Mathematics Theses and Dissertations
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Phase transitions in gene networks evolved under different selection rules
(2016)Mathematical models of gene regulation are a powerful tool for understanding the complex features of genetic control. While various modeling efforts have been successful at explaining gene expression dynamics, much less ... 
Multiscale Modeling and Simulation of Stepped Crystal Surfaces
(2016)A primary goal of this dissertation is to understand the links between mathematical models that describe crystal surfaces at three fundamental length scales: The scale of individual atoms, the scale of collections of atoms ... 
THE STOCHASTIC NAVIER STOKES EQUATIONS FOR HEAT CONDUCTING, COMPRESSIBLE FLUIDS
(2016)This dissertation is devoted to the equations of motion governing the evolution of a fluid or gas at the macroscopic scale. The classical model is a PDE description known as the NavierStokes equations. The behavior of ... 
Vehicle Routing Problems that Minimize the Completion Time: Heuristics, WorstCase Analyses, and Computational Results
(2016)In the standard Vehicle Routing Problem (VRP), we route a fleet of vehicles to deliver the demands of all customers such that the total distance traveled by the fleet is minimized. In this dissertation, we study variants ... 
Classical Invariants for Principal Series and Isomorphisms of Root Data
(2016)We develop some new techniques to calculate the Schur indicator for selfdual irreducible Langlands quotients of the principal series representations. Using these techniques we derive some new formulas for the Schur indicator ...