Technical Reports (Mathematics)
http://hdl.handle.net/1957/13738
2016-02-06T00:34:32ZConvergence Analysis of Yee Schemes for Maxwell's Equations in Debye and Lorentz Dispersive Media
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.
2013-05-06T00:00:00ZIdentification via completeness for discrete covariates and orthogonal polynomials
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.
2012-01-06T00:00:00ZA Sequential Operator Splitting Method for Electromagnetic Wave Propagation in Dispersive Media
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.
2011-09-08T00:00:00ZAn Analysis of the Coexistence of Three Competing Species with a Shared Pathogen
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