Lattice Monte Carlo Simulations Research Articles

Lattice Monte Carlo Simulations in Search of Zeolite Analogues: Effects of Structure Directing Agents

We use parallel tempering Monte Carlo simulations to search for crystalline states of a lattice model of silica polymerization in the presence of structure directing agents (SDAs). Following previous work where we have discretized continuous space into a body-centered cubic (bcc) lattice, we have modeled tetrahedral molecules (T(OH)4) as corner-sharing tetrahedra on a bcc unit cell. The SDAs were represented as quasi-spherical species with diameters of 6.4 and 10.4 Å to study the effect of SDA size on the resulting crystal structures. Our parallel tempering Monte Carlo simulations produce fully connected crystalline structures finding the emergence of 3D microporous materials with SDAs occupying the pore spaces and 2D layered materials with SDAs occupying the gallery space in between layers. We have found that the strength of SDA–oxygen attraction plays a significant role in directing final micropore structures. For relatively strong attractions (>1.2 kcal/mol SDA–oxygen contacts) we have found only 2D layered materials; for attractions below this cutoff we observed 3D microporous crystals; and for no attraction—modeling the SDA as a quasi-hard sphere—we again found only 2D layered materials. In the space of 3D microporous crystals, we have also found that using larger SDAs or a lower concentration of a given SDA generate crystals with larger rings.

Benders Decomposition and Normal Boundary Intersection Method for Multiobjective Decision Making Framework for an Electricity Retailer in Energy Markets

In midterm planning, the objective of an electricity retailer is to manage a portfolio of different contracts and determine the selling price offered to its clients. Assuming that, within an electricity market framework, rival retailers compete for prices in order to achieve the largest possible number of clients. In addition, the reasonable criterion for the retailer is to select a solution that attains the minimum selling prices while satisfying the constraints. The proposed framework in this paper is modeled in the form of a multiobjective framework to simultaneously maximize retailers' profit and minimize selling prices to clients. The normal boundary intersection method is implemented to generate Pareto-optimal solutions. The best compromise solution is adopted using a fuzzy decision maker. Roulette wheel mechanism and lattice Monte Carlo simulation are employed for random scenario generation wherein the stochastic optimization problem is converted into its respective deterministic equivalents. Benders decomposition has been employed as a robust algorithm to reach the optimal solution. The efficiency of the presented method is verified by making a comparison of its performance with another multiobjective optimization method through a real case study to show its superiority.

Ab initio alpha-alpha scattering.

Processes such as the scattering of alpha particles ((4)He), the triple-alpha reaction, and alpha capture play a major role in stellar nucleosynthesis. In particular, alpha capture on carbon determines the ratio of carbon to oxygen during helium burning, and affects subsequent carbon, neon, oxygen, and silicon burning stages. It also substantially affects models of thermonuclear type Ia supernovae, owing to carbon detonation in accreting carbon-oxygen white-dwarf stars. In these reactions, the accurate calculation of the elastic scattering of alpha particles and alpha-like nuclei--nuclei with even and equal numbers of protons and neutrons--is important for understanding background and resonant scattering contributions. First-principles calculations of processes involving alpha particles and alpha-like nuclei have so far been impractical, owing to the exponential growth of the number of computational operations with the number of particles. Here we describe an ab initio calculation of alpha-alpha scattering that uses lattice Monte Carlo simulations. We use lattice effective field theory to describe the low-energy interactions of protons and neutrons, and apply a technique called the 'adiabatic projection method' to reduce the eight-body system to a two-cluster system. We take advantage of the computational efficiency and the more favourable scaling with system size of auxiliary-field Monte Carlo simulations to compute an ab initio effective Hamiltonian for the two clusters. We find promising agreement between lattice results and experimental phase shifts for s-wave and d-wave scattering. The approximately quadratic scaling of computational operations with particle number suggests that it should be possible to compute alpha scattering and capture on carbon and oxygen in the near future. The methods described here can be applied to ultracold atomic few-body systems as well as to hadronic systems using lattice quantum chromodynamics to describe the interactions of quarks and gluons.

Creation of chiral adsorbed structures using external inputs: results from lattice Monte Carlo simulations

Patterning of solid surfaces with organic molecules has been recognized as a promising method to create functional 2D matrices with tunable structure and properties. In this work we use the lattice Monte Carlo simulations to study chiral pattern formation in adsorbed systems comprising simple molecular building blocks differing in shape. To that end we consider five-membered rigid isomers whose composite segments can occupy vertices of a triangular lattice and interact with short-range (nearest neighbors) forces. Our main focus is on those molecules which are prochiral, that is they can adopt mirror-image planar configurations when adsorbed. Moreover, the effect of orientational in-plane confinement of the molecules, which reflects their coupling with an external directional field, on the structure formation and chiral resolution in 2D is explored. The obtained results demonstrate that the confinement imposed on the surface enantiomers can induce their resolution and formation of extended homochiral domains. However, it is also shown that for certain molecular shapes the confinement can produce mixed racemic crystals instead of the homochiral assemblies. The insights from our simulation studies can be helpful in preliminary screening of molecular libraries to select optimal building blocks able to self-assembly into chiral 2D patterns with predefined architecture.

Two-dimensional Ostwald ripening on a patterned support and in a mixed overlayer

The author presents lattice Monte Carlo simulations of Ostwald ripening of islands formed of monomers with attractive nearest-neighbor interaction in two situations. The first one implies that monomers of one kind are located on a heterogeneous support which itself includes embedded frozen patterns of the Ostwald type. This feature is demonstrated to be able to terminate the island ripening. In the second case, the support is considered to be uniform while the overlayer is assumed to contain monomers of two kinds. This complicating factor is found to nearly not modify the ripening kinetics or make it somewhat slower despite appreciable correlations in the arrangement of different monomers.

Molecular mechanisms for surfactant-aided oil removal from a solid surface

In this work, the detachment mechanism of oil molecules from the hydrophobic solid surface in the aqueous surfactant solution is studied with lattice Monte Carlo simulations. Three different mechanisms for oil removal, including oil carrying microemulsion model, oil film stripping model, and surfactant-aided diffusion model are identified. The molecular mechanisms that agree with experimental observations are found to be dependent sensitively on surfactant structure.

Uncertainty management in multiobjective hydro-thermal self-scheduling under emission considerations

In this paper, a stochastic multiobjective framework is proposed for a day-ahead short-term Hydro Thermal Self-Scheduling (HTSS) problem for joint energy and reserve markets. An efficient linear formulations are introduced in this paper to deal with the nonlinearity of original problem due to the dynamic ramp rate limits, prohibited operating zones, operating services of thermal plants, multi-head power discharge characteristics of hydro generating units and spillage of reservoirs. Besides, system uncertainties including the generating units’ contingencies and price uncertainty are explicitly considered in the stochastic market clearing scheme. For the stochastic modeling of probable multiobjective optimization scenarios, a lattice Monte Carlo simulation has been adopted to have a better coverage of the system uncertainty spectrum. Consequently, the resulting multiobjective optimization scenarios should concurrently optimize competing objective functions including GENeration COmpany's (GENCO's) profit maximization and thermal units’ emission minimization. Accordingly, the ɛ-constraint method is used to solve the multiobjective optimization problem and generate the Pareto set. Then, a fuzzy satisfying method is employed to choose the most preferred solution among all Pareto optimal solutions. The performance of the presented method is verified in different case studies. The results obtained from ɛ-constraint method is compared with those reported by weighted sum method, evolutionary programming-based interactive Fuzzy satisfying method, differential evolution, quantum-behaved particle swarm optimization and hybrid multi-objective cultural algorithm, verifying the superiority of the proposed approach.

Modeling of precipitation kinetics in multicomponent systems: Application to model superalloys

Abstract A new general model dealing with nucleation, growth and coarsening simultaneously has been developed for the simulation of precipitation in non-dilute multicomponent alloys. Nucleation is implemented using the Zeldovich theory that includes regression effects. Growth and coarsening are modeled using the recently developed growth law in multicomponent alloys that accounts for capillarity, mass balance at the interface matrix-precipitate and diffusion-flux couplings. Numerical results are confronted to atom probe tomography (APT) experiments on model NiCrAl superalloys and to rigid lattice kinetics Monte Carlo (LKMC) simulations and are found in very good agreement with both APT experiments and LKMC simulations. We emphasize this work on the evolution of phase concentrations. The temporal evolution of the mean precipitate composition is found to be non-monotonic during the phase transformation, and phase composition does not follow the tie line due to a complex interplay between capillarity and diffusion process. The widespread availability of both thermodynamic and mobility databases makes this new model very suitable for material design.

Method for the analysis of contribution of sliding and hopping to a facilitated diffusion of DNA-binding protein: Application to in vivo data.

DNA-binding protein searches for its target, a specific site on DNA, by means of diffusion. The search process consists of many recurrent steps of one-dimensional diffusion (sliding) along the DNA chain and three-dimensional diffusion (hopping) after dissociation of a protein from the DNA chain. Here we propose a computational method that allows extracting the contribution of sliding and hopping to the search process in vivo from the measurements of the kinetics of the target search by the lac repressor in Escherichia coli [P. Hammar et al., Science 336, 1595 (2012)]. The method combines lattice Monte Carlo simulations with the Brownian excursion theory and includes explicitly steric constraints for hopping due to the helical structure of DNA. The simulation results including all experimental data reveal that the in vivo target search is dominated by sliding. The short-range hopping to the same base pair interrupts one-dimensional sliding while long-range hopping does not contribute significantly to the kinetics of the search of the target in vivo.

Kinetic Monte Carlo simulations of vacancy evolution in graphene

Kinetic lattice Monte Carlo simulations, implementing ab initio calibrated energetics, are applied to study the evolution of vacancy systems in graphene. The evolution of the under-coordinated atomic layer proceeds, in general, by island nucleation and growth. However, the first stage (nucleation) is strongly influenced by the stability of small aggregates (e.g. di-vacancies) and by the effective coalescence/attachment barriers. Quantitative predictions of the system kinetics in terms of crystal state and defects' morphology as a function of the initial state and the temperature can be obtained and readily compared with experimental structural characterization of processed samples.

Energy–momentum tensor from the Yang–Mills gradient flow

The product of gauge fields generated by the Yang-Mills gradient flow for positive flow times does not exhibit the coincidence-point singularity and a local product is thus independent of the regularization. Such a local product can furthermore be expanded by renormalized local operators at zero flow time with finite coefficients that are governed by renormalization group equations. Using these facts, we derive a formula that relates the small flow-time behavior of certain gauge-invariant local products and the correctly-normalized conserved energy-momentum tensor in the Yang-Mills theory. Our formula provides a possible method to compute the correlation functions of a well-defined energy-momentum tensor by using lattice regularization and Monte Carlo simulation.

Structure and dynamics of confined polymer melts from attractive interaction to repulsive interaction between polymer and smooth wall

We studied the static and dynamic properties of unentangled polymer chains which have a variable strength of interaction with the confining smooth walls by means of the lattice Monte Carlo simulation based on the bond-fluctuation model, that is, investigated the wall-polymer interactions which systematically vary from attraction to repulsion. A critical value of attractive potential(ewc) is found to be–0.6kBT, and only below it can the adsorption layer of monomers be formed near the wall. At the critical point of attraction ewc, attractive interaction counterbalances the wall-polymer excluded volume effect, which minimizes the confinement effects on both chain dimension and mobility. Influences on both chain dimension and mobility increase with the increasing of either attraction or repulsion imposed by the walls. Despite of the nature and strength of the wall-polymer interaction, with the decrease of film thickness, configurations more parallelly aligned and flattened are adopted by confined chains, and a systematic trend of deceleration is found. Variations of chain dynamics with both film thickness and wall-polymer interaction can be well explained by the corresponding changes in the confinement of the nearest-neighboring particles that surround the chains. Besides, the thickness of the interfacial layer inside polymer films, where chains adopt a flattened “pancake” shape, is about two times the bulk radius of gyration and independent of the wall-polymer interaction.

A Monte Carlo study on LCCC characterization of graft copolymers at the critical condition of side chains

Liquid chromatography at the critical condition (LCCC) has been used to characterize graft copolymers based on the assumption that one of the copolymer blocks becomes chromatographically “invisible” at the critical condition of the corresponding homopolymer. We investigate the validity of this assumption with lattice Monte Carlo simulations of A-g-B graft copolymers modeled as either random walk (RW) or self-avoiding walk (SAW) chains composed of multiple invisible B blocks grafted to an A backbone that is either in size-exclusion chromatography (SEC) or liquid adsorption chromatography (LAC) mode. The simulations show that, in agreement with recent experimental results, the B blocks have a small, but noticeable, impact on the overall elution of the graft copolymer. This influence exists even when the chains are modeled as RWs, indicating that its fundamental origin is due to chain connectivity, not excluded volume interactions. In general, both models show that grafting B blocks to an A backbone in SEC mode tends to increase copolymer retention, while grafting B blocks to an A backbone in LAC mode tends to decrease copolymer retention. When the copolymer is modeled as a SAW, the excluded volume interaction increases the entropic penalty associated with the addition of a B block and, therefore, the addition of B blocks in SAW chains is more likely to result in a decrease in the retention time of the copolymer when the A backbone is in LAC mode.

Double-winding Wilson loops and monopole confinement mechanisms

We consider ``double-winding'' Wilson loops in SU(2) gauge theory. These are contours which wind once around a loop ${C}_{1}$ and once around a loop ${C}_{2}$, where the two co-planar loops share one point in common, and where ${C}_{1}$ lies entirely in (or is displaced slightly from) the minimal area of ${C}_{2}$. We discuss the expectation value of such double-winding loops in Abelian confinement pictures, where the spatial distribution of confining Abelian fields is controlled by either a monopole Coulomb gas, a caloron ensemble, or a dual Abelian Higgs model, and argue that in such models an exponential falloff in the sum of areas ${A}_{1}+{A}_{2}$ is expected. In contrast, in a center vortex model of confinement, the behavior is an exponential falloff in the difference of areas ${A}_{2}\ensuremath{-}{A}_{1}$. We compute such double-winding loops by lattice Monte Carlo simulation, and find that the area law falloff follows a difference-in-areas law. The conclusion is that even if confining gluonic field fluctuations are, in some gauge, mainly Abelian in character, the spatial distribution of those Abelian fields cannot be the distribution predicted by the simple monopole gas, caloron ensemble, or dual Abelian Higgs actions, which have been used in the past to explain the area law falloff of Wilson loops.

Enhancing Corrected Transient Energy Margin in Electricity Energy Market Operation Using Stochastic Multiobjective Mathematical Programming

In this paper, a new stochastic multiobjective model for the market clearing of the joint energy and reserve auctions is proposed wherein both supply and demand sides can participate as reserves. The proposed framework considers the dynamic security aspect of the power system in the scenario-based market operation. To solve the problem, first, on the basis of lattice Monte Carlo simulation, different scenarios are generated to model the uncertainties of power system (including generating units and transmission line contingencies). Then, the competing objective functions of the proposed framework, including the expected social welfare function and expected corrected transient energy margin (CTEM), are simultaneously optimized for each scenario in the multiobjective framework. To calculate the CTEM, a sensitivity analysis based on the ac power flow formulation is incorporated before solving the optimization problem of the market clearing. The optimization problem is solved considering dc power flow constraints and system reserve requirements. Eventually, the scenarios are aggregated based on the expected value of decision variables to produce the final results of the market clearing framework. The model is applied to the New England test system, and simulation studies are implemented to demonstrate the effectiveness of the proposed method.

Lattice Monte Carlo simulation of single coal char particle combustion under oxy–fuel conditions

A descriptive model for isolated char particle combustion under conventional and oxy–fuel conditions was developed. Suggested model is based on the percolation theory and Monte Carlo simulation technique. Char particle was modeled as a square lattice consisting of a large number of small sites. Sites correspond either to fixed carbon, ash, or pore, and they were distributed randomly inside char lattice using percolation concept, at the start of simulation. Random walk model was used to represent gaseous species diffusion through particle pores. Char combustion was modeled using power law Arrhenius model which assumes that reaction rate depends of particle temperature and oxygen partial pressure on particle surface. The main aim of the proposed model was to take into account influence of heterogeneous char particle structure to randomness of the char combustion process. The suggested model’s behavior was validated by qualitative comparison with experimental data obtained in single particle reactor. It was found that simulated combustion time, char burnout and particle temperature values are in good agreement with experimentally determined data. Special emphasis was given to the CO2 gasification reaction influence on char conversion and particle temperature values. Further development of the proposed model with appropriate simplifications would enable its inclusion in comprehensive CFD codes.

Lattice Monte Carlo simulation of Galilei variant anomalous diffusion

The observation of an increasing number of anomalous diffusion phenomena motivates the study to reveal the actual reason for such stochastic processes. When it is difficult to get analytical solutions or necessary to track the trajectory of particles, lattice Monte Carlo (LMC) simulation has been shown to be particularly useful. To develop such an LMC simulation algorithm for the Galilei variant anomalous diffusion, we derive explicit solutions for the conditional and unconditional first passage time (FPT) distributions with double absorbing barriers. According to the theory of random walks on lattices and the FPT distributions, we propose an LMC simulation algorithm and prove that such LMC simulation can reproduce both the mean and the mean square displacement exactly in the long-time limit. However, the error introduced in the second moment of the displacement diverges according to a power law as the simulation time progresses. We give an explicit criterion for choosing a small enough lattice step to limit the error within the specified tolerance. We further validate the LMC simulation algorithm and confirm the theoretical error analysis through numerical simulations. The numerical results agree with our theoretical predictions very well.

Molecular organization of nematic liquid crystals between concentric cylinders: role of the elastic anisotropy.

The orientational order in a nematic liquid crystal sample confined to an annular region between two concentric cylinders is investigated by means of lattice Monte Carlo simulations. Strong anchoring and homeotropic orientations, parallel to the radial direction, are implemented at the confining surfaces. The elastic anisotropy is taken into account in the bulk interactions by using the pair potential introduced by Gruhn and Hess [T. Gruhn and S. Hess, Z. Naturforsch. A 51, 1 (1996)] and parametrized by Romano and Luckhurst [S. Romano, Int. J. Mod. Phys. B 12, 2305 (1998); Phys. Lett. A 302, 203 (2002); G. R. Luckhurst and S. Romano, Liq. Cryst. 26, 871 (1999)], i.e., the so-called GHRL potential. In the case of equal elastic constants, a small but appreciable deformation along the cylinder axis direction is observed, whereas when the values of K(11)/K(33) if K(22)=K(33) are low enough, all the spins in the bulk follow the orientation imposed by the surfaces. For larger values of K(11)/K(33), spontaneous deformations, perpendicular to the polar plane, increase significantly. Our findings indicate that the onset of these deformations also depends on the ratio K(22)/K(33) and on the radius of the cylindrical surfaces. Although expected from the elastic theory, no tangential component of the deformations was observed in the simulations for the set of parameters analyzed.

Multi-objective decision-making framework for an electricity retailer in energy markets using lexicographic optimization and augmented epsilon-constraint

SUMMARY The objective of the retailer in medium-term planning is managing the portfolio of contracts from different sources as well as determining the optimal selling price offered to its customers. When supplying the electricity sold to the costumers, two main challenges are faced by retailers. The first problem occurs during the electricity procurement procedure. In this stage, the retailer must deal with the uncertainty due to the pool price that propels the retailers to move towards agreeing to forward contracts signed at higher average prices. Besides, when the retailer decides on selling the electricity, another problem is to face the uncertainty caused by the demand while taking into consideration the possibility of reducing its clients in the case of high selling price. In this regard, this paper proposes a stochastic multi-objective framework for the retailer with profit maximization and risk minimization as two objective functions. The risk, due to the market price uncertainty, is modeled, employing the expected downside risk. The problem is formulated as mixed-integer programming while the stochastic optimization problem is characterized using the roulette wheel mechanism and lattice Monte Carlo simulation. Furthermore, lexicographic optimization and augmented epsilon-constraint method are used to solve the proposed multi-objective problem, and the best compromise solution is determined employing a fuzzy satisfying method. The presented model has been implemented using a realistic case study to verify the effectiveness of the method used in this paper. Copyright © 2015 John Wiley & Sons, Ltd.

Non-empirical phase equilibria in the Cr–Mo system: A combination of first-principles calculations, cluster expansion and Monte Carlo simulations

In this work, the low temperature part of the Cr–Mo phase diagram is calculated by a combination of first-principles calculations, cluster expansion, and Monte Carlo simulations without the use of empirical parameters. In brief, the miscibility gap in the bcc phase is computed through lattice Monte Carlo simulations with the energetics of the Cr–Mo system represented by cluster expansion Hamiltonians, wherein the Hamiltonians are firstly constructed using first-principles calculations of formation energies for supercells of various bulk compositions. It is demonstrated that the onset (critical) temperature of the miscibility gap is preliminarily computed to be Tc = 1720 K, and is significantly decreased to 1150 K once excess vibrational contribution to the free energy is considered. The resulting solid-state miscibility gap of the Cr–Mo binary system, largely improved by the contributions of atomic relaxation and positive excess volume of mixing in the Cr–Mo bcc alloys, also favors the approaches that extrapolate the Gibbs energy of the bcc phase retrieved at high temperatures, as in the CALPHAD method.