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Recent developments in semiconductor physics have led to a new field of study, namely the study of nanostructures. Nanostructures are the future for electronic devices. In this project the conductance of electrons through nanostructures will be considered. The structures examined in this project are similar in design. The goal will be to examine the conductance through these structures.The methodology in use for finding the conductance of a nanostructure is the recursive Green's function method. This includes finding the transverse eigenvalues and eigenfunctions and computing hopping integrals to determine the Green's propagators. The conductance is obtained following these steps. For the numerical calculations a structured FORTRAN computer program was developed.As stated earlier, the future electronic devices will utilize the developments of conductance through components having dimensions on the nanometer scale. These dimensions, theoretically, will allow faster operation and smaller units. The theoretical development of this project will propagate the knowledge and understanding of conductance in this regime. / Department of Physics and Astronomy

This thesis is in the area of ultrasound tomography, which is a non-destructive imaging method that attempts to create quantitative images of the acoustical properties of an object of interest (OI). Specifically, three quantitative images per OI are created in this thesis, two of which correspond to the complex compressibility profile of the OI, and the other corresponds to its density profile. The focus of this thesis is on the development of an appropriate two-dimensional inverse scattering algorithm to create these quantitative images. The core of this algorithm is the Born iterative method that is used in conjunction with a fast and efficient method of moments forward solver, a Krylov subspace regularization technique, and a balancing method. This inversion algorithm is capable of simultaneous inversion of multiple-frequency data, and can handle a large imaging domain. This algorithm is finally tested against synthetic and measured data.

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A number of diffraction problems which have practical applications are examined using the Wiener-Hopf-Hilbert technique. Each problem is formulated as a matrix Wiener-Hopf equation, the solution of which requires the factor~sation of a matrix kernel. Since the determinant of the matrix kernel has poles in the cut plane, the Wiener-Hopf-Hilbert technique is modified to allow the usual arguments to follow through. In each case an explicit matrix factorisation is carried out and asymptotic expressions for the field scattered to infinity are obtained. The first problem solved is that of diffraction by a semi-infinite plane with different face impedances. The solution includes the case of an incident surface wave as well as an incident plane wave for an arbitrary angle of incidence. Graphs of the far-field are provided for various values of the half-plane impedance parameters. The second problem examined is diffraction by a half-plane in a moving fluid. This is solved without restriction on the impedance parameters of the half-plane and includes both the leading edge and trailing edge situations. The final problem is of radiation from an inductive wave-guide. Expressions are obtained for the field radiated at the waveguide mouth and the field reflected in the duct region.

36Ar reaction. The alpha decay width and the total width of this state has been determined. The systematics of T = 2 states in A = 4N nuclei is discussed in connection with this measurement since data are now available on all such nuclei up to mass 44.

A phenomenological description is sought of the dynamics operating in high energy elastic hadron-hadron scattering. The predictions of a simple Pomeron and weak cut model of high energy elastic scattering are compared with the new and surprising ρ̄ρ data from the ISR and Sρ̄ρS Collider. The model, which gives a complete account of all the lower energy data, is incompatible with the unexpected energy dependence of the differential cross-section shown by the Collider data. Modifications within the original framework of the model are examined but found inadequate and it is concluded that new contributions are necessary. Two avenues are explored as likely candidates for the correct approach. The first approach considered is the possible existence of a small odd charge conjugation term with constant or increasing contribution to the cross-section. Two existing models of such an "Odderon" effect are studied which give good agreement with the new data but neither of which are entirely satisfactory. A reggeized Odderon contribution, analagous to these models, is examined and limitations are placed on its effect. The second possibility considered as a description of the additional contributions to the model are the correction terms necessary to prevent the violation of unitarity and the breaking of asymptotic bounds. An eikonalization model, in which a-channel unitarity is explicitly satisfied, is reviewed but several theoretical problems emerge due to the nature of the basic exchange and the model gives a relatively poor description of the data. A" similar model in which the born term is described by a Pomeron with the appropriate Regge phase is developed. This clears up some of the theoretical problems but is found to exaggerate the problems encountered in fitting the data and it is concluded that such an eikonal description is unlikely to work. A simple model of the unitarity corrections which gives a better chance of reproducing the data is proposed. The results of the phenomenology of the asymptotic and perturbative Reggeon field theory approaches to elastic scattering are briefly reviewed.

This thesis describes work on the problem of the scattering of water waves by fixed objects. The method used to solve this problem is that of finite and infinite elements. In particular the development of a new wave infinite element is described. Various aspects of the wave scattering problem are considered, but always from the perspective of the numerical methods, the algorithms and the computer implementations used. These deal not only with the modelling of the wave equations, but also the pre and post processing of the finite element algorithms. This encompasses the generation of suitable finite element meshes, in an accurate and economical way, and the presentation of the results, particularly as accurate contour plots of the wave surface. The first two chapters gives a brief introduction to water waves, and a summary of the basic concepts of finite and infinite elements. In the third chapter the new infinite element for waves, which is a development of an earlier infinite element, is described in detail, including the new mapping, the necessary shape functions and the integration of the element matrix. The earlier infinite element was restricted to the exterior of circular problems. For scattering objects of large aspect ratio this led to meshes with many finite elements, which performed no useful function, and which were computationally wasteful. The mapping in the new infinite element allows the mesh of infinite elements to be tailored to the shape of the diffracting body, without any observed loss of accuracy. It is therefore much more flexible and computationally efficient, because the infinite elements no longer need to be placed radially. The next three chapters, concentrate on the computer science aspects of the implementation of the finite and infinite elements dealing with the linked list data structures for storage of the element information, the special purpose mesh generation programs, which make it possible to analyse a large range of practical scattering problems and the plotting programs for the display of the results. The chief work in chapter six is the implementation of the Akin and Grey accurate predictor-corrector contour plotting algorithm, with colour fill. The advantage of an accurate contour plotting algorithm is that any discontinuities in the contours represent discontinuities in the results, rather than plotting deficiencies. Chapter seven shows results which validate the new infinite element, particularly on the problem of waves diffracted by an ellipse. In the remaining chapters eight to eleven, the emphasis is on a practical problem of the wave forces on groups of risers, which are the tubes which carry hydrocarbons from the sea-bed to the working areas of offshore platforms. The aim was to see if the forces on a group of risers were different from the sum of the forces on the individual risers, calculated on the assumption that the risers do not modify the wave field. The conclusion is that more detailed studies may well bring financial benefits to the companies operating offshore installations.

Two related lines of research in experimental electron density determination are reported in this thesis. In the first case, the well-proven and popular multipole modeling technique is applied to three high resolution, single-crystal X-ray diffraction data sets. The preliminary part of this thesis (Chapters 2-5) deals with the theoretical aspects of the multipole model, and also some of the theoretical and practical aspects of data collection and reduction. Chapter 6 reports an experimental charge density determination of a nitrogen ylide. Chapter 7 contains details of the treatment of data from a large, pendant-arm macrocyclic complex of nickel, while Chapter 8 reports the characteristics of the experimentally determined charge density for a substituted acetylene molecule which exhibits interesting intramolecular interactions. The charge densities for all three cases are analysed using Bader's Theory of Atoms in Molecules. The latter part of this thesis deals with more novel ways of treating experimental data. Chapter 9 gives a thorough review of the literature on the application of Maximum Entropy techniques to image reconstruction in general and charge density determination in particular, followed in Chapter 10 by an application to diffraction data from the cubic phase of acetylene. The novel approach of removing core scattering from the data is developed and gives improved results. Chapter 11 reviews some aspects of fermion density matrices and their relationship to electron density functions and X-ray scattering, followed in Chapter 12 by results from the density matrix refinement method applied to diffraction data from formamide. Particular emphasis is placed upon basis set effects, idempotency and various N-representable approximations to the experimentally determined density matrix.