Equation of Motion in Hybrid Monte Carlo

The equation of motion and molecular dynamics for simulating lattice field theory using the Hybrid Monte Carlo (HMC) algorithm are described. Some techniques for improving the HMC efficiency are discussed.     

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.     

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.     

蒙特卡罗模拟元素特征X射线注量的展宽技术

蒙特卡罗模拟技术可以有效提高核辐射探测分析效率、降低分析成本,在促进X荧光分析技术发展过程中也发挥了重要作用。在应用蒙特卡罗模拟能量色散X荧光分析中,为使蒙特卡罗模拟元素特征X射线注量谱与实验能谱之间的物理差异更小,提出了一种模拟注量展宽算法。首先依据离散统计物理理论,建立了Si-PIN半导体探测器对X射线的响应函数模型,并利用加权非线性最小二乘法拟合得到各系数,再对系数进行归一化处理,得到归一化后的响应函数R(E, E′)。然后利用R(E, E′)对模拟注量进行展宽转换,得到脉冲幅度谱(pulse height spectrum, PHS),使模拟谱更趋近于实验谱,这样就可以通过蒙特卡罗模拟得到与实测能谱一致性较高的模拟能谱。研究中最后利用建立的探测器响应函数模型对Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, As, Sn元素K系全能峰拟合χ2_r值在1.04～1.18范围内,对铜合金样品中六种元素特征X射线模拟注量转换结果与实验值一致性较好,并实现了对多元素混合样品复杂重迭谱的有效模拟和展宽。     

太赫兹光脉冲在生物介质中传播的蒙特卡罗法模拟

太赫兹光脉冲照射生物组织,利用蒙特卡罗方法模拟光脉冲在生物介质内的散射传播过程。光脉冲准垂直入射的情况下,得到了介质表面总漫反射率和总漫透射率与介质散射系数、吸收系数、平均散射余弦,以及介质厚度之间的关系;散射系数越大,总漫反射率越大;平均散射余弦值越小,总漫反射率也越大;同时总漫反射光强随着介质厚度的增加而增大,但存在一个极限值。     

用改进的两步模拟退火法进行二元光学元件的设计

为了减少二元光学元件设计的计算量并提高设计精度,在对现有算法机理进行深入分析的基础上,提出了适用于二元光学元件设计的两步模拟退火法.该算法在整个退火过程中采用先量化后优化的策略,并将优化过程分为两个阶段：搜索并锁定最优解区间;快速收敛到最优解.模拟实验显示,与传统设计方法相比,该算法不仅保持了全局寻优的特点,而且提高了稳健性和效率.算法剔除了对设计结果影响较大的量化误差,提高了设计精度.用此法实例设计了单焦面辐射聚焦元件,得到了与目标图像一致的光学实验结果.     

Monte Carlo法模拟油滴的理论分布

在密立根油滴实验中,应用Monte Carlo法数值地模拟实验室条件下可能的油滴带电量Q、平衡电压U和匀速运动时间t的理论分布,分别从三维分布、时间分布及数量方面比较3种选择油滴的标准,给出较合理的结论.     

A Monte Carlo Study of the Half-Filled Two-Dimensional Hubbard Model

Using the path integral representation,bulk thermodynamic properties of the two-dimensional Hubbard model on a square lattice are studied numerically using the hybrid Monte Carlo simulation algorithm.Results for averaged energy,spin-spin correlation functions and Cooper pair correlation functions are presented.All these results suggest that the system exhibits an anti-ferromagnetic correlation at half-filling for a wide range of temperature.``     

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.     

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.     

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.     

求解中子动力学方程的加权蒙特卡罗方法

为了实现基于蒙特卡罗方法的中子动力学计算,在传统的直接蒙特卡罗动力学方法的基础上,提出了一种加权蒙特卡罗动力学方法。该方法通过引入粒子权重的概念,隐式考虑中子俘获反应和裂变反应过程中中子数目的变化,避免了模拟粒子的数目随时间的变化,降低了统计偏差,消除了程序计算过程中粒子的存库操作,提高了计算精度。基于单能点堆模型,开发了中子动力学计算程序NECP-Dandi,进行了大量数值验证与分析,包括无缓发中子、单组缓发中子、六组缓发中子、正阶跃反应性引入、负阶跃反应性引入、正脉冲反应性、负脉冲反应性和正线性反应性引入等情况。数值结果表明,相比于直接蒙特卡罗动力学方法,加权蒙特卡罗动力学方法在计算结果的精度和计算效率上有较为明显的改进,程序结构更为简洁。     

用蒙特卡罗哈密顿量方法研究非S态

以氢原子为例，验证了Monte Carlo Hamiltonian(MCH)方法推广应用到量子力学系统中在原点发散的势的非S态的有效性，给出估计误差的新思路，得到和解析解相符的能谱和约化径向波函数.     

A Monte Carlo Study of the Half-Filled Two-Dimensional Hubbard Model

Using the path integral representation,bulk thermodynamic properties of the two-dimensional Hubbard model on a square lattice are studied numerically using the hybrid Monte Carlo simulation algorithm.Results for averaged energy,spin-spin correlation functions and Cooper pair correlation functions are presented.All these results suggest that the system exhibits an anti-ferromagnetic correlation at half-filling for a wide range of temperature.     

Monte Carlo simulation using the Fourier transform of the interatomic potential

When doing Monte Carlo simulations using continuous potentials, the evaluation of the configurational potential energy ink-space by Fourier transformation is shown to be a computationally attractive scheme for systems where the long-range interatomic interaction spans a dimension comparable to the size of the simulated system.     

Auxiliary-field Monte Carlo methods

I discuss Monte Carlo algorithms for quantum many-body systems that employ an auxiliary field to linearize a two-body interaction. These reduce the evaluation of the partition function to sampling many one-body evolutions in a fluctuating field. Fermions and bosons are treated on an equal footing. Applications to potential models and to quantum spin systems are discussed. This work was supported in part by the National Science Foundation, grants PHY82-07332 and PHY85-05682. The potential-model studies were done in collaboration with G. Sugiyama, while A. Khan and T. Troudet were responsible for the work on the quantum spin systems.     

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.     

Monte Carlo Shell Model Mass Predictions

The nuclear mass calculation is discussed in terms of large-scale shell model calculations. First, the development and limitations of the conventional shell model calculations are mentioned. In order to overcome the limitations, the Quantum Monte Carlo Diagonalization (QMCD) method has been proposed. The basic formulation and features of the QMCD method are presented as well as its application to the nuclear shell model, referred to as Monte Carlo Shell Model (MCSM). The MCSM provides us with a breakthrough in shell model calculations: the structure of low-lying states can be studied with realistic interactions for a nearly unlimited variety of nuclei. Thus, the MCSM can contribute significantly to the study of nuclear masses. An application to N∼20 unstable nuclei far from the β-stability line is mentioned. This revised version was published online in July 2006 with corrections to the Cover Date.     

气泡幕后向散射光信号特性的蒙特卡罗方法研究

利用蒙特卡罗方法对水介质中的气泡幕的后向光散射回波信号进行了系统仿真。通过对计算结果与实验结果的比较,证明了蒙特卡罗方法的有效性。根据仿真结果,结合理论分析的方法,对气泡幕位置、厚度和接收器视场角等参数对回波信号的影响进行了分析,结果表明:回波信号出现时间与气泡幕位置存在一一对应的关系;在气泡幕的衰减系数ρσt不变的情况下,存在一个有效气泡幕厚度,当大于该厚度时,气泡幕的后向光散射回波信号基本不变;在系统各项参数不变的情况下,适当增加接收器的视场角,可有效地提高回波信号的信噪比。     

Transition Matrix Monte Carlo Method

We present a formalism of the transition matrix Monte Carlo method. A stochastic matrix in the space of energy can be estimated from Monte Carlo simulation. This matrix is used to compute the density of states, as well as to construct multi-canonical and equal-hit algorithms. We discuss the performance of the methods. The results are compared with single histogram method, multi-canonical method, and other methods. In many aspects, the present method is an improvement over the previous methods.