Nonlinear noise reduction through Monte Carlo sampling

We consider the problem of nonlinear noise reduction within the framework of Bayesian Theory. This enables us to place appropriate weights on the measurement and dynamic errors and thereby avoid over cleaning the data. Using a Metropolis-Hastings sampler, we are able to achieve robust noise reduction without the introduction of ad hoc parameters but at the expense of higher computational complexity. Such an algorithm should also allow us to explore the potential and limitations of other noise reduction methods. (c) 1998 American Institute of Physics.     

Monte Carlo Effective Hamiltonian in 1+1 Dimensional Case'

Using a recently developed Monte Carlo effective Hamiltonian method,we study the low energy physics of 1+1 dimensional quantum mechanical system V(x)=μ²x²+λx⁴(here μ²<0,λ>0),which is similar to Higgs potential in the standard model of unified electroweak theory.Good results of the spectra,wavefunctions and thermodynamical observables are obtained.It shows that the new Monte Carlo Hamiltonian method has potential application to systems with many degrees of freedom and lattice gauge theory.     

蒙特卡罗等效哈密顿量的1+1维检验

用最近发展起来的蒙特卡罗等效哈密顿量新方法,研究了与量子场论中Φ4模型相似的1+1维量子力学系统V(x)=μ²x²+λx⁴(其中μ²<0,λ>0)的低能物理特性.计算了能谱、波函数以及热力学可观察量.获得良好的结果,表明这种新方法有希望推广到多自由度系统和格点规范场论.     

基于蒙特卡罗正算输运的全局减方差方法

蒙特卡罗方法是当前形势下辐射屏蔽计算的首选分析工具。小概率深穿透问题则是屏蔽计算的关键与亟待解决的核心问题,需要使用有效的减方差技巧。针对全局问题,利用蒙特卡罗正算输运得到的粒子通量或探测响应来构建权重窗参数,将现有的粒子位置偏移拓展到位置和能量偏倚。利用国际屏蔽基准题进行测试验证,通过使用该方法,粒子被引导到模型的所有位置。平均相对误差降低到10%以下,几乎所有网格区域都有粒子统计。结果表明,基于蒙特卡罗正算输运的输运偏倚参数构建方法能够实现全局减方差。     

Multilayer adsorption by Monte Carlo simulation

Adsorption phenomena are characterized by models that include free parameters trying to reproduce experimental results. In order to understand the relationship between the model parameters and the material properties, the adsorption of small molecules on a crystalline plane surface has been simulated using the bond fluctuation model. A direct comparison between the Guggenheim–Anderson–de Boer (GAB) model for multilayer adsorption and computer simulations allowed us to establish correlations between the adsorption model parameters and the simulated interaction potentials.     

Monte Carlo Hamiltonian

We construct an effective Hamiltonian via Monte Carlo from a given action. This Hamiltonian describes physics in the low energy regime. We test it by computing spectrum, wave functions and thermodynamical observables (average energy and specific heat) for the free system and the harmonic oscillator. The method is shown to work also for other local potentials.     

Momentum-space Monte Carlo

Using the quenched, reduced form of large-N field theories, we show that it is possible to directly measure momentum-space Green functions, via Monte Carlo, without going through the intermediate step of measurement in position space plus Fourier transformation. This promises to be useful tool for investigating the infrared structure of planar field theories. As an application (and test) of the method, we compute mass-gaps in the quenched U(N) × U(N) lattice chiral model, in D = 1 and 2 dimensions.     

Broad histogram Monte Carlo

We propose a new Monte Carlo technique in which the degeneracy of energy states is obtained with a Markovian process analogous to that of Metropolis used currently in canonical simulations. The obtained histograms are much broader than those of the canonical histogram technique studied by Ferrenberg and Swendsen. Thus we can reliably reconstruct thermodynamic functions over a much larger temperature scale also away from the critical point. We show for the two-dimensional Ising model how our new method reproduces exact results more accurately and using less computer time than the conventional histogram method. We also show data in three dimensions for the Ising ferromagnet and the Edwards Anderson spin glass. Received: 8 August 1997 / Revised: 11 August 1997 / Accepted: 30 October 1997     

系综Monte Carlo方法

本文系统地给出了Monte Carlo模拟的一般方法在各种系综条件下的表述以及它们的算法。     

Monte Carlo renormalization group

Monte Carlo computer simulations have long been used to obtain information on the behavior of thermodynamic systems. The method has the advantages of being applicable to a very large class of models and of using only systematically improvable approximations (finite size of system, statistical errors, etc.). However, in the critical region, finite-size effects mask the critical singularities, and put severe practical limits onto the accuracy to which the true critical behavior can be determined. By combining Monte Carlo simulations with a real-space renormalization-group analysis, a large increase in efficiency and accuracy can be achieved—without the uncertainties of the usual truncation approximations. The methods are illustrated by explicit calculations on models exhibiting critical and tricritical behavior.     

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.     

Virial-bias Monte Carlo methods

A new sampling technique is proposed for the isothermal-isobaric (T, P, N) ensemble Monte Carlo computer simulation. The new method selects the volume perturbations by using the partial derivative of the volume with respect to the internal energy. Test calculations on the Lennard-Jones fluid show significant improvements over the conventionally used method.     

基于舰船尾流激光雷达的Monte Carlo模型及方差消减方法研究

对舰船尾流激光散射机理及探测过程的数值模拟是研究舰船尾流激光探测与制导的重要基础.首先分析了Monte Carlo方法引入到尾流激光雷达数值模拟领域研究的可行性.结合自行研制的尾流激光雷达实际参数,建立了尾流激光探测的Monte Carlo数值仿真模型.通过对仿真结果进行统计,深入剖析了仿真结果方差大及光子利用率低等问题的成因.为解决该问题,基于有偏采样理论和分裂-轮盘赌基本原理提出了接收光学视场内光子强行碰撞方法和以光子自由程总长度为准则的光子分裂方法,并进行了两方法的融合.仿真与实验结果的对比分析表明,提出的模型仿真结果与实验数据符合较好,验证了模型的正确性;提出的接收光学视场内光子强行碰撞方法和光子分裂方法能有效减小方差并提高光子利用率;解决了Monte Carlo方法引入到尾流激光雷达模拟过程中的适用性问题.     

Dimensional reduction caused by a cosmological constant

It is shown that a general class of solutions to Einstein's empty-space equation, with a cosmological constant, give automatic confinement of a scalar field to an approximately flat space of one dimension less.     

Monte Carlo Simulation of Cooling Induced by Parametric Resonance

We demonstrate that the parametric resonance in a magnetic quadrupole trap can be exploited to cool atoms by using Bird＇s method. In our programme the parametric resonance was realized by anisotropically modulating the trap potential. The modulation frequency dependences of temperature and fraction of the trapped atoms are explored. Furthermore, the temperature after the modulation as functions of the modulation amplitude and the mean elastic collision time are also studied. These results are valuable for the experiment of parametric resonance in a quadrupole trap.     

Dynamic Monte Carlo renormalization group

A new and simple method of applying the idea of real space renormalization group theory to the analysis of Monte Carlo configurations is proposed and applied to the Glauber kinetic Ising model in two and three dimensions, and to the Kawasaki model in two dimensions. Our method, if correct, utilizes how the system approaches its equilibrium; in contrast to most other Monte Carlo investigations there is no need to wait until equilibrium is established. The renormalization analysis takes only a small fraction of the computer time needed to produce the Monte Carlo configurations, and the results are obtained as the system relaxes atT =T _c , the critical temperature. The values obtained for the dynamical critical exponent,z, are 2.12 (d=2) and 2.11 (d=3) for the Glauber model, the 3.90 for the two-dimensional Kawasaki model. These results are in good agreement with those obtained by other methods but with smaller error bars in three dimensions.     

Monte Carlo simulation of mictomagnets

Monte Carlo simulations of a binary alloy with impurity concentrations between 20 and 45 at.% have been carried out. The proportion of large clusters relative to that of small clusters increases with the number of MC diffusion steps as well as impurity concentration. Magnetic susceptibility peaks become more prominent and occur at higher temperatures with increasing impurity concentration. The different peaks in the susceptibility and specific heat curves seem to correspond to different sized clusters. A freezing model would explain the observed behaviour with the large clusters freezing first and the small clusters contributing to susceptibility (specific heat) peaks at lower temperatures.Contribution No. 153 from the Solid State and Structural Chemistry Unit