Thesis (Ph.D)--Electrical and Computer Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Smith, Glenn; Committee Member: Buck, John; Committee Member: Goldsztein, Guillermo; Committee Member: Peterson, Andrew; Committee Member: Scott, Waymond. Part of the SMARTech Electronic Thesis and Dissertation Collection.

The work in this thesis focuses primarily on equilibrium and stability properties of collisionless current sheet models, in particular of the force-free Harris sheet model. A detailed investigation is carried out into the properties of the distribution function found by Harrison and Neukirch (Physical Review Letters 102, 135003, 2009) for the force-free Harris sheet, which is so far the only known nonlinear force-free Vlasov-Maxwell equilibrium. Exact conditions on the parameters of the distribution function are found, which show when it can be single or multi-peaked in two of the velocity space directions. This is important because it may have implications for the stability of the equilibrium. One major aim of this thesis is to find new force-free equilibrium distribution functions. By using a new method which is different from that of Harrison and Neukirch, it is possible to find a complete family of distribution functions for the force-free Harris sheet, which includes the Harrison and Neukirch distribution function (Physical Review Letters 102, 135003, 2009). Each member of this family has a different dependence on the particle energy, although the dependence on the canonical momenta remains the same. Three detailed analytical examples are presented. Other possibilities for finding further collisionless force-free equilibrium distribution functions have been explored, but were unsuccessful. The first linear stability analysis of the Harrison and Neukirch equilibrium distribution function is then carried out, concentrating on macroscopic instabilities, and considering two-dimensional perturbations only. The analysis is based on the technique of integration over unperturbed orbits. Similarly to the Harris sheet case (Nuovo Cimento, 23:115, 1962), this is only possible by using approximations to the exact orbits, which are unknown. Furthermore, the approximations for the Harris sheet case cannot be used for the force-free Harris sheet, and so new techniques have to be developed in order to make analytical progress. Full analytical expressions for the perturbed current density are derived but, for the sake of simplicity, only the long wavelength limit is investigated. The dependence of the stability on various equilibrium parameters is investigated.

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The constantly increasing volume of information in modern society demands a better understanding of the physics and modeling of optical phenomena, and in particular, optical waveguides which are the central component of information systems. Two ways of advancing this physics are to push current technologies into new regimes of operation, and to study novel materials which offer superior properties for practical applications. This dissertation considers two problems, each addressing the above-mentioned demands. The first relates to the influence of high-order nonlinear effects on pulse collisions in existing high-speed communication systems. The second part is a study of pulse dynamics in a novel nanocomposite medium which offers great potential for both optical waveguide physics and applications. The nanocomposite consists of metallic nanoparticles embedded in a host medium. Under resonance conditions, the optical field excites plasmonic oscillations in the nanoparticles, which induce a strong nonlinear response.Analytical and computational tools are used to study these problems. In the first case, a double perturbation method, in which the small parameters are the reciprocal of the relative frequency of the colliding solitons and the coefficient of quintic nonlinearity, reveals that the leading order effects on collisions are radiation emission and phase shift of the colliding solitons. The analytical results are shown to agree with numerics. For the case of pulse dynamics in nanocomposite waveguides, the resonant interaction of the optical field and material excitation is studied in a slowly-varying envelope approximation, resulting in a system of partial differential equations. A family of solitary wave solutions representing the phenomenon of self-induced transparency are derived. Stability analysis reveals the solitary waves are conditionally stable, depending on the sign of the perturbation parameter. A characterization of two-pulse interaction indicates high sensitivity to relative phase, and collision dynamics vary from highly elastic to the extreme case where one wave is immediately destroyed by the collision, depositing its energy into a localized hotspot of material excitation. This last scenario represents a novel mechanism for "stopping light".

Zeolite membranes are considered to be a promising alternative to polymeric membranes and they have the potential to separate gases under harsh conditions. Silicalite-1 membranes in particular are easy to prepare and suitable for several industrial applications. In this research project, silicalite-1/ceramic composite membranes were prepared using the pore plugging hydrothermal synthesis method and supports with zirconium oxide and/or titanium oxide as active layers. The effect of the support’s pore size on the morphology and permeation performance of the prepared membranes was investigated using five supports with different active layer pore sizes in the range of 0.14 – 1.4 m. The prepared membranes were characterized by X-ray diffraction (XRD), scanning electron microscope (SEM), electron diffraction spectrometer (EDS), single gas and binary gas mixtures permeation tests. The results confirmed the presence of a typical silicalite-1 zeolite structure with a high internal crystalline order grown inside the pores of the active layer of the supports, with a dense film covering most of the supports active layers. Silicalite-1 crystals in the prepared membranes were preferably oriented with either a- or b-axes perpendicular to the support surface. Single gas permeation results illustrated that the observed permeances were not directly related to the kinetic diameter of permeants. Instead, the transport of the studied gases through the prepared membranes occurred by adsorption followed by surface diffusion mechanism. Binary gas tests performed with CO2 and N2 mixtures showed that the prepared membranes were selective and very permeable with CO2/N2 permselectivities up to 30 and a CO2 permeances in the order of 10-6 mol m-2 Pa-1 s-1. A model was developed, based on Maxwell−Stefan equations and Extended Langmuir adsorption isotherm, to describe the transport of binary CO2 and N2 mixtures through the prepared silicalite-1 membranes. The model results showed that the exchange diffusivities (D12 and D21) were less dependent on the feed pressure and feed composition compared to the permeances and the permselectivities. Hence, they are more appropriate to characterize the intrinsic transport properties of the prepared silicalite-1 membranes.

In this thesis, firstly the original G&ouml / del&#039 / s metric is examined in detail. Then a more general class of G&ouml / del-type metrics is introduced. It is shown that they are the solutions of Einstein field equations with a physically acceptable matter distribution provided that some conditions are satisfied. Lastly, some examples of the G&ouml / del-type metrics are given.

In traffic safety analysis, a large number of distributions have been proposed to analyze motor vehicle crashes. Among those distributions, the traditional Poisson and Negative Binomial (NB) distributions have been the most commonly used. Although the Poisson and NB models possess desirable statistical properties, their application on modeling motor vehicle crashes are associated with limitations. In practice, traffic crash data are often over-dispersed. On rare occasions, they have shown to be under-dispersed. The over-dispersed and under-dispersed data can lead to the inconsistent standard errors of parameter estimates using the traditional Poisson distribution. Although the NB has been found to be able to model over-dispersed data, it cannot handle under-dispersed data. Among those distributions proposed to handle over-dispersed and under-dispersed datasets, the Conway-Maxwell-Poisson (COM-Poisson) and double Poisson (DP) distributions are particularly noteworthy. The DP distribution and its generalized linear model (GLM) framework has seldom been investigated and applied since its first introduction 25 years ago. The objectives of this study are to: 1) examine the applicability of the DP distribution and its regression model for analyzing crash data characterized by over- and under-dispersion, and 2) compare the performances of the DP distribution and DP GLM with those of the COM-Poisson distribution and COM-Poisson GLM in terms of goodness-of-fit (GOF) and theoretical soundness. All the DP GLMs in this study were developed based on the approximate probability mass function (PMF) of the DP distribution. Based on the simulated data, it was found that the COM-Poisson distribution performed better than the DP distribution for all nine mean-dispersion scenarios and that the DP distribution worked better for high mean scenarios independent of the type of dispersion. Using two over-dispersed empirical datasets, the results demonstrated that the DP GLM fitted the over-dispersed data almost the same as the NB model and COM-Poisson GLM. With the use of the under-dispersed empirical crash data, it was found that the overall performance of the DP GLM was much better than that of the COM-Poisson GLM in handling the under-dispersed crash data. Furthermore, it was found that the mathematics to manipulate the DP GLM was much easier than for the COM-Poisson GLM and that the DP GLM always gave smaller standard errors for the estimated coefficients.

Thesis (PhD)--Montana State University--Bozeman, 2009. / Typescript. Chairperson, Graduate Committee: Sarah L. Codd. Includes bibliographical references (leaves 119-132).

Th.--Sci. phys.--Clermont-Ferrand 2, 1979. N°: 261.

The use of conformal transformation as a method for generating solutions of Einstein's equations has been mainly studied in the cases where the original spacetime is vacuum. The generated spacetimes then frequently belong to the class of pp-waves. In the present work, the electrovacuum spacetimes are stud- ied, i.e the solutions of coupled Einstein's and Maxwell's equations. By using the conformal transformation, it is possible to circumvent solving the later equa- tions. This method is concretely studied for null Einstein-Maxwell fields and it turns out that the admissible spacetimes are pp-waves again. However, if the method is generalized, it is possible to enlarge the class of conformal null Einstein-Maxwell fields to a wider family of Kundt spacetimes. 1