but arbitrary) given network and study the computational complexity of these problems using reductions from well-known network reliability problems. We show that computing both quantities exactly is intractable, but that the expected spreading size can be efficiently approximated with Monte Carlo sampling. When nodes are weighted to reflect their importance, the problem becomes as hard as the s-t reliability problem, which is not known to yield an efficient randomized approximation scheme up to now. Finally, we give a formal complexity-theoretic argument why there is most likely no randomized constant-factor approximation for the probability of large spreadings, even for the unweighted case. A hybrid Monte Carlo sampling algorithm is proposed that resorts to specialized s-t reliability algorithms for accurately estimating the infection probability of those nodes that are rarely affected by the spreading process.