重力场中理想气体密度分布的 Monte Carlo 模拟

利用Monte Carlo 方法模拟了重力场中理想气体的密度分布,直观展现了重力场中气体分子位置的改变和分布特点,讨论了分子质量和系统温度对气体密度分布曲线以及重力势能零点处密度n0的影响.模拟结果与玻耳兹曼分布律完全吻合.另外,模拟结果表明玻耳兹曼分布律不仅对纯的理想气体成立,而且对混合理想气体中各成分气体也成立.     

Monte Carlo simulation of a lattice gas model of multilayer adsorption

A lattice gas model of physical adsorption of atoms on a periodic substrate has been studied using Monte Carlo simulations. Adsorption isotherms and layer coverage isotherms are determined and from these we find distinct phase boundaries for transitions on successive layers. In contrast to mean field results our data suggests that the critical temperature increases only slowly with increasing layer number, and appears to approach the roughening temperature for infinite layer number.     

Monte Carlo simulation of a confined hard ellipse fluid

The structural and thermodynamic properties of a confined hard ellipse fluid are studied using Monte Carlo simulation. The angular, average number densities and order parameters of hard ellipses confined between hard parallel walls are obtained for various bulk densities, aspect ratios and wall separations. The results show that the effect of the existence of the wall on the molecular fluid structure, either on their directions or their locations, with respect to the bulk, especially close to the walls, is significant. For this system the pressure is also obtained and it is shown that the average density at the wall is proportional to the pressure, βP=〈ρ_w〉. Our simulation results show that the order parameters depend on the number of the particles in the box unless it exceeds thousand.     

Monte Carlo values for the radial distribution function of a system of fluid hard spheres

The perturbation theory recently developed by Weeks, Chandler, and Andersen is applied to the solid phase of a rare gas near its melting line. The potential is separated into two parts: a reference part containing all the repulsive forces and a perturbation part containing all the attractions. We show that the expansion of the free energy in the perturbation potential is, as in the liquid phase, rapidly convergent for a temperature of the order of the triple-point temperature. On the contrary, the representation of the reference system by hard spheres with an appropriate diameter is less accurate than in the liquid phase. This representation requires the knowledge of the radial distribution functions of the hard-sphere solid for which we give a tabulation as well as an analytical representation. The perturbation theory is applied to the determination of the fluid-solid transition.     

Sensitivity analysis of a Monte Carlo atmospheric diffusion model

Summary A Monte Carlo model simulating atmospheric transport and diffusion in the PBL is presented. In a previous study, it was shown that it works well in homogeneous turbulence and fits well the Willis and Deardorff water tank simulations in convective nonhomogeneous conditions. In the present paper a sensitivity analysis aimed at estimating the importance and effectiveness of the model parameters is performed and discussed. Our model makes use of Hanna's scheme for the vertical structure of the turbulent parameters, and of an empirical parametrization of updrafts and downdrafts in convective unstable conditions. Emitting the particles either from a point source or uniformly distributed along the vertical we found that the model avoids the particle accumulation at the top and bottom of the PBL and recovers the Eulerian turbulent statistics. This demonstrates that our numerical scheme is consistent with the physical constraints,i.e. mass and energy are preserved and an initial uniform distribution remains so. Finally it is shown that considering the contribution of the cross-correlation term does not improve significantly the model performances.

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Riassunto Si presenta un modello Monte Carlo atto a simulare il trasporto e la diffusione nello strato limite atmosferico che era stato validato in uno studio precedente ove si era trovato che esso lavora bene in condizioni di turbolenza omogenea e riproduce bene i risultati delle misure in vasca idraulica di Willis e Deardorff relativi a condizioni di turbolenza non omogenea. Nel presente lavoro è stata effettuata un'analisi di sensitività del modello volta alla valutazione dell'importanza ed efficacia dei parametri del modello stesso. Esso utilizza lo schema di Hanna per la descrizione dell'andamento verticale dei parametri turbolenti in atmosfera ed una parametrizzazione empirica delle celle convettive in condizioni instabili. Emettendo le particelle sia da una sorgente puntiforme, sia distribuite uniformemente lungo la verticale si è trovato che il modello evita l'accumulo di particelle ai limiti superiore ed inferiore del PBL e conserva la statistica euleriana delle grandezze turbolente. Ciò dimostra che il nostro schema numerico è fisicamente consistente dato che soddisfa i seguenti vincoli fisici: la massa e l'energia sono conservate ed una distribuzione iniziale uniforme rimane tale. Infine, si è mostrato che il considerare il contributo del termine di cross-correlazione non migliora in modo significativo le prestazioni del modello.

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Резюме Предлагается модель Моите Карло для моделирования процессов диффузии и переноса в атмосфере. Ранее было показано, что эта модель хорошо работает в условиях однородной турбулентности и хорошо воспроизводит результаты Виллиса и Дирдорфа измерений в водоеме при условиях неоднородной турбулентности. В данной статье проводится и обсуждается анализ чувствительности с целью определения важности и эффективности параметров модели. В предложенной модели используется схема Хана для вертикальной структуры параметров турбулентности атмосферы и эшпирическая параметризация для конвективных ячеек в нестационарных условиях. Испуская частиы либо из точечного источника, либо из однородно распределенных источников вдоль вертикали, мы находим, что модель не дает накапливания частиц на верхней и нижней границах PBL и сохраняет Эйлерову статистику турбулентности. Мы показываем, что наша численная схема согласуется с физическими ограничениями: масса и энергия сохраняются и начальное однородное распределение остается тем же. В заключение покаывается, что рассмотрение вклада перекрестного члена значительно не улучшает характеристики модели.

     

Monte Carlo simulation of photoelectron angular distribution

A practical simulation method has been performed for studies of the influence of surface excitations on the angular distributions of photoelectron peak intensities. The surface effects have been incorporated into simulations by using the surface excitation parameters (SEPs) which have been calculated with the extended Drude dielectric function. Also, elastic scattering cross sections are calculated using the finite difference method for a Hartree-Fock-Wigner-Seitz potential in the Dirac equation to take into account the solid-state effect. Results of Monte Carlo simulations reveal that surface effects lead to a reduction of the intensities at small detection angles and a sharp decrease at large angles since the surface excitation is most probable for glancing electrons. The calculated results taking into account surface effects are in better agreement with the experimental data.     

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.     

Monte Carlo simulation of the three-dimensional Potts model

The phase transition of the three-dimensional 3-state Potts model at zero field is investigated by a careful Monte Carlo analysis. The transition is found to be of first order. Fluctuations appear to be very strong and critical exponents can be defined with reasonable accuracy. The results are compared with those of the 4-state Potts model.     

Monte Carlo simulation of the massive Schwinger model

In this article we apply a previously proposed defermionization method to the study of two-dimensional QED (massive Schwinger model). We find good evidence for the spontaneous breaking of axial symmetry, i.e., $\text{〈}\text{ψ}\text{ψ〉≠0}$ in the massless limit.     

Monte Carlo simulation of the two-dimensional planar model

We present results for the two-dimensional planar model on the square lattice. We have developed a Monte Carlo routine which is more efficient than the single-spin-flip algorithms used previously. We report on the variation of the following quantities with temperature: specific heat, energy, magnetization, susceptibility, correlation function, helicity modulus, the density of vortex/ antivortex pairs, the average distance between a vortex and its nearest antivortex, and the average distance between a vortex/antivortex pair and the nearest pair. Our results are in excellent agreement with the reliable results reported in the literature and are in accord with the general features of the Kosterlitz-Thouless theory.     

Monte Carlo simulation of a coarse-grained model of polyelectrolyte networks

The structure and properties of a coarse-grained model of a polyelectrolyte network is studied by means of Monte Carlo simulations. Counterions are treated explicitly, and permanent tetrafunctional cross-linking sites are annealed. The resulting pressure-density relationships exhibit a strong dependence on the strength of electrostatic interactions. A discontinuous volume change is observed when electrostatic interactions are strong. The structure of the model networks is examined at various conditions, and it is found to be considerably different from that of noncross-linked polyelectrolytes.     

An expansion method for the Monte Carlo distribution function

We present and test an expansion method for calculating the distribution function of mobile electrons in semiconductors in a drifting homogeneous electric field. This expansion represents an extension of the drifted Maxwellian method and correctly reproduces the exact Monte Carlo distribution function even in high fields.     

Monte Carlo simulation of three-dimensional dilute Ising model

A multispin coding program for site-diluted Ising models on large simple cubic lattices is described in detail. The spontaneous magnetization is computed as a function of temperature, and the critical temperature as a function of concentration is found to agree well with the data of Marro et al.⁽⁴⁾ and Landau⁽³⁾ for smaller systems.The first successful epsilon expansion seems to be by D. E. Khmelnitskii,ZhETF 68:1960 (1975), English translationSov. Phys. JETP 41:981 (1975); for numerical estimates see K. E. Newman and E. K. Riedel,Phys. Rev. H25:264 (1982), for experiments see R. J. Birgenau, R. A. Cowley, G. Shirane and H. Yoshizawa,J. Stat. Phys. 34:817 (1984).     

Quantum Monte Carlo simulation of the high-pressure molecular-atomic crossover in fluid hydrogen

A first-order liquid-liquid phase transition in high-pressure hydrogen between molecular and atomic fluid phases has been predicted in computer simulations using ab initio molecular dynamics approaches. However, experiments indicate that molecular dissociation may occur through a continuous crossover rather than a first-order transition. Here we study the nature of molecular dissociation in fluid hydrogen using an alternative simulation technique in which electronic correlation is computed within quantum Monte Carlo methods, the so-called coupled electron-ion Monte Carlo method. We find no evidence for a first-order liquid-liquid phase transition.     

Monte Carlo simulation of a kinetic Ising model of the glass transition

Results of Monte Carlo experiments for the two-spin facilitated kinetic Ising model on a cubic lattice are presented and compared with a theoretical prediction.