http://hdl.handle.net/1957/13738 2013-05-25T06:20:48Z http://hdl.handle.net/1957/38475 Convergence Analysis of Yee Schemes for Maxwell's Equations in Debye and Lorentz Dispersive Media Bokil, V. A.; Gibson, N. L. We present discrete energy decay results for the Yee scheme applied to Maxwell's equations in Debye and Lorentz dispersive media. These estimates provide stability conditions for the Yee scheme in the corresponding media. In particular, we show that the stability conditions are the same as those for the Yee scheme in a nondispersive dielectric. However, energy decay for the Maxwell-Debye and Maxwell-Lorentz models indicate that the Yee schemes are dissipative. The energy decay results are then used to prove the convergence of the Yee schemes for the dispersive models. We also show that the Yee schemes preserve the Gauss divergence laws on its discrete mesh. Numerical simulations are provided to justify the theoretical results. 2013-05-06T00:00:00Z http://hdl.handle.net/1957/26537 Identification via completeness for discrete covariates and orthogonal polynomials Kovchegov, Yevgeniy; Yildiz, Nese 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 completeness in Newey and Powell (2003). Thus, in addition to extending the set of econometric models for which nonparametric or semiparametric identification of structural functions is guaranteed to hold, our approach provides a natural way of estimating these functions. Finally, we extend our polynomial basis approach to Pearson-like and Ord-like families of distributions. 2012-01-06T00:00:00Z http://hdl.handle.net/1957/23059 A Sequential Operator Splitting Method for Electromagnetic Wave Propagation in Dispersive Media Bokil, Vrushali; Leung, Aubrey 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 unconditionally stable. We also conduct a trun- cation error analysis to show that the scheme is rst order accurate in time and second order accurate in space. We compare the operator splitting method to the Yee scheme for discretizing the Maxwell-Debye system via stability, dispersion, and dissipation analyses. Numerical simulations validate the unconditional stability of the scheme. 2011-09-08T00:00:00Z http://hdl.handle.net/1957/22518 An Analysis of the Coexistence of Three Competing Species with a Shared Pathogen Bokil, Vrushali A.; Leung, Margaret-Rose We consider an SI model of three competing species that are all a ffected 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 infected coexistence in the model is determined by the values of the basic reproduction numbers as well as the relative strengths of intra-specific crowding versus inter-specific competition for all three species. 2011-08-11T00:00:00Z