Rings of single-walled carbon nanotubes: molecular-template directed assembly and Monte Carlo modeling

Rings of single-walled carbon nanotubes (SWNTs) were assembled by dip-pen nanolithography (DPN) generated molecular templates consisting of COOH-terminated monolayers in circular patterns surrounded by passivating CH3-terminated SAMs. Experimental data and atomic-level Monte Carlo simulations show that SWNTs assemble into rings with radii as small as 100 nm at the edge of the COOH templates. This directed assembly is strongly length-dependent; only when the length of a SWNT is longer than half of the circumference of the circle does the SWNT bend to precisely follow the interface of the COOH-terminated monolayer. The theoretical modeling shows that the strain energy of each SWNT is balanced by the energy difference between the van der Waals interactions of the tube with COOH and CH3 templates to produce the resulting ring structure.     

Lanczos and recursion techniques for multiscale kinetic Monte Carlo simulations

We review an approach to the simulation of the class of microstructural and morphological evolution involving both relatively short-ranged chemical and interfacial interactions and long-ranged elastic interactions. The calculation of the anharmonic elastic energy is facilitated with Lanczos recursion. The elastic energy changes affect the rate of vacancy hopping, and hence the rate of microstructural evolution due to vacancy-mediated diffusion. The elastically informed hopping rates are used to construct the event catalog for kinetic Monte Carlo simulation. The simulation is accelerated using a second-order residence time algorithm. The effect of elasticity on the microstructural development has been assessed. This article is related to a talk given in honor of David Pettifor at the DGP60 Workshop in Oxford.     

Monte Carlo simulation of the hysteresis phenomena on ferromagnetic nanotubes

In this work the hysteretic properties of single wall ferromagnetic nanotubes were studied. Hysteresis loops were computed on the basis of a classical Heisenberg model involving nearest neighbor interactions and using a Monte Carlo method implemented with a single spin movement Metropolis dynamics. Nanotubes with square and hexagonal unit cells were studied varying their diameter, temperature and magneto-crystalline anisotropy. Effects of the diameter were found stronger in the square unit cell magnetic nanotubes (SMNTs) than in the hexagonal unit cell magnetic nanotubes (HMNTs). The ferromagnetic behavior was observed in SMNTs at higher temperature than in HMNTs. Moreover in both cases, SMNTs and HMNTs, the magneto-crystalline anisotropy in the longitudinal direction showed a linear correspondence with the coercive field.     

A kinetic Monte Carlo study of mixed 1D/3D defect migration

Defect clusters form readily in collision cascades in metals, and some of the self-interstitial atom clusters form as crowdion clusters that diffuse by one-dimensional migration along a close-packed direction. Defect interactions and thermal fluctuations can cause the direction of one-dimensional migration to change, resulting in a mixed one-dimensional/ three-dimensional migration. Kinetic Monte Carlo computer simulations applied to model systems are used to investigate the effects of one-dimensional, three-dimensional and mixed one-dimensional/ three-dimensional migration on defect reaction kinetics. The functional relationships between the sink strength, the size of sinks and the average distance between direction changes during mixed one-dimensional/three-dimensional migration are explored. This revised version was published online in July 2006 with corrections to the Cover Date.     

A blend of first-principles and kinetic lattice Monte Carlo computation to optimize samarium-doped ceria

Solid oxide fuel cells (SOFCs) have been acknowledged as a possible future source for clean and efficient electric power generation. One of the most important goals in the SOFCs research is to decrease the operating temperature, which in turn will improve the stability and decrease the cost of various components enabling its widespread utilization. For realizing the aforementioned goal, it is imperative to identify suitable electrolyte materials that show enhanced conductivity in the intermediate temperature range (773–1,073 K). Sm-doped ceria (SDC) is considered a promising candidate for use as an electrolyte material for SOFC operation in intermediate temperature range due to the high oxygen ion conductivity. In this article, we present a theoretical investigation using first-principles and kinetic lattice Monte Carlo (KLMC) computations to highlight the trends in oxygen ion conductivity as a function of dopant content and temperature in SDC. Using first-principles calculations, oxygen vacancy formation and migration were examined at first, second, and third nearest neighbor positions to a Sm ion. The activation energies for oxygen vacancy migration along various pathways in SDC computed using first-principles were used as input to the KLMC model to study vacancy mediated diffusion. SDC with 20 % mole fraction of dopant content yields the maximum conductivity, which is in very good agreement with experimentally identified compositions. Rationale for increase in conductivity as a function of increase in dopant content and subsequent decrease in conductivity at higher dopant fractions in SDC is presented. This combined methodology of first-principles and KLMC computations is a useful tool for the design and identification of various ceria-based electrolyte materials used in SOFCs.     

A Monte Carlo program for quantitative electron-induced X-ray analysis of individual particles

A versatile Monte Carlo program for quantitative particle analysis in electron probe X-ray microanalysis is presented. The program includes routines for simulating electron-solid interactions in microparticles lying on a flat surface and calculating the generated X-ray signal. Simulation of the whole X-ray spectrum as well as phi(z) curves is possible. The most important facility of the program is the reverse Monte Carlo quantification of the chemical composition of microparticles, including low-Z elements, such as C, N, O, and F. This quantification method is based on the combination of a single scattering Monte Carlo simulation and a robust successive approximation. An iteration procedure is employed; in each iteration step, the Monte Carlo simulation program calculates characteristic X-ray intensities, and a new set of concentration values for chemical elements in the particle is determined. When the simulated X-ray intensities converge to the measured ones, the input values of elemental concentrations used for the simulation are determined as chemical compositions of the particle. This quantification procedure was evaluated by investigating various types of standard particles, and good accuracy of the methodology was demonstrated. A methodology for heterogeneity assessment of single particles is also described.     

An overview of spatial microscopic and accelerated kinetic Monte Carlo methods

The microscopic spatial kinetic Monte Carlo (KMC) method has been employed extensively in materials modeling. In this review paper, we focus on different traditional and multiscale KMC algorithms, challenges associated with their implementation, and methods developed to overcome these challenges. In the first part of the paper, we compare the implementation and computational cost of the null-event and rejection-free microscopic KMC algorithms. A firmer and more general foundation of the null-event KMC algorithm is presented. Statistical equivalence between the null-event and rejection-free KMC algorithms is also demonstrated. Implementation and efficiency of various search and update algorithms, which are at the heart of all spatial KMC simulations, are outlined and compared via numerical examples. In the second half of the paper, we review various spatial and temporal multiscale KMC methods, namely, the coarse-grained Monte Carlo (CGMC), the stochastic singular perturbation approximation, and the τ-leap methods, introduced recently to overcome the disparity of length and time scales and the one-at-a time execution of events. The concepts of the CGMC and the τ-leap methods, stochastic closures, multigrid methods, error associated with coarse-graining, a posteriori error estimates for generating spatially adaptive coarse-grained lattices, and computational speed-up upon coarse-graining are illustrated through simple examples from crystal growth, defect dynamics, adsorption–desorption, surface diffusion, and phase transitions.     

Curing behavior and kinetic analysis of epoxy resin/multi-walled carbon nanotubes composites

The effect of multi-walled carbon nanotubes (MWNTs), both amino-functionalized (f-MWNTs) and unfunctionalized (p-MWNTs) on the curing behavior of epoxy resin (EP) cured with triethanolamine (TEA), was investigated using differential scanning calorimetry (DSC). Because the triethylenetetramine (TETA) grafted on the f-MWNTs could act as curing agent and the produced tertiary amine as negative ionic catalysts of curing reaction of EP, so the activation energy of the EP/TEA system was decreased by the addition of f-MWNTs. Viscosity played a key role in the curing behavior of the EP/TEA/MWNTs system, for high viscosity of the EP/TEA/MWNTs system could hinder the motion of the functional groups. The curing heat in EP/TEA/f-MWNTs (weight ratio 1/0.1/0.01) system was higher than the neat EP/TEA (weight ratio 1/0.1) system, while the curing heat in EP/TEA/p-MWNTs (weight ratio 1/0.1/0.01) was lower than the neat system. When the content of f-MWNTs was increased to 2 phr (weight ratio of 1/0.1/0.02), the curing heat became lower than that of the neat EP/TEA system, which was the result of the higher viscosity of the EP/f-MWNTs/TEA system. Since the curing heat indicated the curing degree of the system generally, the addition of the f-MWNTs was thought to increase the curing degree of the epoxy matrix at a relatively low content.     

The structure and the percolation behavior of a mixture of carbon nanotubes and molecular junctions: a Monte Carlo simulation study

The structure and the percolation behavior of the composite of carbon nanotubes (CNTs), CNT molecular junctions and polymers are studied using Monte Carlo (MC) simulations. We model a CNT as a rigid rod composed of hard spheres. "X" and "Y" molecular junctions of CNTs are constructed by joining four and three segments of CNTs, respectively. The model system consists of CNTs mixed with either "X" or "Y" molecular junctions. The system is equilibrated using Monte Carlo simulations and the equilibrated configurations are used to locate the clusters of connected molecules via a recursive algorithm. The fraction (P(perc)) of configurations with a percolating cluster is then estimated for a given total volume fraction (phi(t)) of molecules. When P(perc) reaches 0.5, phi(t) of the system is considered a percolation threshold concentration (phi(c)). The percolation behavior is found to be sensitive to the aspect ratio of CNTs and the concentration and the shape of molecular junctions. phi(c) is decreased with an increase in the aspect ratio of CNTs. As the mole fraction of molecular junctions is increased, phi(c) is decreased significantly, which suggests that molecular junctions could enhance the electric conductivity of CNT-polymer composites. X junctions are found to construct a percolating network more effectively than Y junctions. More interestingly, even though molecular junctions change the percolation behavior significantly, the site-site pair correlation functions of CNTs hardly show any difference as the mole fraction of molecular junctions is increased. This implies that the percolation of CNTs is determined by the subtle many-body correlation of CNTs that is not captured by the site-site pair correlation functions.     

Cascade damage evolution: rate theory versus kinetic Monte Carlo simulations

The thermal evolution of defects produced by ion irradiation is studied by kinetic Monte Carlo and Rate Theory approaches. An isochronal annealing is simulated to evidence the different thermally activated mechanisms that govern defect evolution. KMC simulations show that in the case of ion irradiation, additional recovery peaks should be expected, in comparison to electron irradiation conditions. A comparison between kMC and RT results indicates that some of these peaks are due to spatially – correlated recombinations that occur at low temperature. Therefore kMC and RT approaches differ at low temperature. However, at higher temperature results obtained by both models are in near perfect agreement. In addition, we studied the influence of vacancy cluster mobility on the evolution of damage. KMC simulations show that the mobility of V₂, V₃ and V₄ clusters does not significantly affect the evolution of defects and can be neglected in these conditions.     

Calculations of diffusion in FCC binary alloys using on-the-fly kinetic Monte Carlo

We present a systematic, microscopic approach to diffusion for intermetallic alloys using accelerated molecular dynamics. On-the-fly kinetic Monte Carlo is combined with an efficient saddlepoint search to find the saddlepoints exiting a valley, based on energetics from the embedded atom method. With this technique, we compute the tracer diffusivities, migration energies, short-range order and long-range order as a function of composition and temperature for examples of moderately ordered (Cu₃Au), weakly ordered (Au–Ag) and weakly clustered (Cu–Ni) alloys. We find that away from any critical temperature, the calculations produce reliable results, but when critical behavior dominates the approach is overcome by critical fluctuations.     

A Monte Carlo code for nuclear astrophysics experiments

A Monte Carlo code, suited for nuclear astrophysics experiments, is described. The code has been developed in the frame of the LUNA pilot project at the Laboratori Nazionali del Gran Sasso. An accurate evaluation of ion energy and angular straggling, and Doppler broadening has been implemented, which are important at subCoulomb energies. The considered effects are compared with experimental data.     

A model of carbon ion interactions in water using the classical trajectory Monte Carlo method

In this paper, model calculations for interactions of C(6+) of energies from 1 keV u(-1) to 1 MeV u(-1) in water are presented. The calculations were carried out using the classical trajectory Monte Carlo method, taking into account the dynamic screening of the target core. The total cross sections (TCS) for electron capture and ionisation, and the singly and doubly differential cross sections (SDCS and DDCS) for ionisation were calculated for the five potential energy levels of the water molecule. The peaks in the DDCS for the electron capture to continuum and for the binary-encounter collision were obtained for 500-keV u(-1) carbon ions. The calculated SDCS agree reasonably well with the z(2) scaled proton data for 500 keV u(-1) and 1 MeV u(-1) projectiles, but a large deviation of up to 8-folds was observed for 100-keV u(-1) projectiles. The TCS for ionisation are in agreement with the values calculated from the first born approximation (FBA) at the highest energy region investigated, but become smaller than the values from the FBA at the lower-energy region.     

A Monte Carlo formulation of the Bogolubov theory

Abstract

We propose an efficient stochastic method to implement numerically the Bogolubov approach to study finite-temperature Bose-Einstein condensates. Our method is based on the Wigner representation of the density matrix describing the non-condensed modes and a Brownian motion simulation to sample the Wigner distribution at thermal equilibrium. Allowing it to sample any density operator Gaussian in the field variables, our method is very general and it applies both to the Bogolubov and to the Hartree-Fock Bogolubov approach, in the equilibrium case as well as in the time-dependent case. We think that our method can be useful to study trapped Bose-Einstein condensates in two or three spatial dimensions without rotational symmetry properties, as in the case of condensates with vortices, where the traditional Bogolubov approach is difficult to implement numerically due to the need to diagonalize very big matrices.     

Kinetic Monte Carlo模拟PVD薄膜生长的算法研究

提出kinetic Monte Carlo模拟物理气相沉积（physical vapor deposition,简写为PVD）薄膜生长的新算法：用红黑树搜索实现跃迁路径选择及系统跃迁概率更新,通过比较红黑树搜索、线性查找、满二元树搜索的计算效率,综合分析了这3种方法的时间复杂度和空间复杂度.结果表明红黑树搜索优于其它两种搜索方法,模拟效率最高,更适合用于执行大系统的kinetic Monte Carlo模拟.     

Coupling kinetic dislocation model and Monte Carlo algorithm for recrystallized microstructure modeling of severely deformed copper

By coupling a kinetic dislocation model and Monte Carlo algorithm, the recrystallized microstructure of severely deformed Oxygen Free High Conductivity Copper (OFHC) is predicted at different strains imposed by Equal-Channel-Angular-Pressing (ECAP) and annealing temperatures. From a flow field model, the strain rate distribution during the ECAP of the material in a curved die is calculated. Then using the kinetic dislocation model, the total dislocation density and correspondingly the stored energy after each ECAP pass is estimated. Utilizing the Monte Carlo algorithm and the stored energy, the recrystallized microstructure is predicted. The results show that the recrystallized grain size is decreased rapidly from the strain of first to fourth pass and then it is decreased slowly. Also, it is achieved that with increasing the annealing temperature, the grain size is increased. Moreover, a good agreement is observed between the predicted results and experimental data.     

Monte Carlo and variance reduction methods for structural reliability analysis: A comprehensive review

Monte Carlo methods have attracted constant and even increasing attention in structural reliability analysis with a wide variety of developments seamlessly presented over decades. Along the way, a number of specialized reviews and benchmark studies have been provided from time to time, aiming at summarizing and comparing selected few approaches in detail, mainly from an implementation point of view. In contrast, the aim of the present survey is to play a comprehensive role as a methodological guidebook on Monte Carlo simulation and its related, especially variance reduction, techniques through a covering of 444 references in the relevant literature. To achieve this goal, we present an extensive review of formulations and techniques along with insightful summaries of developments of existing numerical methods, ranging from the general formulation, sub-categories and variants, to their combined uses with other simulation techniques and surrogate models, as well as the key advantages and assumptions.     

A Monte Carlo simulation model for stationary non-Gaussian processes

A class of stationary non-Gaussian processes, referred to as the class of mixtures of translation processes, is defined by their finite dimensional distributions consisting of mixtures of finite dimensional distributions of translation processes. The class of mixtures of translation processes includes translation processes and is useful for both Monte Carlo simulation and analytical studies. As for translation processes, the mixture of translation processes can have a wide range of marginal distributions and correlation functions. Moreover, these processes can match a broader range of second order correlation functions than translation processes. The paper also develops an algorithm for generating samples of any non-Gaussian process in the class of mixtures of translation processes. The algorithm is based on the sampling representation theorem for stochastic processes and properties of the conditional distributions. Examples are presented to illustrate the proposed Monte Carlo algorithm and compare features of translation processes and mixture of translation processes.     

A novel Monte Carlo simulation method for Ising systems

We propose a Monte Carlo method to obtain the thermodynamic functions of Ising systems. We perform a random sampling of spin configurations to determine the degeneracy of the energies of the system, from which an approximant to the partition function is determined. The main advantage of the method over conventional Metropolis lies in the fact that only a single Monte Carlo run is needed to obtain results valid for all temperatures, magnetic fields, and coupling parameters (FM or AFM). As an illustration of the method, we present results for the Ising model in a magnetic field on a 8x8 lattice. The method can be adapted to tackle the random field Ising model (RFIM), the dilute Ising model, and the Ising spin glass, in any spatial dimension.     

A Monte Carlo solution of transport equations

A local method is developed for solving partial differential transport equations. The method is local in the sense that the value of the unknown solution of these equations can be calculated at arbitrary space and time coordinates directly rather than extracting its value from the field solution as done when using current numerical methods for solution. The proposed method is based on an analogy between the partial differential operator of transport equations and the infinitesimal generator of Itô processes, the Itô formula, the Dynkin formula, and Monte Carlo simulation. The method can be applied to solve transport problems with Dirichlet and Neumann boundary conditions. The solution of transport problems with Neumann boundary conditions is less simple because it requires the use of reflected Brownian motion and Itô processes.