Information Loss in Coarse-Graining of Stochastic Particle Dynamics

Recently a new class of approximating coarse-grained stochastic processes and associated Monte Carlo algorithms were derived directly from microscopic stochastic lattice models for the adsorption/desorption and diffusion of interacting particles^(12,13,15). The resulting hierarchy of stochastic processes is ordered by the level of coarsening in the space/time dimensions and describes mesoscopic scales while retaining a significant amount of microscopic detail on intermolecular forces and particle fluctuations. Here we rigorously compute in terms of specific relative entropy the information loss between non-equilibrium exact and approximating coarse-grained adsorption/desorption lattice dynamics. Our result is an error estimate analogous to rigorous error estimates for finite element/finite difference approximations of Partial Differential Equations. We prove this error to be small as long as the level of coarsening is small compared to the range of interaction of the microscopic model. This result gives a first mathematical reasoning for the parameter regimes for which approximating coarse-grained Monte Carlo algorithms are expected to give errors within a given tolerance. MSC (2000) subject classifications: 82C80; 60J22; 94A17     

Asymmetric Coupling in Two-Lane Asymmetric Simple Exclusion Processes with Unequal Injection Rates: Effect of Different Hoping Rates

This paper investigates the effect of both unequal injection rates and different hopping rates on two-lane asymmetric simple exclusion processes(ASEPs) with asymmetric coupling. When the hopping rates of both lanes are different, the system includes six steady phases, however, when the hopping rates of both lanes are same, the seventh phase(MC, MC) will exist in the system. Interestingly, with different hopping rates of both lanes, the densities of the system cannot be influenced by the non-zero vertical transition rate. Our theoretical arguments are in well agreement with extensively performed Monte Carlo simulations.     

Simulation study of random sequential adsorption of mixtures on a triangular lattice

Random sequential adsorption of binary mixtures of extended objects on a two-dimensional triangular lattice is studied numerically by means of Monte Carlo simulations. The depositing objects are formed by self-avoiding random walks on the lattice. We concentrate here on the influence of the symmetry properties of the shapes on the kinetics of the deposition processes in two-component mixtures. Approach to the jamming limit in the case of mixtures is found to be exponential, of the form: θ(t) ∼ θ_jam - Δθ exp(- t/σ), and the values of the parameter σ are determined by the order of symmetry of the less symmetric object in the mixture. Depending on the local geometry of the objects making the mixture, jamming coverage of a mixture can be either greater than both single-component jamming coverages or it can be in between these values. Results of the simulations for various fractional concentrations of the objects in the mixture are also presented.     

EAST托卡马克杂质输运蒙特卡洛模拟

介绍DIVIMP程序的基本思想和采用的物理模型,研究EAST托卡马克欧姆放电条件下碳杂质的产生与输运.模拟结果与实验测量具有较好的一致性,说明将该程序应用于EAST装置中杂质输运模拟的合理性.并利用DIVIMP程序预测EAST在8MW加热功率条件下钨杂质的输运特性.     

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.     

Effects of Spatial Nonlocality versus Nonlocal Causality for Bound Electrons in External Fields

Using numerically exact solution of the time-dependent Schrödinger equation together with time-dependent quantum Monte Carlo (TDQMC) calculations, here we compare the effects of spatial nonlocality versus nonlocal causality for the ground state and for real-time evolution of two entangled electrons in parabolic potential in one spatial dimension. It was found that the spatial entanglement quantified by the linear quantum entropy is predicted with good accuracy using the spatial nonlocality, parameterized naturally within the TDQMC approach. At the same time, the nonlocal causality predicted by the exact solution leads to only small oscillations in the quantum trajectories which belong to the idler electron as the driven electron is subjected to a strong high frequency electric field, without interaction between the electrons.     

Modelling of an obliquely deposited thin film in three dimensions by kinetic Monte Carlo method

A simulation of the growth of an obliquely deposited thin film in a three-dimensional lattice was made using kinetic Monte Carlo method. Cu growth in three dimensions on a (001) substrate with high deposition rates has been simulated in this model. We mainly investigated the variation of three-dimensional morphology and microstructure offilms with incidence angle of sputtered flux. The relation of roughness and densities of films with incidence angle was also investigated. The simulation results show that the surface roughness increases and the relative density of thin film decreases with increasing incidence angle, respectively; the columnar structures were separated by void regions for large incidence angle and high deposition rate. The simulation results are in good agreement with experimental results.However, the orientation angle of columns is not completely consistent with the classical tangent rule.     

非均匀磁场约束条件下的电子束空气等离子体特性

为了揭示大气环境电子束等离子体的性质,基于蒙特卡罗程序包Geant4建立了一个包含电离、激发以及轫致辐射等物理过程的计算模型,用于模拟非均匀磁场约束条件下高能强流稳态电子束的输运特性、以及大气环境等离子体的性质。结果表明:非均匀磁场可以有效控制电子束在空气中的输运轨迹,显著降低电子束的发散;随着电子束在空气中行程的增加,电子束能谱开始展宽并向低能区移动;输运装置出口能量损失比电子束射程末端高2个量级,且随着电子束输运距离的增加,等离子体密度降低;等离子体密度的高低与电子束能量直接相关。     

Multiple-scaling methods for Monte Carlo simulations of radiative transfer in cloudy atmosphere

Two multiple-scaling methods for Monte Carlo simulations were derived from integral radiative transfer equation for calculating radiance in cloudy atmosphere accurately and rapidly. The first one is to truncate sharp forward peaks of phase functions for each order of scattering adaptively. The truncated functions for forward peaks are approximated as quadratic functions; only one prescribed parameter is used to set maximum truncation fraction for various phase functions. The second one is to increase extinction coefficients in optically thin regions for each order scattering adaptively, which could enhance the collision chance adaptively in the regions where samples are rare. Several one-dimensional and three-dimensional cloud fields were selected to validate the methods. The numerical results demonstrate that the bias errors were below 0.2% for almost all directions except for glory direction (less than 0.4%) and the higher numerical efficiency could be achieved when quadratic functions were used. The second method could decrease radiance noise to 0.60% for cumulus and accelerate convergence in optically thin regions. In general, the main advantage of the proposed methods is that we could modify the atmospheric optical quantities adaptively for each order of scattering and sample important contribution according to the specific atmospheric conditions.     

Ordering kinetics in quasi-one-dimensional Ising-like systems

We present results of a Monte Carlo simulation of the kinetics of ordering in the two-dimensional nearest-neighbor Ising model in anL xM geometry with two free boundaries of length ML. This model can be viewed as representing an adsorbant on a stepped surface with mean terrace widthL. We follow the ordering kinetics after quenches to temperatures 0.25 T/T_c 1 starting from a random initial configuration at a coverage of=0.5 in the corresponding lattice gas picture. The systems evolve in time according to a Glauber kinetics with nonconserved order parameter. The equilibrium structure is given by a one-dimensional sequence of ordered domains. The ordering process evolves from a short initial two-dimensional ordering process through a crossover region to a quasi-one-dimensional behavior. The whole process is diffusive (inverse half-width of the structure factor peak 1/q_{¦¦ t}), in contrast to a model proposed by Kawasakiet al., where an intermediate logarithmic growth law is expected. All results are completely describable in the picture of an annihilating random walk (ARW) of domain walls.     

Kinetics versus thermodynamics in materials modeling: The case of the di-vacancy in iron

Monte Carlo models are widely used for the study of microstructural and microchemical evolution of materials under irradiation. However, they often link explicitly the relevant activation energies to the energy difference between local equilibrium states. We provide a simple example (di-vacancy migration in iron) in which a rigorous activation energy calculation, by means of both empirical interatomic potentials and density functional theory methods, clearly shows that such a link is not granted, revealing a migration mechanism that a thermodynamics-linked activation energy model cannot predict. Such a mechanism is, however, fully consistent with thermodynamics. This example emphasizes the importance of basing Monte Carlo methods on models where the activation energies are rigorously calculated, rather than deduced from widespread heuristic equations.     

Monte carlo study of the interacting self-avoiding walk model in three dimensions

We consider self-avoiding walks on the simple cubic lattice in which neighboring pairs of vertices of the walk (not connected by an edge) have an associated pair-wise additive energy. If the associated force is attractive, then the walk can collapse from a coil to a compact ball. We describe two Monte Carlo algorithms which we used to investigate this collapse process, and the properties of the walk as a function of the energy or temperature. We report results about the thermodynamic and configurational properties of the walks and estimate the location of the collapse transition.     

梯度场中荧光关联谱测量的Monte Carlo模拟

荧光关联谱（FCS）利用少量分子的荧光涨落获得分子运动和反应信息,是一种探测活细胞内生物过程的有力工具。本文利用Monte Carlo方法模拟激光梯度场下瑞利粒子的布郎运动,分析梯度场对FCS测量得到的扩散时间、粒子数等参数的影响,模拟与初步实验结果定性吻合。文中还讨论了Monte Carlo模拟预测的一些实验现象。     

Growth of Ordered Domains in a Computer Model Alloy with Lattice Misfit

We study via Monte Carlo simulations the influence of elastic interactions on the ordering and decomposition of a two-dimensional model binary alloy with antiferromagnetic nearest and ferromagnetic next nearest neighbor type interactions following a quench into the coexistence region. The elastic interaction leads to the development of a platelet morphology for the segregated ordered and disordered regions. A length scale characterizing the coarsening process follows a law of the type R=a+bt ^1/3 with the growth b decreasing with the amount of ordered phase; this appears to be due to the presence of anti-phase boundaries between neighboring domains ordered on different sublattices which are difficult to eliminate. The application of uniaxial external stress results in rafting of the domains. Many of the simulation results are in agreement with experimentally observed effects in nickel-base superalloys.     

Blocking effects in irreversible adsorption of linear macromolecules

A new variant of random sequential adsorption (RSA), namely random sequential ballistic adsorption (RSBA), is proposed to explore the possible role of blocking effects in the adsorption dynamics of ballistically arriving objects. These objects upon adsorption can protrude outside the substrate and in turn can obstruct and hence reject the adsorption of newly arriving objects. Adsorption of linear macromolecules (modeled as infinitesimally thin needles), on a two-dimensional continuum substrate is studied using RSBA model. It is shown analytically that in late time regime, the number n(t) of adsorbed objects at time t follows a power law n(t) ∼ t^α, as in RSA, but with a different exponent, α = 2/3. Computer simulations are also carried out. The simulation results are found to be in close agreement with the analytical results. The exponent behavior for real experimental conditions is also analyzed.     

N2介质阻挡放电中有效电场的光谱测定

采用蒙特卡罗方法，模拟了N2非平衡态直流放电等离子体过程。计算了不同E／N条件下电子在氮气中的漂移速度，结果与实验数据符合得很好。模拟了电子激发态粒子数随E／N的变化关系。提出在介质阻挡放电研究和应用中，通过监测两条紫外谱线145和201nm强度之比来监测有效电场的方法。     

Influence of thyroid volume reduction on absorbed dose in 131I therapy studied by using Geant4 Monte Carlo simulation

A simulation study has been performed to quantify the effect of volume reduction on the thyroid absorbed dose per decay and to investigate the variation of energy deposition per decay due to β- and γ-activity of 131I with volume/mass of thyroid, for water, ICRP- and ICRU-soft tissue taken as thyroid material. A Monte Carlo model of the thyroid, in the Geant4 radiation transport simulation toolkit was constructed to compute the β- and γ-absorbed dose in the simulated thyroid phantom for various values of its volume. The effect of the size and shape of the thyroid on energy deposition per decay has also been studied by using spherical, ellipsoidal and cylindrical models for the thyroid and varying its volume in 1-25 cm3 range. The relative differences of Geant4 results for different models with each other and MCNP results lie well below 1.870%. The maximum relative difference among the Geant4 estimated results for water with ICRP and ICRU soft tissues is not more than 0.225%. S-values for ellipsoidal, spherical and cylindrical thyroid models were estimated and the relative difference with published results lies within 3.095%. The absorbed fraction values for beta particles show a good agreement with published values within 2.105% deviation. The Geant4 based simulation results of absorbed fractions for gammas again show a good agreement with the corresponding MCNP and EGS4 results （±6.667%） but have 29.032% higher values than that of MIRD calculated values. Consistent with previous studies, the reduction of the thyroid volume is found to have a substantial effect on the absorbed dose. Geant4 simulations confirm dose dependence on the volume/mass of thyroid in agreement with MCNP and EGS4 computed values but are substantially different from MIRD8 data. Therefore, inclusion of size/mass dependence is indicated for 131I radiotherapy of the thyroid.     

Influence of thyroid volume reduction on absorbed dose in ~(131)I therapy studied by using Geant4 Monte Carlo simulation

A simulation study has been performed to quantify the effect of volume reduction on the thyroid absorbed dose per decay and to investigate the variation of energy deposition per decay due to β- and γ-activity of ~(131)I with volume/mass of thyroid,for water,ICRP- and ICRU-soft tissue taken as thyroid material.A Monte Carlo model of the thyroid,in the Geant4 radiation transport simulation toolkit was constructed to compute the β- and γ-absorbed dose in the simulated thyroid phantom for various values of its volume.The effect of the size and shape of the thyroid on energy deposition per decay has also been studied by using spherical,ellipsoidal and cylindrical models for the thyroid and varying its volume in 1-25 cm~3 range.The relative differences of Geant4 results for different models with each other and MCNP results he well below 1.870%.The maximum relative difference among the Geant4estimated results for water with ICRP and ICRU soft tissues is not more than 0.225%.S-values for ellipsoidal,spherical and cylindrical thyroid models were estimated and the relative difference with published results lies within3.095%.The absorbed fraction values for beta particles show a good agreement with published values within 2.105%deviation.The Geant4 based simulation results of absorbed fractions for gammas again show a good agreement with the corresponding MCNP and EGS4 results(±6.667%) but have 29.032%higher values than that of MIRD calculated values.Consistent with previous studies,the reduction of the thyroid volume is found to have a substantial effect on the absorbed dose.Geant4 simulations confirm dose dependence on the volume/mass of thyroid in agreement with MCNP and EGS4 computed values but are substantially diiferent from MIRD8 data.Therefore,inclusion of size/mass dependence is indicated for ~(131)I radiotherapy of the thyroid.     

Selective-pivot sampling of radial distribution functions in asymmetric liquid mixtures

We present a new method for selectively sampling radial distribution functions and effective interaction potentials in asymmetric liquid mixtures using a Monte Carlo simulation. We demonstrate its efficiency for hard-sphere mixtures, and for model systems with more general interactions, and compare our simulations with several analytical approximations. For interaction potentials containing a hard-sphere contribution, the algorithm yields the contact value of the radial distribution function.