Green's functions

In this thesis we have introduced and extensively studied a model for describing some essential non-equilibrium transport properties of a quantum system with reduced dimensionality. The problem of finding some of the kinetic characteristics of such a model system is formulated as that of finding a solution of a tunneling Hamiltonian with a Hubbard term. To solve this Hamiltonian we first make use of the path integral formalism, generalized for systems far from equilibrium, to perform the quantum-statistical average. The spectral function for the electrons in the well is calculated for different relevant sets of parameters. The possible presence of a Kondo peak in the interacting density of states is discussed. We calculate the frequency-driven conductance and energy losses in the linear response approximation. Numerical simulations of the general expressions show that for a given set of parameters consistent with the particular physical situation of interest, a resonant behavior is obtained for both the conductance and energy absorption for external frequencies equal to the Coulomb repulsion energy E(C).

An acoustic compliant coating is applied on a fluid-loaded structure to control the radiated pressure, by decoupling the fluid medium from the vibrating surface. In this thesis the problem of an infinite cylindrical shell immersed in a fluid and entirely covered with an acoustic compliant layer, excited either by a ring force or an incident acoustic plane wave is considered. To model this problem two different approaches are used. The first one, which is available in the literature, is based on multi-layer shell theory. In this approach the scalar and the vector potential formulation are used to solve for the response and the scattering from the cylinder. The second approach is based on modeling the compliant layer by a normally reacting impedance layer on the surface of the shell. The velocity response Green's function of the shell is found using the hybrid numerical/analytical method. Results for the radiated and scattered pressure from the shell are also presented. The advantage of this second approach is that it can be used to model complex coating geometries. The results obtained with both approaches are compared.

Sound propagation in a waveguide is greatly dependent on the acoustic properties of the boundaries. The effect of these properties can be described by a bottom reflection coefficient RB, and surface reflection coefficient RS. Two methods for estimating reflection coefficients are used in this research. The first, the ratio method, is based on the variations of the Green's function with depth utilizing the ratio of the wavenumber spectra at two depths. The second, the pole method, is based on the wavenumbers of the modal peaks in the spectrum at a particular depth. A method to invert for sound speed and density is also examined. Estimates of RB and RS based on synthetic data by the ratio method were very close to their predicted values, especially for higher frequencies and longer apertures. The pole method returned less precise estimates though with longer apertures, the estimates were better. Using experimental data, results of the pole method as well a geoacoustic inversion technique based on them were mixed. The ratio method was used to estimate RS based on the actual data and returned results close to the predicted phase of p.