Wave interactions in periodic structures and periodic dielectric waveguides

This work is concerned with a general analysis of wave interactions in periodic structures and particularly periodic thin film dielectric waveguides.

The electromagnetic wave propagation in an asymmetric dielectric waveguide with a periodically perturbed surface is analyzed in terms of a Floquet mode solution. First order approximate analytical expressions for the space harmonics are obtained. The solution is used to analyze various applications: (1) phase matched second harmonic generation in periodically perturbed optical waveguides; (2) grating couplers and thin film filters; (3) Bragg reflection devices; (4) the calculation of the traveling wave interaction impedance for solid state and vacuum tube optical traveling wave amplifiers which utilize periodic dielectric waveguides. Some of these applications are of interest in the field of integrated optics.

A special emphasis is put on the analysis of traveling wave interaction between electrons and electromagnetic waves in various operation regimes. Interactions with a finite temperature electron beam at the collision-dominated, collisionless, and quantum regimes are analyzed in detail assuming a one-dimensional model and longitudinal coupling.

The analysis is used to examine the possibility of solid state traveling wave devices (amplifiers, modulators), and some monolithic structures of these devices are suggested, designed to operate at the submillimeter-far infrared frequency regime. The estimates of attainable traveling wave interaction gain are quite low (on the order of a few inverse centimeters). However, the possibility of attaining net gain with different materials, structures and operation condition is not ruled out.

The developed model is used to discuss the possibility and the theoretical limitations of high frequency (optical) operation of vacuum electron beam tube; and the relation to other electron-electromagnetic wave interaction effects (Smith-Purcell and Cerenkov radiation and the free electron laser) are pointed out. Finally, the case where the periodic structure is the natural crystal lattice is briefly discussed. The longitudinal component of optical space harmonics in the crystal is calculated and found to be of the order of magnitude of the macroscopic wave, and some comments are made on the possibility of coherent bremsstrahlung and distributed feedback lasers in single crystals.

Characterization and modeling of premixed turbulent n-heptane flames in the thin reaction zone regime

n-heptane/air premixed turbulent flames in the high-Karlovitz portion of the thin reaction zone regime are characterized and modeled in this thesis using Direct Numerical Simulations (DNS) with detailed chemistry. In order to perform these simulations, a time-integration scheme that can efficiently handle the stiffness of the equations solved is developed first. A first simulation with unity Lewis number is considered in order to assess the effect of turbulence on the flame in the absence of differential diffusion. A second simulation with non-unity Lewis numbers is considered to study how turbulence affects differential diffusion. In the absence of differential diffusion, minimal departure from the 1D unstretched flame structure (species vs. temperature profiles) is observed. In the non-unity Lewis number case, the flame structure lies between that of 1D unstretched flames with "laminar" non-unity Lewis numbers and unity Lewis number. This is attributed to effective Lewis numbers resulting from intense turbulent mixing and a first model is proposed. The reaction zone is shown to be thin for both flames, yet large chemical source term fluctuations are observed. The fuel consumption rate is found to be only weakly correlated with stretch, although local extinctions in the non-unity Lewis number case are well correlated with high curvature. These results explain the apparent turbulent flame speeds. Other variables that better correlate with this fuel burning rate are identified through a coordinate transformation. It is shown that the unity Lewis number turbulent flames can be accurately described by a set of 1D (in progress variable space) flamelet equations parameterized by the dissipation rate of the progress variable. In the non-unity Lewis number flames, the flamelet equations suggest a dependence on a second parameter, the diffusion of the progress variable. A new tabulation approach is proposed for the simulation of such flames with these dimensionally-reduced manifolds.

Special Frobenius Traces in Galois Representations

This thesis studies Frobenius traces in Galois representations from two different directions. In the first problem we explore how often they vanish in Artin-type representations. We give an upper bound for the density of the set of vanishing Frobenius traces in terms of the multiplicities of the irreducible components of the adjoint representation. Towards that, we construct an infinite family of representations of finite groups with an irreducible adjoint action.

In the second problem we partially extend for Hilbert modular forms a result of Coleman and Edixhoven that the Hecke eigenvalues a_p of classical elliptical modular newforms f of weight 2 are never extremal, i.e., a_p is strictly less than 2[square root]p. The generalization currently applies only to prime ideals p of degree one, though we expect it to hold for p of any odd degree. However, an even degree prime can be extremal for f. We prove our result in each of the following instances: when one can move to a Shimura curve defined by a quaternion algebra, when f is a CM form, when the crystalline Frobenius is semi-simple, and when the strong Tate conjecture holds for a product of two Hilbert modular surfaces (or quaternionic Shimura surfaces) over a finite field.

Special Sewage Problem : Report on the Sewage Problem of the City of Los Angeles with Conclusions and Recommendations

Not available.

Investigations into electronic stopping regime sputtering of uranium tetrafluoride

Yields were measured for ²³⁵U sputtered from UF₄ by ¹⁶O, ¹⁹F, and ³⁵Cl over the energy range ~.12 to 1.5 MeV/ amu sing a charge equilibrated beam in the stripped beam arrangement for all the incident ions and in the transmission arrangement for ¹⁹F and ³⁵Cl. In addition, yields were measured for ¹⁹F incident in a wide range of discrete charge states. The angular dependence of all the measured yields were consistent with cosʋ. The stripped beam and transmission data were well fit by the form (Az²eqln(BƐ)/Ɛ)⁴ (where Ɛ was the ion energy in MeV/amu and z_eq(Ɛ) was taken from Zeigler(80). The fitted values of B for the various sets of data were consistent with a constant B₀, equal to 36.3 ± 2.7, independent of incident ion. The fitted values of A show no consistent variation with incident ion although a difference can be noted between the stripped beam and transmission values, the transmission values being higher.

The incident charge data were well fit by the assumptions that the sputtering yield depended locally on a power of the incident ion charge and that the sputtering from the surface is exponentially correlated to conditions in the bulk. The equilibrated sputtering yields derived from these data are in agreement with the stripped beam yields.

In addition, to aid in the understanding of these data, the data of Hakansson(80,81a,81b) were examined and contrasted with the UF₄ results. The thermal models of Seiberling(80) and Watson(81) were discussed and compared to the data.