Abhijit Chatterjee

Bio: Abhijit Chatterjee is an academic researcher from Indian Institute of Technology Bombay. The author has contributed to research in topics: Kinetic Monte Carlo & Monte Carlo method. The author has an hindex of 22, co-authored 72 publications receiving 1740 citations. Previous affiliations of Abhijit Chatterjee include University of Delaware & Indian Institute of Technology Delhi.

An overview of spatial microscopic and accelerated kinetic Monte Carlo methods

Abstract: 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.

Binomial distribution based τ-leap accelerated stochastic simulation

Abstract: Recently, Gillespie introduced the τ-leap approximate, accelerated stochastic Monte Carlo method for well-mixed reacting systems [J. Chem. Phys. 115, 1716 (2001)]. In each time increment of that method, one executes a number of reaction events, selected randomly from a Poisson distribution, to enable simulation of long times. Here we introduce a binomial distribution τ-leap algorithm (abbreviated as BD-τ method). This method combines the bounded nature of the binomial distribution variable with the limiting reactant and constrained firing concepts to avoid negative populations encountered in the original τ-leap method of Gillespie for large time increments, and thus conserve mass. Simulations using prototype reaction networks show that the BD-τ method is more accurate than the original method for comparable coarse-graining in time.

Accurate acceleration of kinetic Monte Carlo simulations through the modification of rate constants.

Abstract: We present a novel computational algorithm called the accelerated superbasin kinetic Monte Carlo (AS-KMC) method that enables a more efficient study of rare-event dynamics than the standard KMC method while maintaining control over the error. In AS-KMC, the rate constants for processes that are observed many times are lowered during the course of a simulation. As a result, rare processes are observed more frequently than in KMC and the time progresses faster. We first derive error estimates for AS-KMC when the rate constants are modified. These error estimates are next employed to develop a procedure for lowering process rates with control over the maximum error. Finally, numerical calculations are performed to demonstrate that the AS-KMC method captures the correct dynamics, while providing significant CPU savings over KMC in most cases. We show that the AS-KMC method can be employed with any KMC model, even when no time scale separation is present (although in such cases no computational speed-up is observed), without requiring the knowledge of various time scales present in the system.

Time accelerated Monte Carlo simulations of biological networks using the binomial τ-leap method

Abstract: Summary: Developing a quantitative understanding of intracellular networks requires simulations and computational analyses. However, traditional differential equation modeling tools are often inadequate due to the stochasticity of intracellular reaction networks that can potentially influence the phenotypic characteristics. Unfortunately, stochastic simulations are computationally too intense for most biological systems. Herein, we have utilized the recently developed binomial τ-leap method to carry out stochastic simulations of the epidermal growth factor receptor induced mitogen activated protein kinase cascade. Results indicate that the binomial τ-leap method is computationally 100--1000 times more efficient than the exact stochastic simulation algorithm of Gillespie. Furthermore, the binomial τ-leap method avoids negative populations and accurately captures the species populations along with their fluctuations despite the large difference in their size. Availability:http://www.dion.che.udel.edu/multiscale/Introduction.html. Fortran 90 code available for academic use by email. Contact: vlachos@che.udel.edu Supplementary information: Details about the binomial τ-leap algorithm, software and a manual are available at the above website.

Multiscale spatial Monte Carlo simulations: multigriding, computational singular perturbation, and hierarchical stochastic closures.

Abstract: Monte Carlo (MC) simulation of most spatially distributed systems is plagued by several problems, namely, execution of one process at a time, large separation of time scales of various processes, and large length scales. Recently, a coarse-grained Monte Carlo (CGMC) method was introduced that can capture large length scales at reasonable computational times. An inherent assumption in this CGMC method revolves around a mean-field closure invoked in each coarse cell that is inaccurate for short-ranged interactions. Two new approaches are explored to improve upon this closure. The first employs the local quasichemical approximation, which is applicable to first nearest-neighbor interactions. The second, termed multiscale CGMC method, employs singular perturbation ideas on multiple grids to capture the entire cluster probability distribution function via short microscopic MC simulations on small, fine-grid lattices by taking advantage of the time scale separation of multiple processes. Computational strategies for coupling the fast process at small length scales (fine grid) with the slow processes at large length scales (coarse grid) are discussed. Finally, the binomial τ-leap method is combined with the multiscale CGMC method to execute multiple processes over the entire lattice and provide additional computational acceleration. Numerical simulations demonstrate that in the presence of fast diffusion and slow adsorption and desorption processes the two new approaches provide more accurate solutions in comparison to the previously introduced CGMC method.

Fast parallel algorithms for short-range molecular dynamics

Abstract: Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Stochastic Simulation of Chemical Kinetics

Abstract: Stochastic chemical kinetics describes the time evolution of a wellstirred chemically reacting system in a way that takes into account the fact that molecules come in whole numbers and exhibit some degree of randomness in their dynamical behavior. Researchers are increasingly using this approach to chemical kinetics in the analysis of cellular systems in biology, where the small molecular populations of only a few reactant species can lead to deviations from the predictions of the deterministic differential equations of classical chemical kinetics. After reviewing the supporting theory of stochastic chemical kinetics, I discuss some recent advances in methods for using that theory to make numerical simulations. These include improvements to the exact stochastic simulation algorithm (SSA) and the approximate explicit tau-leaping procedure, as well as the development of two approximate strategies for simulating systems that are dynamically stiff: implicit tau-leaping and the slow-scale SSA.

Recent progress in resistive random access memories: Materials, switching mechanisms, and performance

Abstract: This review article attempts to provide a comprehensive review of the recent progress in the so-called resistive random access memories (RRAMs) First, a brief introduction is presented to describe the construction and development of RRAMs, their potential for broad applications in the fields of nonvolatile memory, unconventional computing and logic devices, and the focus of research concerning RRAMs over the past decade Second, both inorganic and organic materials used in RRAMs are summarized, and their respective advantages and shortcomings are discussed Third, the important switching mechanisms are discussed in depth and are classified into ion migration, charge trapping/de-trapping, thermochemical reaction, exclusive mechanisms in inorganics, and exclusive mechanisms in organics Fourth, attention is given to the application of RRAMs for data storage, including their current performance, methods for performance enhancement, sneak-path issue and possible solutions, and demonstrations of 2-D and 3-D crossbar arrays Fifth, prospective applications of RRAMs in unconventional computing, as well as logic devices and multi-functionalization of RRAMs, are comprehensively summarized and thoroughly discussed The present review article ends with a short discussion concerning the challenges and future prospects of the RRAMs

Efficient step size selection for the tau-leaping simulation method

Abstract: The tau-leaping method of simulating the stochastic time evolution of a well-stirred chemically reacting system uses a Poisson approximation to take time steps that leap over many reaction events. Theory implies that tau leaping should be accurate so long as no propensity function changes its value “significantly” during any time step τ. Presented here is an improved procedure for estimating the largest value for τ that is consistent with this condition. This new τ-selection procedure is more accurate, easier to code, and faster to execute than the currently used procedure. The speedup in execution will be especially pronounced in systems that have many reaction channels.

An overview of spatial microscopic and accelerated kinetic Monte Carlo methods

Abstract: 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.