Thesis (Ph. D.)--University of Chicago, Dept. of Physics, August 2002. / Includes bibliographical references (p. 31). Also available on the Internet.

Thesis (Ph. D.)--University of Oregon, 2005. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 79-80). Also available for download via the World Wide Web; free to University of Oregon users.

We present a time-dependent mixed quantum/semiclassical approach to calculating linear absorption spectra. Applying Variational Fixed Vibrational Basis/Gaussian Bath theory (FVB/GB) to the treatment of small molecules isolated in an extended cryogenic medium, an assumed time-scale separation between the few rapid, largely intramolecular modes of the guest and the several slower extended modes of the medium is utilized to partition a system from the surrounding bath. The system dynamics are handled with basis set methods, while the bath degrees of freedom are subject to a semiclasscial thawed Gaussian ansatz. The linear absorption spectrum for a realistic model system is calculated using FVB/GB results and then compared with a numerically exact calculation. Also contained in this dissertation are previously published theoretical works on Transient Absorption and Femtosecond Stimulated Raman Spectroscopy. Both encompass a rebuilding of the theory and elucidate the information content of the respective spectroscopic signals. This dissertation includes previously published co-authored material.

First demonstrated by Isaac Newton in his prism experiment, angular dispersion (AD) is a prevalent effect in optics where each wavelength in a pulsed field propagates at a different angle. Angular dispersion occurs after a collimated pulse traverses a diffractive or dispersive device and, as a result, helps modify the group velocity of a pulse in free space and introduces group-velocity dispersion into the freely propagating wave packet. These are essential ingredients in group-velocity matching and dispersion cancellation in various optical settings. With 300 years of development, it was only recently that a new class of angular dispersion materialized as non-differentiable AD. This non-differentiable AD has also been studied under the moniker space-time wave packets (STWP) and has shown to be propagation-invariant and possess arbitrary group velocity. In this dissertation, I will study (1) the underpinning theory of how non-differentiable AD allows for an optical field to break the pre-conceived notions of group velocity, group velocity dispersion (GVD), and pulse front tilt for on-axis propagation through analytical and experimental demonstrations. From these developments, I will (2) apply these concepts of non-differentiable AD to dispersive materials. I will validate these analytical predictions through experiments showing that propagation-invariant wave packets can also be supported in normal and anomalous media. Moreover, I will prove, through the use of non-differentiable AD, that the dispersive properties of a material can be overwritten to produce arbitrary group velocity and GVD characteristics. With this new information on propagation-invariant fields in dispersive materials, I will (3) exhibit new classes of optical fields that were previously theorized but never synthesized in dispersive materials, such as the X- to O- transition in anomalous GVD materials, which will be connected to the de-Broglie-Mackinnon wave packet and particle wave packets. To address the propagation invariance of non-differentiable AD, I will (4) demonstrate the STWP propagation throughout a kilometer in a turbulent environment and develop a new Rayleigh length for the STWP. Finally, I will (5) establish the consequences of discretization on the non-differentiable AD and produce a new form of the Talbot effect in which the temporal and spatial degrees of freedom are interlocked along with independent spatial and temporal Talbot effects in free space.

In this work, nondispersive wave packet solutions to linear partial differential equations are investigated. These solutions are characterized by infinite energy content; otherwise, they are continuous, nonsingular and propagate in free space without spreading out. Examples of such solutions are Berry and Balazs’ Airy packet, MacKinnon’s wave packet and Brittingham’s Focus Wave Mode (FWM). It is demonstrated in this thesis that the infinite energy content is not a basic problem per se and that it can be dealt with in two distinct ways. First these wave packets can be used as bases to construct highly localized, slowly decaying, time-limited pulsed solutions. In the case of the FWMs, this path leads to the formulation of the bidirectional representation, a technique that provides the most natural basis for synthesizing Brittingham-like solutions. This representation is used to derive new exact solutions to the 3-D scalar wave equation. It is also applied to problems involving boundaries, in particular to the propagation of a localized pulse in an infinite acoustic waveguide and to the launch ability of such a pulse from the opening of a semi-infinite waveguide. The second approach in dealing with the infinite energy content utilizes the bump-like structure of nondispersive solutions. With an appropriate choice of parameters, these bump fields have very large amplitudes around the centers, in comparison to their tails. In particular, the FWM solutions are used to model massless particles and are capable of providing an interesting interpretation to the results of Young’s two slit experiment and to the wave-particle duality of light. The bidirectional representation provides, also, a systematic way of deriving packet solutions to the Klein-Gordon, the Schrodinger and the Dirac equations. Nondispersive solutions of the former two equations are compared to previously derived ones, e.g., the Airy packet and MacKinnon's wave packet. / Ph. D.

Die Ausbreitungspfade und die strukturelle Veränderung von quasi geostrophischen Rossby-Wellenpaketen werden mittels der WKB-Methode untersucht. Es wird angenommen, daß die Wellenpakete an einem in Ost-West-Richtung verlaufenden festen Rand reflektiert werden können. Die Dynamik der Rossby-Wellenpakete wird auf der ß-Ebene aber auch auf der sogenannten d-Oberfiäche - wo auch die zweite Ableitung des Coriolis-Parameters eine Rolle spielt - studiert. Es wird gezeigt, daß die Wellenpakete unter bestimmten Umständen große Entfernungen in zonaler Richtung entlang der Küste zurücklegen können und damit die Strömung weit stromab beeinflussen. Die Wellenpakete sind dabei zwischen dem reflektierenden Rand und einer Umkehrbreite gefangen im Unterschied zu freien Rossbywellen in der Atmosphäre, die zwischen zwei Umkehrbreiten gefangen werden können. Es zeigt sich, daß der d-Term keine besonders wichtige Rolle für die Ausbreitung der Rossby-Wellenpakete spielt, am wichtigsten ist er noch bei der Dynamik von Wellen mit negativer Phasengeschwindigkeit. Es wird vorgeschlagen, daß ein selektiver Rossby-Wellenleiter wie er hier diskutiert wird eine Rolle in der Dynamik des Antarktik-Zirkumpolarstromes spielt. / We study the propagation and the structural change of quasi geostrophic Rossby wave packets by means of a WKB-method. Our approach involves the introduction of a rigid boundary, where the wave packets can be refiected elastically. We study Rossby wave packet dynamics at high latitudes on a modified ß-plane, where the second derivative of the Coriolis parameter with respect to latitude is taken into account (d-term). We show that under certain conditions synoptic-scale wave packets can propagate far distances along an east-west oriented \"coast\" and may affect the fiow far downstream of the source region. In contrast to free propagating Rossby wave packets ( e.g. in the atmosphere), which can be trapped between two turning latitudes, the wave packets considered here are trapped between a turning latitude and the reflecting boundary. lt turns out that the 6-term is most important for wave packets with negative phase speeds. Finally, we suggest that such a selective Rossby waveguide may play a role in the dynamics of the Antarctic Circumpolar Current.

The spatial stability of hypersonic conical boundary layers is investigated utilizing different numerical techniques. First, the development and verification of a Linearized Compressible Navier-Stokes solver (LinCS) is presented, followed by an investigation of different effects that affect the stability of the flow in free-flight/ground tests, such as: high-enthalpy effects, wall-temperature ratio, and three-dimensionality (i.e. angle-of-attack). A temporally/spatially high-order of accuracy parallelized Linearized Compressible Navier-Stokes solver in disturbance formulation was developed, verified and employed in stability investigations. Herein, the solver was applied and verified against LST, PSE and DNS, for different hypersonic boundary-layer flows over several geometries (e.g. flat plate - M=5.35 & 10; straight cone - M=5.32, 6 & 7.95; flared cone - M=6; straight cone at AoA = 6 deg - M=6). The stability of a high-enthalpy flow was investigated utilizing LST, LinCS and DNS of the experiments performed for a 5 deg sharp cone in the T5 tunnel at Caltech. The results from axisymmetric and 3D wave-packet investigations in the linear, weakly, and strongly nonlinear regimes using DNS are presented. High-order spectral analysis was employed in order to elucidate the presence of nonlinear couplings, and the fundamental breakdown of second mode waves was investigated using parametric studies. The three-dimensionality of the flow over the Purdue 7 deg sharp cone at M=6 and AoA =6 deg was also investigated. The development of the crossflow instability was investigated utilizing suction/blowing at the wall in the LinCS/DNS framework. Results show good agreement with previous computational investigations, and that the proper basic flow computation/formation of the vortices is very sensitive to grid resolution.

Thesis (Ph. D.)--University of Texas at Austin, 2009. / Title from PDF title page (University of Texas Digital Repository, viewed on Aug. 6, 2009). Vita. Includes bibliographical references.

xiv, 195 p. : ill. (some col.) A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / We explore the reconstruction of B-state vibrational wave packets in I 2 from simulated two-color nonlinear wave packet interferometry data. As a simplification of earlier proposals, we make use of different vibrational energy ranges in the B-state--rather than different electronic potential surfaces--for the short-pulse preparation and propagation of both target and reference wave packets. Numerical results from noisy interferograms indicate that experimental reconstruction should be possible with high fidelity (>0.99). Time-resolved coherent nonlinear optical experiments on small molecules in low-temperature host crystals are exposing valuable information on quantum mechanical dynamics in condensed media. We make use of generic features of these systems to frame two simple, comprehensive theories that will enable the efficient calculation of their ultrafast spectroscopic signals and support their interpretation in terms of the underlying chemical dynamics. Both treatments rely on the identification of normal coordinates to unambiguously partition the well-structured guest-host complex into a system and a bath and expand the overall wave function as a sum of product states between fully anharmonic vibrational basis states for the system and approximate Gaussian wave packets for the bath degrees of freedom. The theories exploit the fact that ultrafast experiments typically drive large-amplitude motion in a few intramolecular degrees of freedom of higher frequency than the crystal phonons, while these intramolecular vibrations indirectly induce smaller-amplitude--but still perhaps coherent--motion among the lattice modes. The equations of motion for the time-dependent parameters of the bath wave packets are fairly compact in a fixed vibrational basis/Gaussian bath (FVB/GB) approach. An alternative adiabatic vibrational basis/Gaussian bath (AVB/GB) treatment leads to more complicated equations of motion involving adiabatic and nonadiabatic vector potentials. Numerical tests of the FVB/GB are presented. We consider two bilinearly coupled harmonic oscillators with varying coupling strengths and initial conditions and show that the mixed quantum/semiclassical theory compares favorably with the exact results. Linear absorption spectra and wave-packet interferometry signals calculated using the theory are presented. This dissertation includes previously published coauthored material. / Committee in charge: David Herrick, Chairperson, Chemistry; Jeffrey Cina, Advisor, Chemistry; Thomas Dyke, Member, Chemistry Michael Kellman, Member, Chemistry; Hailin Wang, Outside Member, Physics

In this thesis, we present a theoretical investigation of reactive processes involving the HeH$^+$ molecular ion, with applications in laboratory and astrophysical plasma physics. We consider in particular two processes, which are the charge transfer in H + He$^+$ collisions at low energy from a molecular approach and the photodissociation of HeH$^+$.<p><p>At the molecular level, the cross section is the basic quantity that has to be determined in order to achieve an understanding of reactive processes. Its calculation will be based on the description of the reactions using an emph{ab initio}, quantum mechanical approach. In this work, we will rely on the Born-Oppenheimer approximation, which allows the molecular motion to be separated into an electronic and a nuclear motion. The evaluation of cross sections then follows two steps.<p>The first is the determination of the electronic structure of the molecule. We will calculate the adiabatic potential energy curves of the excited electronic states as well as the dipole matrix elements between these states. The non-adiabatic radial and rotational couplings, which result from the breakdown of the Born-Oppenheimer approximation, are also estimated. The second step is to solve the nuclear motion, which we achieve using a time-dependent method based on the propagation of wave packets on the coupled electronic states. <p><p>A particular emphasis will be put on the importance of the excited states and of the non-adiabatic couplings in the description of reactive processes. <p>In the treatment of the charge transfer reaction between H and He$^+$ in excited states, it is well known that the non-adiabatic radial couplings cannot be neglected. However, we will show that the inclusion of the non-adiabatic rotational couplings is also necessary in order to obtain accurate state-to-state cross sections.<p>In the description of the photodissociation of HeH$^+$ from its ground state, we will show the influence of the excited states on the rate constant and the role of the non-adiabatic radial couplings in the determination of partial cross sections.<p>We will also consider the possible astrophysical applications of the first triplet state of HeH$^+$. We will show that this state is metastable by evaluating its lifetime, and calculate the cross sections and rate constants for the photodissociation and radiative association of HeH$^+$ in this state.<p> / Doctorat en Sciences / info:eu-repo/semantics/nonPublished