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You searched for +publisher:"Brown University" +contributor:("Pego, Robert"). One record found.

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1. Klobusicky, Joe J. Kinetic Limits of Piecewise Deterministic Markov Processes and Grain Boundary Coarsening.

Degree: PhD, Applied Mathematics, 2014, Brown University

The subject of this thesis is the development of a stochastic process that can be interpreted as a model of grain coarsening, a central problem in material science. Namely, our objective is the creation of piecewise-deterministic Markov processes (PDMPs) on particles whose empirical densities converge to solutions of kinetic equations. We begin with a study of a simplified model, where particles drift toward the origin on ℝ+. When particles hit the origin, they are redistributed to ℝ+ according to a fixed probability density p(x). This ``dynamic shuffler" is shown to be an instance of a PDMP. From the infinitesimal generator associated with the dynamic shuffler, we then construct a martingale that we show is an approximation to a weak solution to limiting kinetic equations of the density of particles. Properties of these equations are then investigated using Laplace transforms and renewal theory. We then generalize the one-tier model by considering a k-species model, where particles travel on several tiers, and are redistributed with probability distributions that change with time. Obtaining the ``correct" martingale in this ``k-species model" involves an augmented PDMP, which adds variables that keep track of certain types of jumps. The main theorem of this thesis is the existence of limiting kinetic equations for densities of each species. We end by aligning the k-species model to a mean field model of grain coarsening. Several basic properties of this model which are inherent for grain systems are then shown. Finally, we run simulations of the grain coarsening PDMP and raise several conjectures on the universality of certain grain statistics. Advisors/Committee Members: Menon, Govind (Director), Ramanan, Kavita (Reader), Pego, Robert (Reader).

Subjects/Keywords: grain coarsening

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Klobusicky, J. J. (2014). Kinetic Limits of Piecewise Deterministic Markov Processes and Grain Boundary Coarsening. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:386230/

Chicago Manual of Style (16th Edition):

Klobusicky, Joe J. “Kinetic Limits of Piecewise Deterministic Markov Processes and Grain Boundary Coarsening.” 2014. Doctoral Dissertation, Brown University. Accessed November 27, 2020. https://repository.library.brown.edu/studio/item/bdr:386230/.

MLA Handbook (7th Edition):

Klobusicky, Joe J. “Kinetic Limits of Piecewise Deterministic Markov Processes and Grain Boundary Coarsening.” 2014. Web. 27 Nov 2020.

Vancouver:

Klobusicky JJ. Kinetic Limits of Piecewise Deterministic Markov Processes and Grain Boundary Coarsening. [Internet] [Doctoral dissertation]. Brown University; 2014. [cited 2020 Nov 27]. Available from: https://repository.library.brown.edu/studio/item/bdr:386230/.

Council of Science Editors:

Klobusicky JJ. Kinetic Limits of Piecewise Deterministic Markov Processes and Grain Boundary Coarsening. [Doctoral Dissertation]. Brown University; 2014. Available from: https://repository.library.brown.edu/studio/item/bdr:386230/

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