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.     

A bit-string model for biological aging

We present a simple model for biological aging. We study it through computer simulations and fint it to reflect some features of real populations.     

Totally asymmetric exclusion processes at constrained m-input n-output junction points

Totally asymmetric exclusion processes at constrained m-input n-output junction points under random update are studied by theoretical calculation and computer simulation in this paper. At the junction points, the hopping rate of particles from m-input parallel lattices to n-output parallel lattices is assumed to be equal to r/n （0 〈 r 〈 1 ）. The mean-field approach and Monte Carlo simulations show that the phase diagram can be classified into three regions at any value of r. More interestingly, there is a threshold rc = n（ 1 - √1 - m/n）/m. In the cases of r 〉 re and r 〈 rc, qualitatively different phases exist in the system. With the increase of the value of m/n, the regions of （LD, LD） and （MC, LD） or （HD, LD） decrease, and the （HD, HD） is the only phase that increases in the region （LD stands for low density, HD stands for high density, and MC for maximal current）. Stationary current and density profiles are calculated, showing that they are in good agreement with Monte Carlo simulations.     

Surface energies of the solid solutions between Ti, V, Cr, Zr, Nb, Mo, Hf, Ta, and W

The surface energy for different surface orientations of the solid solutions as a function of concentration formed by Ti, V, Cr, Zr, Nb, Mo, Hf, Ta, and W is computed and analyzed using the BFS method for alloys. Similarities and differences among the different binary alloys are examined in terms of strain and chemical effects.     

Nucleus size and Zeldovich factor in two-dimensional nucleation at the Kossel crystal (0 0 1) surface

A Monte Carlo simulation method to determine the growth probability of two-dimensional clusters on the Kossel (0 0 1) surface is described. From this growth probability the nucleus size and the Zeldovich factor for two-dimensional nucleation were obtained. For low supersaturations the Gibbs-Thomson equation describes the supersaturation dependency of the nucleus size very well. At higher supersaturations a deviation from the predicted nucleus sizes is observed. This is mainly due to the size dependence of the apparent specific step free energy and/or the shape factor of the nucleus. A small systematic deviation between the theoretical and actual growth probability is observed and explained.     

Monte Carlo方法计算背散射电子在固体中的空间分布

应用Monte Carlo方法,对不同能量低能电子作用下背散射电子在固体中的空间分布作了计算,电子的弹性散射用Mott截面描述、非弹性散射按文献[3]的方法由Streitwolf、Quinn及Gryrinski的公式计算,大量计算得出一些规律,为低能电子显微学研究提供一定依据。     

The possibility of detection of finite temperature stripe ordering in 2D spinless Falicov–Kimball model

This paper announces a possibility of detection of finite-temperature stripe ordering in the two-dimensional Falicov–Kimball model at half-filling by extensive Monte Carlo simulations. Moreover, the tools to study orderings and to detect phase transition temperatures are presented. The use of Binder's cumulant is supplemented by finite-size magnetization profiles not analyzed previously in this context. Continuous character of phase transitions is announced. Analyses proving the existence of more complicated phases of finite-temperature stripe ordering than the checkerboard one conclude the paper.     

Monte Carlo study of percolation on disordered triangular lattices

A simple model for amorphous solids, consisting of a mixed bond triangular lattice with a fraction of attenuated bonds randomly distributed (which simulate the presence of defects in the surface), is studied here by using computational simulation. The degree of disorder of the surface is tunable by selecting the values of (1) the fraction of regular [attenuated] bonds ρ [1−ρ] (0≤ρ≤1) and (2) the factor r, which is defined as the ratio between the value of the conductivity associated to an attenuated bond and that corresponding to a regular bond (0≤r≤1). The results obtained show how the percolation properties of the disordered system are modified with respect to the standard random bond percolation problem (r=0).     

Segment Motion in the Reptation Model of Polymer Dynamics. II. Simulations

We present simulation data for the motion of a polymer chain through a regular lattice of impenetrable obstacles (Evans–Edwards model). Chain lengths range from N= 20 to N= 640, and time up to 10⁷Monte Carlo steps. For N 160, for the central segment we find clear t ^1/4behavior as an intermediate asymptote. The expected t ^1/2range is not yet developed. For the end segment also the t ^l/4behavior is not reached. All these data compare well to our recent analytical evaluation of the reptation model, which shows that for shorter times (t10⁴) the discreteness of the elementary motion cannot be neglected, whereas for longer times and short chains (N100) tube renewal plays an essential role also for the central segment. Due to the very broad crossover behavior, both the diffusion coefficient and the reptation time within the range of our simulation do not reach the asymptotic power laws predicted by reptation theory. We present results for the center-of-mass motion, showing the expected intermediate t ^1/2behavior, but again only for very long chains. In addition we show results for the motion of the central segment relative to the center of mass, where in some intermediate range we see the expected increase of the effective power beyond the t ^1/4law, before saturation sets in. Analysis and simulations agree on defining a new set of criteria as characteristic for reptation of finite chains.     

Transient yielding of CO2 over oxidized ruthenium surfaces: Monte Carlo simulations

We develop Monte Carlo simulations to study the catalytic oxidation of CO over a surface of ruthenium. The catalyst is exposed to a continuous flux of CO molecules and its surface is pre-covered with an amount of oxygen atoms. Recent experiments performed on this system [R. Blume, W. Christen, H. Niehus, J. Phys. Chem. B 110 (2006) 13912] have shown that three different reaction mechanisms can account for the experimental results. Two of them are based on the Langmuir-Hinshelwood mechanism, where CO molecules are adsorbed at oxygen-free defect sites before reactions take place. The third one proceeds via the Eley-Rideal mechanism, which is almost time independent, and reactions occur at non-defect sites. In our model, we consider a semi-infinite cubic lattice to mimic the surface of the catalyst and oxygen atoms are incorporated into the layers below the surface. A fraction of defects is created at the topmost layer and at the first subsurface layer. Oxygen atoms can diffuse over the surface as well as between adjacent layers of the system. We also assumed a temperature dependent reaction rate that is related to the residence time of CO at the surface. Comparisons are made between the CO₂ yielding at defect-rich and smooth surfaces as a function of temperature.     

A computational predator-prey model, pursuit-evasion behavior based on different range of vision

We studied an extended predator-prey model of three interacting species in a two-dimensional lattice. Numerous factors have been taken into account in our research such as individual mobility and pursuit-evasion abilities. Our major focus is on the stochastic character of vision distribution for predator and prey. The model we made displays the features upon the population evolving through time, the spatial distribution of population, and the cross correlation of three species. What we observed showed the increase of the predators’ pursuit ability works in a negative way on their population, although nature favors the predator with maximum ability during the evolution, and the increasing vision of predators causes the increase of the preys’ population. And the predators’ ability deficiency may lead to the extinction of their population. In addition, the results show that it is not necessary for prey to have more intelligent evasion abilities.     

Phase behavior of hard particles

The phase behavior of hard particles and mixtures thereof is reviewed. Special attention is given to a lattice model consisting of hard hexagons and points on a triangular lattice. This model appears to have two disordered phases and an ordered phase.     

Critical dynamics of the three-dimensional Ising model: A Monte Carlo study

Extensive Monte Carlo simulations have been performed to analyze the dynamical behavior of the three-dimensional Ising model with local dynamics. We have studied the equilibrium correlation functions and the power spectral densities of odd and even observables. The exponential relaxation times have been calculated in the asymptotic one-exponential time region. We find that the critical exponentz=2.09 ±0.02 characterizes the algebraic divergence with lattice size for all observables. The influence of scaling corrections has been analyzed. We have determined integrated relaxation times as well. Their dynamical exponentz _int agrees withz for correlations of the magnetization and its absolute value, but it is different for energy correlations. We have applied a scaling method to analyze the behavior of the correlation functions. This method verifies excellent scaling behavior and yields a dynamical exponentz _scal which perfectly agrees withz.     

A new Monte Carlo power method for the eigenvalue problem of transfer matrices

We propose a new Monte Carlo method for calculating eigenvalues of transfer matrices leading to free energies and to correlation lengths of classical and quantum many-body systems. Generally, this method can be applied to the calculation of the maximum eigenvalue of a nonnegative matrix  such that all the matrix elements of Â^k are strictly positive for an integerk. This method is based on a new representation of the maximum eigenvalue of the matrix  as the thermal average of a certain observable of a many-body system. Therefore one can easily calculate the maximum eigenvalue of a transfer matrix leading to the free energy in the standard Monte Carlo simulations, such as the Metropolis algorithm. As test cases, we calculate the free energies of the square-lattice Ising model and of the spin-1/2XY Heisenberg chain. We also prove two useful theorems on the ergodicity in quantum Monte Carlo algorithms, or more generally, on the ergodicity of Monte Carlo algorithms using our new representation of the maximum eigenvalue of the matrixÂ.     

Steady-state and transient electronic transport properties of β-(AlxGa1-x)2O3/Ga2O3 heterostructures: An ensemble Monte Carlo simulation

The steady-state and transient electron transport properties of $beta $-(Al$_{x}$Ga$_{1-x}$)$_{2}$O$_{3}$/Ga$_{2}$O$_{3}$ heterostructures were investigated by Monte Carlo simulation with the classic three-valley model. In particular, the electronic band structures were acquired by first-principles calculations, which could provide precise parameters for calculating the transport properties of the two-dimensional electron gas (2DEG), and the quantization effect was considered in the $varGamma $ valley with the five lowest subbands. Wave functions and energy eigenvalues were obtained by iteration of the Schrödinger-Poisson equations to calculate the 2DEG scattering rates with five main scattering mechanisms considered. The simulated low-field electron mobilities agree well with the experimental results, thus confirming the effectiveness of our models. The results show that the room temperature electron mobility of the $beta $-(Al$_{0.188}$Ga$_{0.812}$)$_{2}$O$_{3}$/Ga$_{2}$O$_{3}$ heterostructure at 10 kV$ cdot$cm$^{-1}$ is approximately 153.669 cm$^{2}cdot$V$^{-1}cdot$s$^{-1}$, and polar optical phonon scattering would have a significant impact on the mobility properties at this time. The region of negative differential mobility, overshoot of the transient electron velocity and negative diffusion coefficients are also observed when the electric field increases to the corresponding threshold value or even exceeds it. This work offers significant parameters for the $beta$-(Al$_{x}$Ga$_{1-x}$)$_{2}$O$_{3}$/Ga$_{2}$O$_{3}$ heterostructure that may benefit the design of high-performance $beta$-(Al$_{x}$Ga$_{1-x}$)$_{2}$O$_{3}$/Ga$_{2}$O$_{3}$ heterostructure-based devices.     

第一性原理计算和Monte Carlo算法耦合对共掺杂稀磁半导体磁学性质的研究

将第一性原理计算和Monte Carlo算法耦合,对共掺杂稀磁半导体进行模拟,预测其磁学性质,并与同种过渡金属原子单掺杂稀磁半导体相比较进行分析.首先用第一性原理计算掺杂原子间的磁相互作用强度,作为后面Monte Carlo模拟的输入参数;然后利用Monte Carlo方法结合海森堡自旋模型和磁相互作用强度来模拟体系热力学磁化强度和磁化率,由此得到居里温度;用同样的方法模拟掺杂磁性体系的磁滞回线.计算结果显示,对应于掺Co、Al-Co、Fe、Al-Fe的ZnO基稀磁半导体的居里温度分别为346 K、450 K、743 K、467 K,与实验值很吻合;模拟这四种掺杂情况得到的磁滞回线也很符合理论分析和实验结果,且呈现和居里温度相同的变化规律.