Billion-atom Synchronous Parallel Kinetic Monte Carlo Simulations of Critical 3D Ising Systems

An extension of the synchronous parallel kinetic Monte Carlo (pkMC) algorithm developed by Martinez {\it et al} [{\it J.\ Comp.\ Phys.} {\bf 227} (2008) 3804] to discrete lattices is presented. The method solves the master equation synchronously by recourse to null events that keep all processors time clocks current in a global sense. Boundary conflicts are rigorously solved by adopting a chessboard decomposition into non-interacting sublattices. We find that the bias introduced by the spatial correlations attendant to the sublattice decomposition is within the standard deviation of the serial method, which confirms the statistical validity of the method. We have assessed the parallel efficiency of the method and find that our algorithm scales consistently with problem size and sublattice partition. We apply the method to the calculation of scale-dependent critical exponents in billion-atom 3D Ising systems, with very good agreement with state-of-the-art multispin simulations

A rigorous sequential update strategy for parallel kinetic Monte Carlo simulation

The kinetic Monte Carlo (kMC) method is used in many scientific fields in applications involving rare-event transitions. Due to its discrete stochastic nature, efforts to parallelize kMC approaches often produce unbalanced time evolutions requiring complex implementations to ensure correct statistics. In the context of parallel kMC, the sequential update technique has shown promise by generating high quality distributions with high relative efficiencies for short-range systems. In this work, we provide an extension of the sequential update method in a parallel context that rigorously obeys detailed balance, which guarantees exact equilibrium statistics for all parallelization settings. Our approach also preserves nonequilibrium dynamics with minimal error for many parallelization settings, and can be used to achieve highly precise sampling

Synchronous parallel kinetic Monte Carlo simulation of AL3SC precipitation

The main objective of the present work is to profound the applicability of a synchronous parallel kinetic Monte Carlo (spkMC) algorithm for simulating the nucleation of Al3Sc precipitates. Parallel processes communication is implemented through Message Passing Interface (MPI). Consequently, the capability of extending time and length scales of atomistic kinetic Monte Carlo (kMC) will be attested. Lastly, we present the results obtained from simulations of nucleation of Al3Sc precipitates, which include a comparative view between sequential and parallel algorithms

Parallelization of kinetic Monte Carlo algorithm to simulate AL3Sc precipitation

The present paper reports the precipitation process of Al3Sc structures in an aluminum scandium alloy, which has been simulated with a synchronous parallel kinetic Monte Carlo (spkMC) algorithm. The spkMC implementation is based on the vacancy diffusion mechanism. To filter the raw data generated by the spkMC simulations, the density-based clustering with noise (DBSCAN) method has been employed. spkMC and DBSCAN algorithms were implemented in the C language and using MPI library. The simulations were conducted in the SeARCH cluster located at the University of Minho. The Al3Sc precipitation was successfully simulated at the atomistic scale with the spkMC. DBSCAN proved to be a valuable aid to identify the precipitates by performing a cluster analysis of the simulation results. The achieved simulations results are in good agreement with those reported in the literature under sequential kinetic Monte Carlo simulations (kMC). The parallel implementation of kMC has provided a 4x speedup over the sequential version

Kinetic modelling of heterogeneous catalytic systems

The importance of heterogeneous catalysis in modern life is evidenced by the fact that numerous products and technologies routinely used nowadays involve catalysts in their synthesis or function. The discovery of catalytic materials is, however, a non-trivial procedure, requiring tedious trial-and-error experimentation. First-principles-based kinetic modelling methods have recently emerged as a promising way to understand catalytic function and aid in materials discovery. In particular, kinetic Monte Carlo (KMC) simulation is increasingly becoming more popular, as it can integrate several sources of complexity encountered in catalytic systems, and has already been used to successfully unravel the underlying physics of several systems of interest. After a short discussion of the different scales involved in catalysis, we summarize the theory behind KMC simulation, and present the latest KMC computational implementations in the field. Early achievements that transformed the way we think about catalysts are subsequently reviewed in connection to latest studies of realistic systems, in an attempt to highlight how the field has evolved over the last few decades. Present challenges and future directions and opportunities in computational catalysis are finally discussed

Massively parallel kinetic Monte Carlo simulations of charge carrier transport in organic semiconductors

AbstractA parallel, lattice based Kinetic Monte Carlo simulation is developed that runs on a GPGPU board and includes Coulomb like particle–particle interactions. The performance of this computationally expensive problem is improved by modifying the interaction potential due to nearby particle moves, instead of fully recalculating it. This modification is achieved by adding dipole correction terms that represent the particle move. Exact evaluation of these terms is guaranteed by representing all interactions as 32-bit floating numbers, where only the integers between −222 and 222 are used. We validate our method by modelling the charge transport in disordered organic semiconductors, including Coulomb interactions between charges. Performance is mainly governed by the particle density in the simulation volume, and improves for increasing densities. Our method allows calculations on large volumes including particle–particle interactions, which is important in the field of organic semiconductors

Computationally-efficient stochastic cluster dynamics method for modeling damage accumulation in irradiated materials

An improved version of a recently developed stochastic cluster dynamics (SCD) method {[}Marian, J. and Bulatov, V. V., {\it J. Nucl. Mater.} \textbf{415} (2014) 84-95{]} is introduced as an alternative to rate theory (RT) methods for solving coupled ordinary differential equation (ODE) systems for irradiation damage simulations. SCD circumvents by design the curse of dimensionality of the variable space that renders traditional ODE-based RT approaches inefficient when handling complex defect population comprised of multiple (more than two) defect species. Several improvements introduced here enable efficient and accurate simulations of irradiated materials up to realistic (high) damage doses characteristic of next-generation nuclear systems. The first improvement is a procedure for efficiently updating the defect reaction-network and event selection in the context of a dynamically expanding reaction-network. Next is a novel implementation of the $\tau$-leaping method that speeds up SCD simulations by advancing the state of the reaction network in large time increments when appropriate. Lastly, a volume rescaling procedure is introduced to control the computational complexity of the expanding reaction-network through occasional reductions of the defect population while maintaining accurate statistics. The enhanced SCD method is then applied to model defect cluster accumulation in iron thin films subjected to triple ion-beam ($\text{Fe}^{3+}$, $\text{He}^{+}$ and $$\text{H\ensuremath{{}^{+}}}$$) irradiations, for which standard RT or spatially-resolved kinetic Monte Carlo simulations are prohibitively expensive

Coupling the time-warp algorithm with the graph-theoretical kinetic Monte Carlo framework for distributed simulations of heterogeneous catalysts

Despite the successful and ever widening adoption of kinetic Monte Carlo (KMC) simulations in the area of surface science and heterogeneous catalysis, the accessible length scales are still limited by the inherently sequential nature of the KMC framework. Simulating long-range surface phenomena, such as catalytic reconstruction and pattern formation, requires consideration of large surfaces/lattices, at the μm scale and beyond. However, handling such lattices with the sequential KMC framework is extremely challenging due to the heavy memory footprint and computational demand. The Time-Warp algorithm proposed by Jefferson [ACM. Trans. Program. Lang. Syst., 1985. 7: 404-425] offers a way to enable distributed parallelization of discrete event simulations. Thus, to enable high-fidelity simulations of challenging systems in heterogeneous catalysis, we have coupled the Time-Warp algorithm with the Graph-Theoretical KMC framework [J. Chem. Phys., 134(21): 214115; J. Chem. Phys., 139(22): 224706] and implemented the approach in the general-purpose KMC code Zacros. We have further developed a “parallel-emulation” serial algorithm, which produces identical results to those obtained from the distributed runs (with the Time-Warp algorithm) thereby validating the correctness of our implementation. These advancements make Zacros the first-of-its-kind general-purpose KMC code with distributed computing capabilities, thereby opening up opportunities for detailed meso-scale studies of heterogeneous catalysts and closer-than-ever comparisons of theory with experiments

Development of a parallel multiscale 3D model for thrombus growth under flow

Thrombus growth is a complex and multiscale process involving interactions spanning length scales from individual micron-sized platelets to macroscopic clots at the millimeter scale. Here, we describe a 3D multiscale framework to simulate thrombus growth under flow comprising four individually parallelized and coupled modules: a data-driven Neural Network (NN) that accounts for platelet calcium signaling, a Lattice Kinetic Monte Carlo (LKMC) simulation for tracking platelet positions, a Finite Volume Method (FVM) simulator for solving convection-diffusion-reaction equations describing agonist release and transport, and a Lattice Boltzmann (LB) flow solver for computing the blood flow field over the growing thrombus. Parallelization was achieved by developing in-house parallel routines for NN and LKMC, while the open-source libraries OpenFOAM and Palabos were used for FVM and LB, respectively. Importantly, the parallel LKMC solver utilizes particle-based parallel decomposition allowing efficient use of cores over highly heterogeneous regions of the domain. The parallelized model was validated against a reference serial version for accuracy, demonstrating comparable results for both microfluidic and stenotic arterial clotting conditions. Moreover, the parallelized framework was shown to scale essentially linearly on up to 64 cores. Overall, the parallelized multiscale framework described here is demonstrated to be a promising approach for studying single-platelet resolved thrombosis at length scales that are sufficiently large to directly simulate coronary blood vessels

Kinetics of deposition and post evolution relaxation in thin-films

Tese de doutoramento em Ciências (ramo de conhecimento em Física)This thesis is devoted to the use of statistical physics concepts to study the growth of lms, under nonequilibrium conditions. Speci cally, we consider the in uence of the particle/ particle and particle/substrate interacting rules on the morphology of the obtained lm. We report how interesting structures can emerge from interacting rules as simple as the ones from the random sequential adsorption process. In the presence of a patterned substrate, made up of well de ned regions (cells) where particles can irreversibly stick, a rich set of morphologies are obtained at the jammed state. Such structures reveal, not only the order of the pattern, but also the stochastic nature of the adsorption process and the competition during adsorption. Besides, we show that such pattern changes also the kinetics toward the asymptotic limit and report, for the rst time, a transition from power law to exponential, in the functional dependence of the coverage approach to the jamming value. The competitive adsorption of segments with di erent sizes on a line is also considered. The in uence of the size ratio on the jammed state structure is analyzed with the cumulants of the distance between segments, up-to the fourth order. Yet, a probability distribution function of distances is proposed, based on heuristic arguments. The obtained results with the proposed function are in agreement with the ones from simulation. For the growth regime where di usion of particles on the substrate cannot be neglected, the in uence of the ux of impinging particles on the nucleation and growth of islands is studied. A model based on the kinetic Monte Carlo method is then proposed to study the homoepitaxial growth of Ag/Ag(100). Based on symmetry considerations, for both the substrate geometry and the interaction potential, the list of possible processes is reduced from 1024 to 241 elements. The model is able to reproduce previously reported results as well as gain new insights into the nucleation process, specially, for cases where the shape of the island and its local environment, play an important role on the overall kinetics.Nesta tese, aplicam-se conceitos de física estatística ao estudo de crescimento de filmes em condições de não equilíbrio. Considera-se o efeito da interacção partícula/partícula e partícula/substrato na morfologia do filme. Através de simulações de Monte Carlo, mostra-se que estruturas interessantes podem emergir de processos tão simples como a deposição sequencial aleatória. Uma grande variedade de estruturas pode ser obtida na presença de um padrão, constituído por regiões bem definidas (células) onde as partículas podem adsorver irreversivelmente. Estas estruturas devem-se ao efeito conjugado das restrições introduzidas pelo padrão e do efeito cooperativo entre as partículas durante a adsorção. Mostra-se ainda que, na presença do padrão, há uma transição de lei de potência para exponencial, na dependência funcional da aproximação da cobertura ao estado limite. É também estudada a adsorção competitiva de segmentos de dois tamanhos diferentes, numa linha. A influência da relação de tamanhos na estrutura final é caracterizada com base nos momentos (de elevada ordem) da distância entre segmentos. Propõe-se uma função de densidade de probabilidade para as distâncias, estando os resultados obtidos com essa função em concordância com os obtidos computacionalmente. Finalmente, estuda-se a deposição e a relaxação de átomos numa superfície cristalina, desenvolvendo-se um modelo com base no método de Monte Carlo cinético, para estudar o crescimento de Ag/Ag(100). Com considerações de simetria baseadas no substrato e no potencial de interacção, a lista de possíveis processos é reduzida de 1024 para 241 elementos. O modelo considerado é capaz de reproduzir resultados anteriores, bem como permitir obter mais informação sobre o processo de nucleação, em especial nas situações em que tanto a forma da ilha como o meio em que se encontra desempenham um papel fundamental na cinética do sistema