Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

In this thesis we construct rogue waves occurring in the sine-Gordon equation. An algebraic method is used to find explicit solutions to a Lax pair of equations. The Lax pair being studied is compatible with solutions to the sine-Gordon equation. Rotational and librational traveling wave solutions to the sine-Gordon equation are considered in the Lax pair. The Darboux transformation is applied with the Lax pair solutions computed at the rotational and librational waves to generate algebraic solitons and rogue waves, respectively. The rogue waves occur on the end points of the Floquet-Lax spectrum bands and can achieve a magnification factor of at most 3. / Thesis / Master of Science (MSc)

Dissertation (Ph.D.)--Auburn University, / Abstract. Vita. Includes bibliographic references (p.127-144).

Thesis (Ph.D.)--University of Nebraska-Lincoln, 2008. / Title from title screen (site viewed Jan. 13, 2009). PDF text: x, 131 p. : col. ill. ; 3 Mb. UMI publication number: AAT 3315884. Includes bibliographical references. Also available in microfilm and microfiche formats.

Temperature measurements from the HIRDLS instrument on NASA's Aura satellite are analysed for the purposes of detecting and studying internal gravity waves in the terrestrial stratosphere. A detailed description of the methodology used to obtain these data is given, including details of the instrument correction processes used to compensate for errors introduced by a blockage in the instrument optics. A short precis of the relevant theoretical considerations related to atmospheric gravity waves is then outlined. The thesis then discusses the use of the Stockwell (time-frequency) Transform for the detection of gravity waves in HIRDLS data, together with a detailed analysis of the limitations of this method, and the results obtained from this analysis are analysed by comparison to other instruments and climatology. It is concluded that the Stockwell Transform is an appropriate method for the analysis of the HIRDLS dataset, and that the results obtained are robust. We apply these results to analyse stratospheric gravity wave activity during the 2005/06 Arctic sudden stratospheric warming. By comparing the magnitude and form of the gravity wave results to local wind data obtained from ECMWF operational analyses, we conclude that a heavily deformed stratopause observed during this period by other instruments was most probably due to wind-based filtering of the gravity wave spectrum during this period.

Thesis (Ph. D.)--University of Missouri-Columbia, 2003. / Typescript. Vita. Includes bibliographical references (leaves 62-63). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2003. / Typescript. Vita. Includes bibliographical references (leaves 62-63). Also available on the Internet.

This thesis describes a diversity of scattering experiments on a number of different systems. Using time-of-flight neutron scattering, a study of polycrystalline sodium in the highmomentum limit known as the impulse approximation has been performed. The purpose of this study was to look for anharmonic effects in the neutron recoil scattering of sodium as the temperature was increased from 30K to 300K. No such effects were detected and the results agreed with an isotropic harmonic solid to an accuracy of about 4%. Two experiments were carried out on antiferromagnetic systems using triple-axis neutron scattering techniques to measure the spin-wave dispersion relations. The first was on CuO to verify its description as a spin 1/2 one-dimensional antiferromagnet. The dispersion relation was measured along the chain direction up to an energy transfer of 8OmeV. This was done above and below the Néel temperature (T_N =240K). However, no evidence was seen to justify the description of CuO as a one-dimensional antiferromagnet, with the spin waves behaving like those in a classical three-dimensional system. The other spin-wave study examined the two-dimensional antiferromagnet KFeF₄ . The measurement of the spin-wave dispersion relation at two temperatures (50K and 100K) below the Néel temperature (T_N =136.75±0.25K), confirmed the description of KFeF₄ as a two-dimensional Heisenberg antiferromagnet with small Ising anisotropy. Studies of the magnetic phase transition in KFeF₄ revealed that below the Néel temperature, the critical behaviour is described by two-dimensional Ising models, and above a crossover to Heisenberg behaviour is seen. This crossover was detected by measuring the order parameter below T_N, and the static and dynamic susceptibilities above T_N using neutron scattering techniques. The results were compared to power-law behaviour and also to theories for the classical Heisenberg antiferromagnet and the more recent quantum Heisenberg antiferromagnetic model. The final study of KFeF₄ involved an x-ray experiment on the structural phase transition around 400K. It has been suggested that there is a second-order transition at 410K to an incommensurate phase, which then undergoes a first-order lock-in transition at 400K to the low-temperature structure. This single crystal x-ray scattering study confirms the existence of the first-order phase transition, but shows no evidence for a higher temperature second-order transition or for the incommensurate phase.

This thesis presents results on the description of plasma waves in terms of wavepackets. The wave field is decomposed into a distribution of wavepackets in a space of position, wavevector, time, and frequency. A complex structure joining each pair of Fourier conjugate variables into a single complex coordinate allows the efficient derivation of equations of motion for the phase space distribution by exploiting its analytic properties. The Wick symbol calculus, a mathematical tool generalizing many convenient properties of the Fourier transform to a local setting, is used to derive new exact phase space equations which maintain full information on the phase of the waves and include effects nonlocal in phase space such as harmonic generation. A general purpose asymptotic expansion of the Wick symbol product formula is used to treat dispersion, refraction, photon acceleration, and ponderomotive forces. Examples studied include the nonlinear Schrödinger equation, mode conversion, and the Vlasov equation. The structure of partially coherent wave fields is understood in terms of zeros in the phase space distribution caused by dislocations in its complex phase which are shown to be correlated with the field entropy. Simulations of plasma heating by crossing electron beams are understood by representing the resulting plasma waves in phase space. The local coherence properties of the beam driven Langmuir waves are studied numerically.

Increasing observational evidence of wave modes brings us to a closer understanding of the solar corona. Coronal seismology allows us to combine wave observations and theory to determine otherwise unknown parameters. The period ratio, P₁/2P₂, between the period P₁ of the fundamental mode and the period P₂ of its first overtone is one such tool of coronal seismology and its departure from unity provides information about the structure of the corona. In this thesis we consider the period ratio P₁/2P₂ of coronal loops from a theoretical standpoint. Previous theory and observations indicate that the period ratio is likely to be less than unity for oscillations of coronal loops. We consider the role of damping and density structuring on the period ratio. In Chapter 2 we consider analytically the one-dimensional wave equation with the inclusion of a generic damping term for both uniform and non-uniform media. Results suggest that the period ratio is dominated by longitudinal structuring rather than damping. In Chapter 3 we consider analytically the effects of thermal conduction and compressive viscosity on the period ratio for a longitudinally propagating sound wave. We find that damping by either thermal conduction or compressive viscosity typically has a small effect on the period ratio. For coronal values of thermal conduction the effect on the period ratio is negligible. For compressive viscosity the effect on the period ratio may become important for some short hot loops. In Chapter 4 we extend the analysis of Chapter 3 to include radiative cooling and find that it too has a negligible effect on the period ratio for typical coronal values. As an extension to the investigation, damping rates are considered for thermal conduction, compressive viscosity and radiative cooling. The damping time is found to be optimal for each mechanism in a different temperature range, namely below 1 MK for radiative cooling, 2 − 6 MK for thermal conduction and above 6 MK for compressive viscosity. In Chapter 5 we consider analytically the period ratio for the fast kink, sausage and n = N modes of a magnetic slab, discussing both an Epstein density profile and a simple step function profile. We find that transverse density structuring in the form of an Epstein profile or a step function profile may contribute to the shift of the period ratio for long thin slab-like structures. The similarity in the behaviour of the period ratio for both profiles means either can be used as a robust model. We consider also other profiles numerically for the kink mode, which are found to be either slab-like or Epstein-like suggesting again that it is not necessary to distinguish the nature of the density profile when considering the period ratio.