Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms

We present a mathematical framework for constructing and analyzing parallel algorithms for lattice Kinetic Monte Carlo (KMC) simulations. The resulting algorithms have the capacity to simulate a wide range of spatio-temporal scales in spatially distributed, non-equilibrium physiochemical processes with complex chemistry and transport micro-mechanisms. The algorithms can be tailored to specific hierarchical parallel architectures such as multi-core processors or clusters of Graphical Processing Units (GPUs). The proposed parallel algorithms are controlled-error approximations of kinetic Monte Carlo algorithms, departing from the predominant paradigm of creating parallel KMC algorithms with exactly the same master equation as the serial one. Our methodology relies on a spatial decomposition of the Markov operator underlying the KMC algorithm into a hierarchy of operators corresponding to the processors' structure in the parallel architecture. Based on this operator decomposition, we formulate Fractional Step Approximation schemes by employing the Trotter Theorem and its random variants; these schemes, (a) determine the communication schedule} between processors, and (b) are run independently on each processor through a serial KMC simulation, called a kernel, on each fractional step time-window. Furthermore, the proposed mathematical framework allows us to rigorously justify the numerical and statistical consistency of the proposed algorithms, showing the convergence of our approximating schemes to the original serial KMC. The approach also provides a systematic evaluation of different processor communicating schedules.Comment: 34 pages, 9 figure

The Astrophysical Multipurpose Software Environment

We present the open source Astrophysical Multi-purpose Software Environment (AMUSE, www.amusecode.org), a component library for performing astrophysical simulations involving different physical domains and scales. It couples existing codes within a Python framework based on a communication layer using MPI. The interfaces are standardized for each domain and their implementation based on MPI guarantees that the whole framework is well-suited for distributed computation. It includes facilities for unit handling and data storage. Currently it includes codes for gravitational dynamics, stellar evolution, hydrodynamics and radiative transfer. Within each domain the interfaces to the codes are as similar as possible. We describe the design and implementation of AMUSE, as well as the main components and community codes currently supported and we discuss the code interactions facilitated by the framework. Additionally, we demonstrate how AMUSE can be used to resolve complex astrophysical problems by presenting example applications.Comment: 23 pages, 25 figures, accepted for A&

New models for PIXE simulation with Geant4

Particle induced X-ray emission (PIXE) is a physical effect that is not yet adequately modelled in Geant4. The current status as in Geant4 9.2 release is reviewed and new developments are described. The capabilities of the software prototype are illustrated in application to the shielding of the X-ray detectors of the eROSITA telescope on the upcoming Spectrum-X-Gamma space mission.Comment: To be published in the Proceedings of the CHEP (Computing in High Energy Physics) 2009 conferenc

The Role of the Collisional Broadening of the States on the Low-Field Mobility in Silicon Inversion Layers

abstract: Scaling of the Metal-Oxide-Semiconductor Field Effect Transistor (MOSFET) towards shorter channel lengths, has lead to an increasing importance of quantum effects on the device performance. Until now, a semi-classical model based on Monte Carlo method for instance, has been sufficient to address these issues in silicon, and arrive at a reasonably good fit to experimental mobility data. But as the semiconductor world moves towards 10nm technology, many of the basic assumptions in this method, namely the very fundamental Fermi’s golden rule come into question. The derivation of the Fermi’s golden rule assumes that the scattering is infrequent (therefore the long time limit) and the collision duration time is zero. This thesis overcomes some of the limitations of the above approach by successfully developing a quantum mechanical simulator that can model the low-field inversion layer mobility in silicon MOS capacitors and other inversion layers as well. It solves for the scattering induced collisional broadening of the states by accounting for the various scattering mechanisms present in silicon through the non-equilibrium based near-equilibrium Green’s Functions approach, which shall be referred to as near-equilibrium Green’s Function (nEGF) in this work. It adopts a two-loop approach, where the outer loop solves for the self-consistency between the potential and the subband sheet charge density by solving the Poisson and the Schrödinger equations self-consistently. The inner loop solves for the nEGF (renormalization of the spectrum and the broadening of the states), self-consistently using the self-consistent Born approximation, which is then used to compute the mobility using the Green-Kubo Formalism.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201