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Identifier 000366978
Title Spatio-Temporal Acceleration of Kinetic Monte Carlo Methods
Alternative Title Χωροχρονική επιτάχυνση μεδόδων Kinetic Monte Carlo
Author Αραμπατζής, Γεωργιος Θεόδωρος
Thesis advisor Κατσουλάκης Μάρκος
Collaborator Μακριδάκης Χαράλαμπος
Κοσιώρης Γεώργιος
Abstract The main subject of this thesis is the study of molecular simulation accelerations methods of Kinetic Monte Carlo type in Material Science and Chemical Engineer¬ing problems. The main mathematical and algorithmic difficulty in these problems comes from the large number of particles as well as from the macroscopic times that must be simulated and in which interesting mesoscopic and microscopic phe¬nomena take part like nanoparticles concentration, pattern formation and interface metastability phenomena. In the first part of the thesis we study the temporal acceleration of Monte Carlo methods through the, lately proposed by Gillespie, τ-leap method. For the first time in the bibliography we studied this method in phase transition systems and we showed analytically and numerically in specific examples that this method is particularly sensitive in the selection of time window described by the τ parameter. In the second part a new method is developed for the parallelization of Kinetic Monte Carlo algorithms. The proposed method is based on the development of a hierarchical representation of the generator which allows a systematic and equal work load balance into independent processing units. The algorithm is implemented in statistical physics problems that have analytical solutions (e.g. Ising model in 1 and 2 dimensions) that allowed the rigorous certification of the algorithm. The acceleration compared with equivalent serial algorithms can reach in over four orders of magnitude, in implementations on graphics cards (GPU). Therefore we expect that this new method, called Fractional Step Kinetic Monte Carlo (FS-KMC), to give the opportunity, for the first time, of the simulation of molecular models in heterogeneous catalysis under realistic reactor dimensions of magnitude mm. The FS-KMC method also allows the parallel simulation of molecular systems with multiple microscopic mechanisms of multiple time scales e.g. molecular systems of diffusion/reaction.
Language English
Subject Ising
Kinetic Monte Carlo
Issue date 2011-07-15
Collection   School/Department--School of Sciences and Engineering--Department of Applied Mathematics--Post-graduate theses
  Type of Work--Post-graduate theses
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