General Monte Carlo Algorithm Research Articles

Investigation of nucleation and grain growth in 2-dimensional systems by using generalized Monte Carlo simulations

In this study, nucleation and grain growth was studied by using 2-dimensional generalized Monte Carlo simulations and experiments. As an attempt to improve the JMAK model, we proposed a new differential equation to be able to model nucleation and growth phenomena using nonextensive thermostatistics. One of the reasons that we would like to perform generalized Monte Carlo simulations in studying of nucleation and grain growth phenomena is that the generalized Monte Carlo algorithm was shown to be more effective than the standard Monte Carlo algorithm and also than the standard Molecular Dynamic algorithm in locating the minimum energy configuration. Therefore, for a given temperature, the fact that a configuration of the system with lower energy could be obtained by using the generalized Monte Carlo simulation means that a different textural configuration of grain growth could be also expected. In this respect, it is possible to say that the nonextensive statistics might be an appropriate tool in studying of nucleation and growth phenomena.

The cauchy problem for the radiative transfer equation with generalized conjugation conditions

The initial boundary problem for the nonstationary radiative transfer equation in a nonhomogeneous plane layer with generalized conjugation conditions on the material interface is studied. A generalized Monte Carlo algorithm is proposed for solving the problem, and numerical experiments are discussed.

Thermodynamic integration based on classical atomistic simulations to determine the Gibbs energy of condensed phases: Calculation of the aluminum-zirconium system

In this work, an in silico procedure to generate a fully coherent set of thermodynamic properties obtained from classical molecular dynamics (MD) and Monte Carlo (MC) simulations is proposed. The procedure is applied to the Al-Zr system because of its importance in the development of high strength Al-Li alloys and of bulk metallic glasses. Cohesive energies of the studied condensed phases of the Al-Zr system (the liquid phase, the fcc solid solution, and various orthorhombic stoichiometric compounds) are calculated using the modified embedded atom model (MEAM) in the second-nearest-neighbor formalism (2NN). The Al-Zr MEAM-2NN potential is parameterized in this work using ab initio and experimental data found in the literature for the AlZr${}_{3}$-L1${}_{2}$ structure, while its predictive ability is confirmed for several other solid structures and for the liquid phase. The thermodynamic integration (TI) method is implemented in a general MC algorithm in order to evaluate the absolute Gibbs energy of the liquid and the fcc solutions. The entropy of mixing calculated from the TI method, combined to the enthalpy of mixing and the heat capacity data generated from MD/MC simulations performed in the isobaric-isothermal/canonical (NPT/NVT) ensembles are used to parameterize the Gibbs energy function of all the condensed phases in the Al-rich side of the Al-Zr system in a CALculation of PHAse Diagrams (CALPHAD) approach. The modified quasichemical model in the pair approximation (MQMPA) and the cluster variation method (CVM) in the tetrahedron approximation are used to define the Gibbs energy of the liquid and the fcc solid solution respectively for their entire range of composition. Thermodynamic and structural data generated from our MD/MC simulations are used as input data to parameterize these thermodynamic models. A detailed analysis of the validity and transferability of the Al-Zr MEAM-2NN potential is presented throughout our work by comparing the predicted properties obtained from this formalism with available ab initio and experimental data for both liquid and solid phases.

A novel, structure‐tracking monte carlo algorithm for spray fluidized bed agglomeration

AbstractA stochastic modeling approach to fluidized bed agglomeration is presented. First, the fundamentals of a general Monte Carlo algorithm are discussed, namely the correlation of real with simulation time and the size of the simulation box. Two different approaches regarding the morphological description of particle structure development are then compared for different theoretical test cases. The first approach (concept of positions) is a fast and effective geometrical discretization to follow properties such as primary particle number per agglomerate throughout the simulation. The second approach is a new three‐dimensional (3‐D) structure algorithm, which allows a complete, unrestricted description of the spatial evolution of particles related to physical microprocesses. The 3‐D algorithm enables to apply distributed particle and droplet sizes, which is not possible in the concept of positions. In the perspective, the structural growth of particles can be connected to process conditions, opening new possibilities for process and product design. © 2011 American Institute of Chemical Engineers AIChE J, 58: 3016–3029, 2012

Advanced Monte Carlo Algorithm for the Atomistic Simulation of Short- and Long-Chain Branched Polymers: Implementation for Model H-Shaped, A3AA3 Multiarm (Pom-Pom), and Short-Chain Branched Polyethylene Melts

We present a powerful connectivity-altering Monte Carlo (MC) algorithm for simulating atomistically detailed models of long- and short-chain branched polymers. Based on a mix of advanced and simple moves, the algorithm allows the robust simulation of chain systems with a variety of molecular architectures: H-shaped, A3AA3 multiarm (pom-pom), and short-chain branched (SCB) ones. For the H-shaped and A3AA3 architectures (A denotes the backbone and A the arm), in particular, the recently developed intermolecular double bridging (DB) move effecting a new bridging between the chain backbones or the branches of two different chains and the intramolecular double rebridging (IDR) move effecting a new bridging between two branches of the same chain [Karayiannis et al. J. Chem. Phys. 2003, 118, 2451] are shown to provide a robust sampling of their structural and conformational characteristics at the chain level. The double concerted rotation (d-CONROT) and H-shaped branch rebridging (H-BR) moves, on the other hand, which are important in relaxing internal degrees of freedom in the chain and the local structure around branch points, allow complete equilibration at the segmental level, which is prerequisite for the correct prediction of the volumetric and packing properties of the simulated systems. For the case of SCB polymers, a continuum configurational bias move for branched polymers (Br-CCB) has been designed capable of sampling changes in the atomic coordinates in the vicinity of branch points. Along with an effective implementation of the conventional end-bridging (EB) move, this has resulted in a powerful method for simulating SCB polymers with a prespecified distribution of branch points along the chain and given (i.e., fixed) number of carbon atoms per branch. To deal with polydispersity in the simulated systems, the algorithm is executed in a semigrand canonical ensemble by making use of the set of chain relative chemical potentials which for a bulk, linear system produces a uniform distribution of chain lengths [Pant and Theodorou Macromolecules 1995, 28, 7224]. Consistent with recent considerations by Ramos et al. [Macromolecules 2007, 40, 9640], two different chain length distributions should be simultaneously controlled in the course of the simulation for branched systems. The new, generalized MC algorithm is capable of thoroughly equilibrating model H-shaped, multiarm A3AA3, and SCB polymers at all length scales and adequately sampling fluctuations in their structural, volumetric, and conformational properties. Overall, we find that branched polymers are characterized by a stiffer conformation than linear analogues of the same total chain length. For the H-shaped and A3AA3 architectures, in particular, we have observed that each dangling arm exerts an entropically driven tensile force on the chain crossbar (the part of the chain between the two branch points), causing significant chain stretching. Our results extend the previous works of Karayiannis et al. [J. Chem. Phys. 2003, 118, 2451] on the simulation of H-shaped polymers to A3AA3 PE polymers and of Ramos et al. [Macromolecules 2007, 40, 9640] on the simulation of model ethylene−1-hexene copolymers to copolymers with longer α-olefinic side groups, such as the ethylene−1-octene and ethylene−1-decene ones.

Reliability analysis and optimization of weighted voting systems with continuous states input

Weighted voting systems are widely used in many practical fields such as target detection, human organization, pattern recognition, etc. In this paper, a new model for weighted voting systems with continuous state inputs is formulated. We derive the analytical expression for the reliability of the entire system under certain distribution assumptions. A more general Monte Carlo algorithm is also given to numerically analyze the model and evaluate the reliability. This paper further proposes a reliability optimization problem of weighted voting systems under cost constraints. A genetic algorithm is introduced and applied as the optimization technique for the model formulated. A numerical example is then presented to illustrate the ideas.

Determining the density of states for classical statistical models by a flat-histogram random walk

We describe an efficient and general Monte Carlo algorithm using a flat-histogram random walk to obtain a very accurate estimate of the density of states for classical statistical models. Using this method, we not only can avoid repeating simulations at multiple temperatures but can also estimate the free energy and entropy, quantities which are not directly accessible by conventional Monte Carlo simulations. We apply our algorithm to a spin system to show its accuracy. Since all possible points in the random walk space are visited with the same probability, this algorithm is especially useful for complex systems with rough landscapes such as spin glass models.

Molecular representation of complex hydrocarbon feedstocks through efficient characterization and stochastic algorithms

A stochastic method was devised to transform efficient sets of analytical characterizations into molecular representations of complex petroleum feedstocks. Important structural attributes of petroleum molecules (e.g. number of aromatic rings, number of naphthenic rings, number and length of aliphatic side chains) were assembled into molecules according to quantitative probability density functions for each attribute. The outcome was the atomic detail of a large ensemble of representative molecular structures from which both molecular and global product properties were deduced. Critical steps in the stochastic method were the generation of a chemical logic diagram, the compilation of cumulative probability functions for the structural attributes, stochastic sampling of each distribution, and the molecular construction. A general Monte Carlo algorithm provided an unbiased sampling of the probability density functions. The method was applied to three different complex petroleum feedstock fractions: an offshore California asphaltene, a Kern River heavy oil, and sour import heavy gas oil. The asphaltene example predicted the defining solubility protocol to within 1%. The heavy oil and gas oil simulations reproduced boiling point fractionation curves to within standard deviations of 20.8 and 25°C.

Molecular representation of complex hydrocarbon feedstocks through efficient characterization and stochastic algorithms

A stochastic method was devised to transform efficient sets of analytical characterizations into molecular representations of complex petroleum feedstocks. Important structural attributes of petroleum molecules (e.g. number of aromatic rings, number of naphthenic rings, number and length of aliphatic side chains) were assembled into molecules according to quantitative probability density functions for each attribute. The outcome was the atomic detail of a large ensemble of representative molecular structures from which both molecular and global product properties were deduced. Critical steps in the stochastic method were the generation of a chemical logic diagram, the compilation of cumulative probability functions for the structural attributes, stochastic sampling of each distribution, and the molecular construction. A general Monte Carlo algorithm provided an unbiased sampling of the probability density functions. The method was applied to three different complex petroleum feedstock fractions: an offshore California asphaltene, a Kern River heavy oil, and sour import heavy gas oil. The asphaltene example predicted the defining solubility protocol to within 1%. The heavy oil and gas oil simulations reproduced boiling point fractionation curves to within standard deviations of 20.8 and 25°C.

Simple models for evaluating the role of atomic processes in helium enrichment

An analytical solution to a one-dimensional linear kinetic transport equation (slab model) is obtained to investigate the influence of elastic collisions between neutral atoms and plasma ions on neutral gas transport under typical tokamak boundary conditions. By comparing solutions obtained for neutral helium and neutral hydrogen the possibility of local helium enrichment in divertors or pump limiters is investigated. By using a general Monte Carlo algorithm to solve the same kinetic equations, the analytical solutions are verified. Furthermore some of the simplifying approximations in the collision integral and in the boundary conditions, which were necessary to obtain closed form analytical solutions, are then removed in the Monte Carlo solution. This allows a critical assessment of such approximations.