Radial density distribution of fractal clusters

The radial density distributions of fractal clusters generated in both DLCA and RLCA conditions by Monte-Carlo off-lattice cluster-cluster aggregation have been investigated. It has been computed by averaging a large number of clusters of same mass to form an average cluster, which is then considered as spherically symmetric. It is found that the radial density distribution, calculated using the mass center of the cluster as the center point, does not follow the fractal scaling, as sometimes assumed in the literature. An empirical model has been proposed to describe the dependence of the radial density distribution on the number of particles in the cluster. The obtained radial density distribution is used to compute permeability profile of the fractal cluster using several literature models, which is then applied to estimate the cluster hydrodynamic radius, R_h, by considering the cluster as a porous permeable object and using the solution of Brinkman equations for the fluid flow inside the cluster. The so obtained R_h values are compared to those in the literature, computed using the Kirkwood-Riseman (KR) theory. It has been found that, among the five permeability models examined, only the model proposed by Davis (Proceedings of the Institution of Mechanical Engineers Part B 1, 185) provides results in good agreement with those obtained using the KR model. Furthermore, it has been verified that the R_h values are insensitive to the model used for the density distribution.     

Analysis of four Monte Carlo methods for the solution of population balances in dispersed systems

Monte Carlo (MC) constitutes an important class of methods for the numerical solution of the general dynamic equation (GDE) in particulate systems. We compare four such methods in a series of seven test cases that cover typical particulate mechanisms. The four MC methods studied are: time-driven direct simulation Monte Carlo (DSMC), stepwise constant-volume Monte Carlo, constant number Monte Carlo, and multi-Monte Carlo (MMC) method. These MC's are introduced briefly and applied numerically to simulate pure coagulation, breakage, condensation/evaporation (surface growth/dissolution), nucleation, and settling (deposition). We find that when run with comparable number of particles, all methods compute the size distribution within comparable levels of error. Because each method uses different approaches for advancing time, a wider margin of error is observed in the time evolution of the number and mass concentration, with event-driven methods generally providing better accuracy than time-driven methods. The computational cost depends on algorithmic details but generally, event-driven methods perform faster than time-driven methods. Overall, very good accuracy can be achieved using reasonably small numbers of simulation particles, O(10³), requiring computational times of the order 10²−10³ s on a typical desktop computer.     

Monte Carlo simulation of radiation-induced solid state polymerization

A Monte Carlo method was used for a computer simulation of radiation-induced solid state polymerization. The propagation of polymer chains was simulated by means of self-avoiding random walks on a tetrahedral lattice. The initiation and termination of the chains were modelled by pseudorandom processes. The influence of conditions of the in-source process on the post-polymerization kinetics and on the degree of polymerization of the polymers was studied.     

需求依赖于价格情境下基于Copula-CVaR 的报童决策

探讨价格不确定下,需求-价格相关性与风险态度对决策行为的影响.建立随机需求与随机价格相关情境下基于Copula-CVaR的报童决策模型,Copula函数描述相关性,条件风险价值(CVaR)反映风险态度,证明了模型解的存在性和惟一性.蒙特卡罗模拟发现,需求与价格的相关性与风险态度对决策的交互作用使决策行为发生规律性变化,决策者对价格波动有一定容忍度,需求与价格相关性趋于不相关与完全负相关时市场趋于同质性.     

Partitioning of polymers into pores with surface interactions at dilute solution limit

The partitioning of a single polymer chain into a slit in a good solvent with different surface interactions is examined through Monte Carlo simulations from subcritical regime to adsorptive regime. The chain conformation in the subcritical regime is not perturbed by the surface interactions significantly. In the adsorptive regime, the conformation of the chain is strongly perturbed by the surface interactions. The confinement free energy in the two regimes maybe written in a uniform formula, βΔμ_conf∼c₁N(a/D)^xε_w+c₂N(a/D)^1/ν with x∼2.0 or larger in the subcritical regime and ∼1.0 in the adsorptive regime, where ν is the Flory exponent, D is the slit width, N is the chain length, a is the monomer size, and ε_w is the surface interaction energy between the polymer beads and the slit. This formula is valid for a long chain in the narrow slit in the subcritical regime or when the adsorption layer h>D in the adsorptive regime. A critical behavior occurs when ε_w is at the critical adsorption point and x=1/ν, then Δμ_conf will have little dependence on N or D. Higher order terms that are neglected in the above equation, however, may be present that could lead to a weak dependence of K on N and D even in the critical adsorption point.     

一种无须预指定分割区域数的自适应多阈值图像分割方法

为解决多阈值图像分割中分割区域数较难确定的问题,提出一种基于可逆跳跃马尔可夫链蒙特卡罗(RJMCMC)的自适应多阈值图像分割方法.基于图像直方图的多阈值分割的本质是寻找直方图各峰间的谷底,但其个数较难确定且各局部峰并非都是高斯分布.因此文中用更具普适性的混合α稳定分布拟合直方图,建立包含局部峰个数及各分布元参数的分层贝叶斯概率模型.采用RJMCMC后验概率推理自适应确定混合α稳定分布的分布元个数及各自参数,从而获得分割区域数和多阈值参数.针对单晶炉拉晶图像、人脑核磁共振图像及国际标准测试图进行测试,结果表明该方法准确地建立图像分割模型,得到满意的多阈值分割结果.     

TESTS FOR FRACTIONAL INTEGRATION:A MONTE CARLO INVESTIGATION

Abstract. The performance of the Geweke-Porter-Hudak (GPH) test, the modified rescaled range (MRR) test and two Lagrange multiplier (LM) type tests for fractional integration in small samples is examined using Monte Carlo methods. Both the GPH and MRR tests are found to be robust to moderate autoregressive moving-average components, autoregressive conditional heteroskedasticity effects and shifts in the variance. However, these two tests are sensitive to large autoregressive moving-average components and shifts in the mean. It is also found that the LM tests are sensitive to deviations from the null hypothesis. As an illustration, the GPH test is applied to two economic data series.     

A description of phase inversion behaviour in agitated liquid-liquid dispersions under the influence of the Marangoni effect

The influence of the Marangoni effect on phase inversion behaviour is examined by integrating a microscopic study of the drop coalescence process, in which thin film drainage in the presence of insoluble surfactant occurs, into a macroscopic phase inversion model which has been developed previously using a Monte Carlo technique. This is achieved via an immobility factor, obtained from a comparison of the film drainage times for surfactant-laden systems and surfactant-free systems as a function of the drop approach velocity, surface Péclet number, initial surfactant concentration and the Hamaker constant, which is then used to modify the coalescence probability in the phase inversion model. On the one hand, the results indicate that the Marangoni effect removes any influence that the viscosity ratio has on phase inversion due to immobilisation of the interface, thus shielding the flow in the film from the effects of the flow in the dispersed phase; the point at which phase inversion occurs therefore tends towards equivolume holdups with the addition of surfactant. On the other hand, when comparisons are made with pure systems in which surfactant is absent, the system is seen to be either stabilised or de-stabilised from inversion depending on the viscosity ratio of the system. This is attributed to the influence of surfactant on the dispersion morphologies on either side of the inversion (i.e. water-in-oil dispersions and oil-in-water dispersions) and depends on the dispersed phase holdup; the Marangoni effect is felt stronger when the dispersed phase holdup is low.     

A NEW SIMULATION APPROACH TO THE ENTROPY-RELATED PROPERTIES OF FLUIDS——CHEMICAL POTENTIAL AND HELMHOLTZ FREE ENERGY OF HARD SPHERE FLUIDS

A new approach to the computation of entropy-related properties of fluids has been pre-sented.Application of the new technique to hard sphere fluids shows that it is capable of providingreliable estimates of such properties as the chemical potential and Helmholtz free energy,even athigh density where other existing methods are hardly applicable.The chemical potential of an infinitedilute component in hard sphere systems has been estimated,and compared with that calculated fromthe Carnahan-Starling equation.     

Conditional probability Markov chain simulation based reliability analysis method for nonnormal variables

Based on fast Markov chain simulation for generating the samples distributed in failure region and saddlepoint approximation(SA) technique,an efficient reliability analysis method is presented to evaluate the small failure probability of non-linear limit state function(LSF) with non-normal variables.In the presented method,the failure probability of the non-linear LSF is transformed into a product of the failure probability of the introduced linear LSF and a feature ratio factor.The introduced linear LSF wh...