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.     

Monte Carlo simulations of luminescence processes under quasi-equilibrium (QE) conditions

Previous researchers have carried out Monte Carlo simulations of thermoluminescence (TL) phenomena by considering the allowed transitions of charge carriers between the conduction band, electron traps and recombination centers. Such simulations have demonstrated successfully the effect of trap clustering on the kinetics of charge carriers in a solid, and showed that trap clustering can significantly change the observed luminescence properties. While such Monte Carlo simulations have been carried out for TL, there has been no such trap clustering studies for optically stimulated luminescence phenomena (OSL). This paper presents a simplified method of carrying out Monte Carlo simulations for TL and linearly modulated optically stimulated luminescence (LM-OSL) phenomena, based on the General One Trap (GOT) model, which is a special case of the one trap one recombination center model (OTOR) when quasi-equilibrium conditions (QE) hold. The simulated results show that the presence of small clusters consisting of a few traps in a solid can lead to multiple peaks in both the TL and LM-OSL signals. The effects of retrapping and degree of trap filling are simulated for such multi-peak luminescence signals, and insight is obtained into the mechanism producing these peaks. The method presented in this paper can be easily generalized for other types of luminescence solids in which the recombination probability varies with time.     

Monte Carlo calculations of the magnetocaloric effect in gadolinium

In this work we discuss the magnetocaloric effect in metallic gadolinium. We use a model Hamiltonian of interacting 4f spins and treat the 4f spin–spin interaction both in the mean field approximation and in the Monte Carlo simulation. The calculations show that the mean field approximation yields reasonable results for the magnetocaloric potentials ΔS$\mathrm{\Delta }S$ and Δ_Tad$\mathrm{\Delta }{T}_{\mathrm{ad}}$ but it fails in explaining the experimental data of specific heat at the magnetic ordering temperature. On the other hand, our theoretical results show that the Monte Carlo calculation describes well not only the magnetocaloric potentials ΔS$\mathrm{\Delta }S$ and Δ_Tad$\mathrm{\Delta }{T}_{\mathrm{ad}}$ but also the specific heat capacity.     

Atomic diffusion inside a STM junction: simulations by kinetic Monte Carlo coupled to tunneling current calculations

The influence of a static scanning tunneling microscope (STM) tip on the diffusion of xenon atoms adsorbed on a Cu(1 1 0) stepped surface is studied. Semi-empirical potentials for the Xe-surface interaction and a N-body energy based method for the Xe-tip contribution are used to calculate the adsorption energy of adsorbates in the STM junction. First, we analyse the variation of this energy when the adatom is placed near a step edge and for different tip positions. When the tip is situated in the neighbourhood of the step edge, the Ehrlich-Schwoebel barrier experienced by the adatom is lowered. This opens a specific diffusion channel, allowing a possible crossing of the step edge. Second, through a kinetic Monte Carlo approach coupled to the elastic scattering quantum chemistry method, the noisy tunneling current created by the random motion of diffusing atoms in the vicinity of the tip can be analyzed. We show that, by counting the number of diffusion events, we can determine effective barriers related to the most dominant processes contributing to the diffusion at a particular temperature. We also demonstrate that the interaction mode of the tip (attractive or imaging) greatly modifies the diffusion processes.     

Magnetic properties of Ni/Au core/shell studied by Monte Carlo simulations

The magnetic properties of ferromagnetic Ni/Au core/shell have been studied using Monte Carlo simulations within the Ising model framework. The considered Hamiltonian includes the exchange interactions between Ni–Ni, Au–Au and Ni–Au and the external magnetic field. The thermal total magnetizations and total magnetic susceptibilities of core/shell Ni/Au are computed. The critical temperature is deduced. The exchange interaction between Ni and Au atoms is obtained. In addition, the total magnetizations versus the external magnetic field and crystal filed for different temperature are also established.     

Kinetic Monte Carlo simulations of three-dimensional self-assembled quantum dot islands

By three-dimensional kinetic Monte Carlo simulations, the effects of the temperature, the flux rate, the total coverage and the interruption time on the distribution and the number of self-assembled InAs/GaAs(001) quantum dot(QD) islands are studied, which shows that a higher temperature, a lower flux rate and a longer growth time correspond to a better island distribution. The relations between the number of islands and the temperature and the flux rate are also successfully simulated. It is observed that for the total coverage lower than 0.5 ML, the number of islands decreases with the temperature increasing and other growth parameters fixed and the number of islands increases with the flux rate increasing when the deposition is lower than 0.6 ML and the other parameters are fixed.     

Thermodynamic properties of ternary alloys from Monte Carlo simulations

Methods are presented for obtaining both the integral and partial molar energies, entropies and free energies of the components in rigid ternary substitutional alloy systems from the one Monte Carlo simulation. Tests of the methods for some model systems are presented and discussed.     

Monte Carlo simulations of TL and OSL in nanodosimetric materials and feldspars

The study of luminescent materials consisting of nanoclusters is an increasingly active research area. It has been shown that the physical properties of such nanodosimetric materials can be very different from those of similar conventional microcrystalline phosphors. In addition, it has been suggested that traditional energy band models may not be applicable for some of these nanodosimetric materials, because of the existence of strong spatial correlations between traps and recombination centers. The properties of such spatially correlated materials have been previously simulated by using Monte Carlo techniques and by considering the allowed transitions of charge carriers between the conduction band, electron traps and recombination centers. This previous research demonstrated successfully the effect of trap clustering on the kinetics of charge carriers in a solid, and showed that trap clustering can significantly change the observed luminescence properties. This paper presents a simplified method of carrying out Monte Carlo simulations for thermoluminescence (TL) and optically stimulated luminescence (OSL) phenomena, based on a recently published model for feldspar. This model is based on tunneling recombination processes involving localized near-neighbor transitions. The simulations show that the presence of small clusters consisting of a few traps can lead to multiple peaks in both the TL and linearly modulated OSL signals. The effects of donor charge density, initial trap filling and cluster size are simulated for such multi-peak luminescence signals, and insight is obtained into the mechanism producing these peaks.     

The structure of strongly dipolar hard sphere fluids with extended dipoles by Monte Carlo simulations

We have investigated the structural change of dipolar hard sphere fluid while we change the dipole from an idealised point dipole (pDHS fluid) to a physically more realistic extended dipole (eDHS fluid) by increasing the distance d of the two point charges ±q while keeping the dipole moment μ = qd fixed. We discuss our results on the basis of the first- and second-rank orientational order parameters, angular distribution functions, chain-length distributions, and snapshots. At a low density, we have found chain formation with longer chains as the distance d is increased. At a high density, we have found phase transition from an orientationally ordered ferroelectric nematic phase (at low d) into an isotropic liquid containing chains (at large d).     

A hybrid functional first-principles study on the band structure of non-strained Ge_(1-x)Sn_x alloys

Using hybrid-functional first-principles calculation combined with the supercell method and band unfolding technique we investigate the band structure of non-strained Ge_(1-x)Sn_x alloys with various Sn concentrations. The calculations show that at the Sn concentration of ～ 3.1 mol% the Ge Sn alloy presents a direct band gap. The variation of the band structure are ascribed to the weaker electro-negativity of Sn atoms and a slight charge transfer from Sn atoms to Ge atoms.     

Stress modifications induced by dimer vacancies in the Si(0 0 1) surface: Monte Carlo simulations

By means of Monte Carlo simulations, we investigate the local stress modifications induced by dimer vacancies (DVs) in the Si(0 0 1) subsurface layers. In presence of n isolated compact DVs, the sites located below these defect rows are under clearly compressive stress in the third layer and under more and more tensile stress, as n increases, in the fourth layer. At higher DVs densities, analogous trends are observed, but the stress modifications are then slightly extended between the dimer rows. Applying our results to the Ge penetration in Si(0 0 1), we show how the knowledge of the local stress may allow predictions of a given impurity behaviour in the vicinity of the surface, provided that the impurity-defect and impurity-impurity interactions do not play a major role compared to the local stress modification induced by the presence of DVs.     

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.     

蒙特卡罗模拟在非平衡动态系统中的应用

非平衡系统几乎存在于自然和人造系统的各个层面上,它以非零连续的流量为特征。完全非对称简单排他过程被认为是对这类系统建模和模拟的一个范例。对蒙特卡罗方法如何模拟该类系统进行了介绍。分析了通过蒙特卡罗模拟观察到的一些有趣的物理现象如自发性对称破缺、有限尺寸效应和跳跃过程。非对称的低-低密度相破缺与系统的有限尺寸效应密切相关,建议开展更细致的蒙特卡罗模拟以进一步加深对仍处于争论中的非平衡系统有限尺寸效应的认识。     

蒙特卡罗模拟在非平衡动态系统中的应用

非平衡系统几乎存在于自然和人造系统的各个层面上,它以非零连续的流量为特征。完全非对称简单排他过程被认为是对这类系统建模和模拟的一个范例。对蒙特卡罗方法如何模拟该类系统进行了介绍。分析了通过蒙特卡罗模拟观察到的一些有趣的物理现象如自发性对称破缺、有限尺寸效应和跳跃过程。非对称的低-低密度相破缺与系统的有限尺寸效应密切相关,建议开展更细致的蒙特卡罗模拟以进一步加深对仍处于争论中的非平衡系统有限尺寸效应的认识。     

材料中He深度分布演化的Monte Carlo模拟研究

基于He泡生长的迁移-合并机理,用Monte Carlo方法模拟了对材料进行等温退火过程中He深度分布的演化,探讨了不同参数对这一演化的影响.研究表明:材料中He泡的初始浓度和尺寸将影响He深度分布的变化,而退火温度则对演化速率起重要作用但对最终的He深度分布影响较小;随着反应的进行,整个系统的演化是逐渐趋缓的. 关键词： He 深度分布 Monte Carlo模拟     

Multi-site kinetic Monte Carlo simulations of thermal desorption spectroscopy data

Presented is a kinetic Monte Carlo simulation (KMCS) algorithm for simulating experimental thermal desorption spectroscopy (TDS) data. The KMCS is based on the Master equation approach and applies a first-passage-time analysis, i.e., the time dependence of the kinetics is matched correctly. The KMCS–TDS scheme used here includes multiple kinetically distinct adsorption sites and the effect of lateral interactions as required for fitting experimental data. After the results of extensive tests of the algorithm by means of synthetic data are discussed, experimental TDS curves are reproduced by the KMCS. Two applications are demonstrated: iso-butane adsorption on ZnO(0 0 0 1)–Zn and n-pentane adsorption on carbon nanotubes.     

Monte Carlo simulations of electromagnetically induced transparency in a square lattice of Rydberg atoms

We study the steady optical response of a square lattice in which all trapped atoms are driven by a probe and a coupling fields into the ladder configuration of electromagnetically induced transparency(EIT). It turns out to be a manybody problem in the presence of van der Waals(vd W) interaction among atoms in the upmost Rydberg state, so Monte Carlo(MC) calculation based on density matrix equations have been done after introducing a sufficiently large cut-off radius. It is found that the absorption and dispersion of EIT spectra depends critically on a few key parameters like lattice dimension, unitary vd W shift, probe Rabi frequency, and coupling detuning. Through modulating these parameters, it is viable to change symmetries of the absorption and dispersion spectra and control on demand depth and position of the transparency window. Our MC calculation is expected to be instructive in understanding many-body quantum coherence effects and in manipulating non-equilibrium quantum phenomena by utilizing vd W interactions of Rydberg atoms.     

Surface effects on liquid crystals constrained in nanoscaled pores investigated by field cycling NMR relaxometry and Monte Carlo simulations

Proton relaxation rates of nematic liquid crystals confined in nanoporous cavities were measured in a broad frequency range with the help of field cycling nuclear magnetic resonance relaxometry. The shape of relaxation dispersion curves in confined materials strongly deviates from the behavior in bulk, both above and below the bulk isotropization temperature. A strong increase in relaxation rates, exceeding by two orders of magnitude that of the bulk sample, is observed in the range of a few kilohertz. Relaxation rates in bigger pores decreased. Experimental findings are interpreted in terms of surface-induced orientational order and diffusion between sites with different orientations of local directors. With the aid of Monte Carlo simulations, two processes affecting low-frequency relaxation could be identified: (a) exchange losses of molecules from the surface-ordered phase to the bulk-like phase, and (b) Reorientations Mediated by Translational Displacements, which dominate the long-time scale and account for the recovery of correlation in molecular orientations as molecules probe different surface sites. It is shown that the width of the oriented layer may strongly affect the slope of dispersion curves and that cross-over between plateau and power law dispersion regimes shifts towards lower frequencies for bigger pores.     

TLD measurements and Monte Carlo simulations for glandular dose and scatter fraction assessment in mammography: A comparative study

The main purpose of this study was to validate and compare Mean Glandular Dose (MGD) values obtained using Monte Carlo simulations with experimental values obtained from Entrance Surface Dose (ESD) and depth dose measurements performed in a Hospital mammography unit. ESD and depth dose were measured using ThermoLuminescent Dosimeters (TLDs), and a tissue equivalent mammography phantom recommended by the American College of Radiology (ACR). Measurements and Monte Carlo simulations were also compared with the MGD calculated using the Automatic Exposure Control (AEC) system of the mammographic unit. In the simulations the Doppler energy broadening effect was also taken into account. The simulated ESD are about 5%–10% higher than the measured ESD values. The deviation between the measured and simulated MGD values in the phantom is of about 15%. The MGD evaluated using the AEC system is smaller both with respect to the Monte Carlo simulation and experimental result by a factor of about 15% and 25% respectively. Moreover the BackScatter Factor (BSF) estimated by Monte Carlo simulations was used for the MGD calculation according to the Wu’s method. Finally the inclusion of the energy broadening effect on MGD calculation produces negligible variations on the simulated results.     

Finite-size effects at critical points with anisotropic correlations: Phenomenological scaling theory and Monte Carlo simulations

Various thermal equilibrium and nonequilibrium phase transitions exist where the correlation lengths in different lattice directions diverge with different exponentsv ,v : uniaxial Lifshitz points, the Kawasaki spin exchange model driven by an electric field, etc. An extension of finite-size scaling concepts to such anisotropic situations is proposed, including a discussion of (generalized) rectangular geometries, with linear dimensionL in the special direction and linear dimensionsL in all other directions. The related shape effects forL L but isotropic critical points are also discussed. Particular attention is paid to the case where the generalized hyperscaling relationv +(d–1)v =+2 does not hold. As a test of these ideas, a Monte Carlo simulation study for shape effects at isotropic critical point in the two-dimensional Ising model is presented, considering subsystems of a 1024x1024 square lattice at criticality.Visiting Supercomputer Senior Scientist at Rutgers University.