This work consists of two parts. The first part is a comprehensive study of surface-wave propagation along dielectric tube waveguides. It includes the derivation of the characteristic equations and expressions for group velocity and attenuation coefficient, the latter by a perturbation method. Mode designations are justified and the physical distinction between the HE₁₁ and EH₁₁ modes is further illustrated by showing three-dimensional plots of the field configurations. Computed characteristics are given for a wide range of parameters, and are compared with those of standard rectangular waveguides. Finally, a method of shielding the tube from weather conditions is proposed and the resulting changes in characteristics are noted. The second part of this work is essentially a unified analysis of all slow-wave modes in eight cylindrical waveguides. Characteristic equations are derived and expressions are obtained for the group velocity and the attenuation coefficients by a perturbation method. Accurate propagation characteristics for the dominant TM₀₁ mode are computed for four waveguides with no restrictions on their radial dimensions. These guides are the Goubau line and a coaxial cable with dielectric linings on the inner, outer, or both conductors. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

A comprehensive study of potential symmetries admitted by partial differential equations is given using the wave equation utt = c²(x)uxx as a given prototype equation, R. Methods are given for the construction of various conserved forms for R. Potential symmetries for R are nonlocal symmetries realized as local symmetries of auxiliary systems obtained from conserved forms of R. The existence of potential symmetries for R can be determined algorithmically and automatically by the use of a symbolic manipulation program. Most importantly, the potential symmetries obtained through one auxiliary system may or may not include and/or extend those obtained through another auxiliary system. The work in this thesis significantly extends the previously known classes of potential symmetries admitted by R and results in a better understanding of the limits in the construction of potential symmetries for R. / Science, Faculty of / Mathematics, Department of / Graduate

I present a new time-domain method for solving for the stress and particle velocity of normally incident plane waves propagating in a smoothly varying one-dimensional medium. Both the Young's modulus E and the density ⍴ are allowed to vary smoothly with depth. The restriction of geometrical optics, that the wavelength be much less than the material stratification length, is not required in this new method. The infinite geometrical optics expansion is truncated after n terms, imposing a condition on the acoustic impedance I for exact solutions to exist. For the case ռ = 2 there are three general classes of impedance functions for which the resultant expansion is uniform and exact. To check the numerical validity of the "truncated asymptotic" (TA) solution results are calculated for the case of a medium with a linear velocity gradient for which there is an exact solution in the frequency domain. Since a linear velocity gradient is not one of the foregoing classes of impedance functions, a curve-fitting approach is necessary. The TA method compares favourably to the exact solution and is accurate to within the error of the required curve fit. Two classes of synthetic seismograms are calculated for smooth velocity and density variations. The same impedance as a function of traveltime is used for both classes. In the first class the principal variation in impedance is due to velocity, while in the second it is mainly due to density. The amplitudes in both classes of synthetic seismograms are very similar, but, as expected, the traveltime curves for each class are widely separated. For the case ⍴ = constant the TA solution is used as a bench-mark to analyse a two-term WKBJ approximation for three classes of velocity functions. The velocity functions are such that the TA solutions are exact. For two of the classes the WKBJ solution performs well when the length of the transition zone is of the same order, or larger, than the length of the applied wavelet. For steeper velocity gradients the WKBJ solution begins to differ significantly from the exact TA solution. The WKBJ solution for the third class performs extremely well even for steep gradients. Equations governing the validity of the WKBJ solution are examined to explain the above results. Equations are derived to describe the distortion of a stress pulse propagating through a transition zone. For small velocity gradients (relative to the length of the applied pulse) the wavelet changes amplitude but its phase is not effected. As the gradient increases and the velocity function becomes a discontinuity at z = 0 the wavelet travels through undistorted. Only when the transition zone width is of the order of the length of the wavelet is there any visible phase distortion. Reflection and transmission coefficients as functions of time are calculated for low, intermediate and high gradient transition zones. The transmission coefficient is a delta function in each case. The reflection coefficient has the shape of a Hilbert transform for low gradients. For higher gradients the reflection coefficient approaches the shape of a delta function. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

This thesis is mainly concerned with the effects of periodic loading of nonreciprocal waveguides by regular placement of discontinuitie and with the associated problem of the evaluation of a transverse discontinuity in a nonreciprocal ferrite loaded waveguide. The mode-matching technique is used to analyse a transverse discontinuity in a nonreciprocal waveguide. The difficult orthogonality relations are circumvented using a Galerkin approach. The elements of an exact three-element equivalent circuit for an infinitely thin metallic diaphragm are evaluated. Each element has two values, one for each direction of propagation. The numerical results show the same trends as those obtained experimentally in a similar configuration. The properties of a nonreciprocal, ferrite loaded, rectangular waveguide, which is periodically loaded by thin metallic "inductive" diaphragms, are investigated experimentally. The propagation constants of the structures are measured and are compared with predictions based on measured values of the scattering parameters of a single diaphragm in the nonreciprocal waveguide. The agreement between theory and experiment is generally good except for the smaller spacings between the diaphragms. This discrepancy is attributed to the effects of higher mode interaction. An investigation was also made of a magnetized ferrite loaded ridged waveguide. A theoretical and experimental investigation was first made of the preliminary problem of a reciprocal, inhomogeneous ridged waveguide and guided by these results an approximate, theoretical technique was formulated to analyse the nonreciprocal ferrite loaded ridged waveguide problem. It was found that introduction of the ridge had detrimental effects on the differential phase shift characteristics except for a few special cases. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Unknown

Ray-optical methods are used to calculate the coupling between open-ended parallel-plate waveguides, as well as the radiation patterns of finite arrays of coupled parallel-plate waveguides with only the central guide driven. These methods require extensive ray tracing, particularly for the larger arrays, to take into account the many possible ray paths. The coupling coefficients between both two and three guides in isolation agreed remarkably well with those previously derived in the presence of other guides, groundplanes etc., indicating a general lack of sensitivity of the coupling coefficients to the details of the surrounding structure. The calculated patterns were compared with experimental patterns using an H-plane sectoral horn to simulate the parallel-plate waveguide array. Radiation patterns of both three and five element arrays with all waveguide edges in the aperture plane, as well as that of a three element staggered array with the outer edges not in the aperture plane agreed well with the experimental patterns. A wide variety of patterns could be obtained by varying the width, depth, and number of the outer guides in the array. Ray-optical methods may thus be useful in the development of waveguide antennas for a variety of applications. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

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Predictive capability of computational fluid dynamics simulations for the prediction of plunging breaking wave is assessed. Laminar flow simulations are performed for dam break, solitary wave run up on a slope and flow over a submerged bump using OpenFOAM, a finite volume solver with volume-ofluid (VoF) interface capturing method, and Proteus, a finite element solver with coupled level-set/ volume-ofluid (CLSVoF) methods. CLSVoF predicts wave elevation before the plunge, and primary and secondary plunger shapes better than VoF in all the cases. The primary limitation in the simulation is the airflow, which results in diffused plunger tips in VoF simulations, and results in surface peel-off in CLSVoF simulations. Future work should include 3D turbulent flow simulations.

In the first part of this thesis, the nonlinear Schrodinger equation for inviscid cross-waves near onset is found to be modified by viscous linear damping and detuning. The accompanying boundary condition at the wavemaker is also modified by damping from the wavemaker meniscus. The relative contributions of the free-surface, sidewalls, bottom, and wavemaker viscous boundary layers are computed. It is shown that viscous dissipation due to the wavemaker meniscus breaks the symmetry of the neutral curve. In the second part, existence and stability of steady solutions to the nonlinear Schrodinger equation are examined numerically. It is found that at forcing frequency above a critical value, f(c), only one solution exists. However, below f(c), multiple steady solutions, the number of which is determined, are possible. This multiplicity leads to hysteresis for f < f(c), in agreement with observation. A Hopf bifurcation of the steady solutions is found. This bifurcation is compared with the transition from unmodulated to periodically modulated cross-waves observed experimentally.

Thesis (M.Sc.Eng.) PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / The study of wave-wave interactions in the ionosphere is important for designing communication systems, satellite systems, and spacecraft. Ionospheric research also informs laser and magnetic fusion plasma physics. This thesis focuses on two nonlinear wave-wave interactions in the ionosphere. The first interaction is a nonlinear mode conversion. Very Low Frequency (VLF) waves transmitted from the ground travel through the ionosphere as injected whistler waves. The whistler waves interact with naturally-occurring density fluctuations in the ionosphere and are mode converted into lower hybrid waves. The lower hybrid waves accelerate electrons along the geomagnetic field and the resulting beam mode Langmuir waves are detectable by radar. This type of mode conversion may combine additively with a four wave interaction with the same VLF wave as its source. Data collected at the Arecibo Observatory in Puerto Rico during the occurrence of spread F and sporadic E was analyzed. Plasma line enhancements may indicate the nonlinear mode conversion both separately from and in conjunction with the four wave interaction. The second nonlinear wave-wave interaction is the parametric decay instability (PDI) excited by High Frequency (HF) heater waves at the High Frequency Active Auroral Research Program facility in Gakona, Alaska. Resonant PDI cascades downwards, resulting in up-shifted ion line enhancements as detected by radar. This process has been detected in the presence of down-shifted ion line enhancements which may be caused by beating between PDI-produced Langmuir waves, or by naturally occurring ionospheric currents. / 2031-01-01