<p>A theoretical framework for calculating electron transport through molecular junctions is presented. It is based on scattering theory using a Green's function formalism. The model can take both elastic and inelastic scattering into account and treats chemical and physical bonds on equal footing. It is shown that it is quite reliable with respect to the choice of functional and basis set. Applications concerning both elastic and inelastic transport are presented, though the emphasis is on the inelastic transport properties. The elastic scattering application part is divided in two part. The first part demonstrates how the current magnitude is strongly related to the junction width, which provides an explanation why experimentalists get two orders of magnitude differences when performing measurements on the same type of system. The second part is devoted to a study of how hydrogenbonding affects the current-voltage (I-V) characteristics. It is shown that for a conjugated molecule with functional groups, the effects can be quite dramatic. This shows the importance of taking possible intermolecular interactions into account when evaluating and comparing experimental data. The inelastic scattering part is devoted to get accurate predictions of inelastic electron tunneling spectroscopy (IETS) experiments. The emphasis has been on elucidating the importance of various bonding conditions for the IETS. It is shown that the IETS is very sensitive to the shape of the electrodes and it can also be used to discriminate between different intramolecular conformations. Temperature dependence is nicely reproduced. The junction width is shown to be of importance and comparisons between experiment as well as other theoretical predictions are made.</p>

Thesis (Ph. D.)--University of California, Riverside, 2009. / Includes abstract. Title from first page of PDF file (viewed March 12, 2010). Available via ProQuest Digital Dissertations. Includes bibliographical references (p. 117-136). Also issued in print.

Elastic Wave propagation in structures with irregular boundaries is studied by transforming the plates with irregular surfaces to sinusoidal wave-guides. Guided elastic wave in a two-dimensional periodically corrugated plate is studied analytically. The plate material is considered as homogeneous, isotropic and linearly elastic. In a periodically corrugated wave-guide, all possible spectral orders of wave numbers are considered. The dispersion equation is obtained by applying the traction free boundary conditions at the two surfaces. The analysis is carried out in the wave-number domain for both symmetric and anti-symmetric modes. Non-propagating 'stop bands' and propagating 'pass bands' are investigated. Experimental analyses with two different pairs of transducers are also performed and compared with the results from the mathematical analysis. Newly developed semi-analytical DPSM technique has been also adopted in this dissertation to model the ultrasonic field in sinusoidally corrugated plate. Distributed Point Source Method (DPSM) is gradually gaining popularity in the field of Non-Destructive Evaluation (NDE). DPSM can be used to calculate the ultrasonic field (pressure, velocity and displacement in a fluid or stress and displacement in a solid) generated by ultrasonic transducers. So far the technique has been used to model ultrasonic field in homogeneous or multilayered fluid structures. In this dissertation the method is extended to model the ultrasonic field generated in both fluid and solid media. The Prime objective of using DPSM technique in this dissertation is to model the ultrasonic field generated in the corrugated wave guide. This method has never been used to model ultrasonic field in solids. Development of stress and displacement Green's functions in solids are presented. In addition to the wave propagation problem in the sinusoidal wave guide, a few unsolved problems such as ultrasonic field generated by bounded acoustic beams in multilayered fluid structures, near a fluid-solid interface and in flat solid isotropic plates are also presented in this dissertation.

An approximate of the Green's function can be obtained by taking the cross-correlation of ambient noise that has been simultaneously recorded on separate sensors. This method is applied for two experiments, which illustrate the advantages and challenges of this technique. The first experiment is in the ultrasonic regime [5-30] MHz and uses capacitive micromachined ultrasonic transducer arrays to image the near field and compares the passive imaging to the conventional pulse-echo imaging. Both the array and target are immersed in a fluid with the sensors recording the fluid's random thermal-mechanical motion as the ambient noise. The second experiment is a passive ocean monitoring experiment, which uses spatiotemporal filtering to rapidly extract coherent arrivals between two vertical line arrays. In this case the ambient noise in the frequency band [250 1500] Hz is dominated by non-stationary shipping noise. For imaging purposes, the cross-correlation needs to extract the Green's function so that the imaging can be done correctly. While for monitoring purposes, the important feature is the change in arrivals, which corresponds to the environment changing. Results of both experiments are presented along with the advantages of this passive method over the more accepted active methods.

We consider the motion of a Brownian particle trapped in an arbitrary bounded two or three-dimensional domain, whose boundary is reflecting except for a small absorbing window through which the particle can escape. We use the method of matched asymptotic expansions to calculate the mean first passage time, defined as the time taken for the Brownian particle to escape from the domain through the absorbing window. This is known as the narrow escape problem. Since the mean escape time diverges as the window shrinks, the calculation is a singular perturbation problem. We extend our results to include N absorbing windows of varying length in two dimensions and varying radius in three dimensions. We present findings in two dimensions for the unit disk, unit square and ellipse and in three dimensions for the unit sphere. The narrow escape problem has various applications in many fields including finance, biology, and statistical mechanics.

The purpose of this thesis is to report a theoretical investigation on the current-current correlation and noise in the tmnsient quantum transport regime. In particular, we calculate current correlations when the bias voltage of a LDL quantum device is suddenly turned off. Namely, we consider the situation that when time t < 0 the device is in a steady-state under bias Vb, when t > 0 the bias is turned off to zero. Under such a bias, the transport current l goes from a finite steady-state value 10 at t < 0 to zero at large times. When electronic structure of the leads as well as well as the device scattering region are to be taken into account, it is a difficult problem to calculate the time dependent current-current correlation. However, for the sharp step-down bias shape, we discover that the time-dependent problem can be solved exactly for non-interacting systems.

We consider the motion of a Brownian particle trapped in an arbitrary bounded two or three-dimensional domain, whose boundary is reflecting except for a small absorbing window through which the particle can escape. We use the method of matched asymptotic expansions to calculate the mean first passage time, defined as the time taken for the Brownian particle to escape from the domain through the absorbing window. This is known as the narrow escape problem. Since the mean escape time diverges as the window shrinks, the calculation is a singular perturbation problem. We extend our results to include N absorbing windows of varying length in two dimensions and varying radius in three dimensions. We present findings in two dimensions for the unit disk, unit square and ellipse and in three dimensions for the unit sphere. The narrow escape problem has various applications in many fields including finance, biology, and statistical mechanics.

Errata inserted inside back end-paper. / Bibliography: p. 243-249. / xvi, 249 p. : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis presents a brief overview of microstrip antenna analysis and describes the connections between spectral and spatial domain periodic Green's functions in integral equation methods. A hybrid formulation is applied to a variety of problems from simple metal strip dipoles to more complicated microstrip geometries. A further development to finite array analysis is described. An improvement in the accuracy of this approximative technique is explored. / Thesis (Ph.D.)--University of Adelaide, Dept. of Electrical and Electronic Engineering, 1997

Errata inserted inside back end-paper. / Bibliography: p. 243-249. / xvi, 249 p. : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis presents a brief overview of microstrip antenna analysis and describes the connections between spectral and spatial domain periodic Green's functions in integral equation methods. A hybrid formulation is applied to a variety of problems from simple metal strip dipoles to more complicated microstrip geometries. A further development to finite array analysis is described. An improvement in the accuracy of this approximative technique is explored. / Thesis (Ph.D.)--University of Adelaide, Dept. of Electrical and Electronic Engineering, 1997

Thesis (C.E.)--Lehigh University, 1888. / Manuscript. Also available online.