We present a methodology for creating a simulated foam microstructure for use in forward simulations of wave equations to quantitatively analyze the expected scattering phenomenon primarily responsible for the attenuation of interrogating signals in Sprayed-On Foam Insulation (SOFI). Our approach builds off of the popular use of Voronoi Tessalations for...
We solve a class of identification problems for nonparametric and semiparametric models when the endogenous covariate is discrete with unbounded support. Then we proceed with an approach that resolves a polynomial basis problem for the above class of discrete distributions, and for the distributions given in the sufficient condition for...
In this report we consider the Debye model along with Maxwell's equations (Maxwell-Debye) to model electromagnetic wave propagation in dispersive media that exhibit orientational polarization. We construct and analyze a sequential operator splitting method for the discretization of the Maxwell-Debye system. Energy analysis indicates that the operator splitting scheme is...
We consider an SI model of three competing species that are all affected by a single pathogen which is transmitted directly via mass action. The total population sizes of the three species satisfy a three-dimensional Lotka-Volterra competition model. We address the interaction between competition and disease dynamics, and show that...
For the probabilistic model of shuffling by random transpositions we provide a coupling construction
with the expected coupling time of order C*n*log(n), where C is a moderate constant. We enlarge the
methodology of coupling by including intuitive non-Markovian coupling rules. We discuss why a typical
Markovian coupling is not always...
In this paper we consider models of two competing species that are both affected by a pathogen which is transmitted directly. We consider both mass action as well as frequency incidence models of disease spread, and Lotka-Volterra competition. Our aim is to address the interaction between competition and disease dynamics....
We construct a quantum interchange walk, related to classical walks with memory. This gives us a coinless discrete walk, while the origin in classical walks with memory offers the promise of use of existing tools from classical memoried walks. This approach readily reproduces all standard approaches. We briefly discuss its...
In recent years quantum random walks have garnered much interest among quantum information researchers. Part of the reason is the prospect that many hard problems can be solved efficiently by employing algorithms based on quantum random walks, in the same way that classical random walks have played a central role...
We use a combinatorial approach to study the trajectory of a light ray constrained to Euclidian plane R^2 with random reflecting obstacles placed throughout R^2. For the 2D Lorentz lattice gas (LLG) model we derive an analogue of Russo's formula of increasing events in percolation.
We study the stability properties of, and the phase error present in, several higher order (in space) staggered finite difference schemes for Maxwell's equations coupled with a Debye or Lorentz polarization model. We present a novel expansion of the symbol of finite difference approximations, of arbitrary (even) order, of the...