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A new technique is presented to study radio propagation and rough surface scattering problems based on a reformulation of the Magnetic Field Integration Equation (MFIE) called the Single-Scatter Subtraction (S^3) method. This technique amounts to a physical preconditioning by separating the single- and multiple-scatter currents and removing the single-scattering contribution from the integral term that is present in the MFIE. This requires the calculation of a new quantity that is the kernel of the MFIE integral call the kernel integral or Gbar. In this work, 1-dimensional deterministically rough surfaces are simulated by surfaces consisting of single and multiple cosines. In order to truncate the problem domain, a beam illumination is used as the source term and it is shown that this also causes the kernel integral to have a finite support. Using the Single Scatter Subtraction method on these surfaces, closed-form expressions are found for the kernel integral and thus the single-scatter current for a well defined region of validity of surface parameters which may then be efficiently radiated into the far field numerically. Both the closed-form expressions, and the computed radiated fields are studied for their physical significance. This provides a clear physical intuition for the technique as an augmentation to existing ones as a bent-plane approximation as shown analytically and also validated by numeric results. Further analysis resolves a controversy on the nature of Bragg scatter which is found to be a multiple-scatter phenomenon. Error terms present in the kernel integral also raise new questions on the effect of truncation for any MFIE-based solution. Additionally, a dramatic enhancement of backscatter predicted by this new approach versus the Kirchhoff method is observed as the angle of incidence increases due to the error terms. / Doctor of Philosophy / A new technique is presented to study the interaction of electromagnetic waves with rough surfaces. Building on the technique called the Magnetic Field Integral Equation (MFIE) which allows the solution for the electromagnetic fields scattered from the surface by considering only the induced electric and magnetic currents on the surface, the Single-Scatter Substraction (S 3 ) method separates the surface currents into those that interact with the surface only once or single-scatter, and those that interact multiple times called multiple-scatter. Since this is the introduction of this technique, only the former is investigated. In this study, a new quantity which is an integral of one of the components of the standard MFIE is studied and closed-form approximations are presented along with bounds of validity. This provides closed form solutions for the single-scattering currents, from which the radiated fields may be efficiently found numerically. Since they are closed form, the expressions provide insight into the nature of the physical scattering process. Numerical results of these expressions are compared to the standard approximate technique as well as the ”exact” solution found by numerically solving the MFIE. Compared to the standard approximate technique which approximates the surface by a tangent plane at each point on the surface, the single-scatter currents approximate the surface with a bent-plane at each point. This shifts the scattered fields from certain directions to others, and highlights where single- and multiple-scattering have an effect.

A poroelastic finite element formulation originally derived for modeling porous absorbing material in air is adapted to the problem of acoustic scattering from a poroelastic seafloor with a one-dimensional randomly rough interface. The developed formulation is verified through calculation of the plane wave reflection coefficient for the case of a flat surface and comparison with the well known analytical solution. The scattering strengths are then obtained for two different sets of material properties and roughness parameters using a Monte Carlo approach. These numerical results are compared with those given by three analytic scattering models---perturbation theory, the Kirchhoff approximation, and the small-slope approximation---and from those calculated using two finite element formulations where the sediment is modeled as an acoustic fluid. / text

The aim of this work has been to make use of surface scattering techniques to study soft matter at interfaces. The work presented herein is composed of two distinct bodies of work. The first comprises a fundamental study of the physical and structural properties of Langmuir monolayers composed of sulfobetaine surfactants. Physiochemical properties of the films have been investigated through the use of Langmuir trough techniques. This has been used to support x-ray and neutron reflectometry data, from which structural parameters were derived. The second body of work involves attempts to find and/or characterize novel ways of aligning proteins at interfaces. Soluble proteins at lipid interfaces have been characterized in terms of their interactions with functionalized lipid monolayers. Specific interactions have been utilized to adsorb protein layers at the interface through interactions with His-tag chelating lipids within the monolayer. These have been characterized using neutron reflectometry and quartz crystal microbalance studies. Work has also been completed to design a suitable system for the adsorption of membrane proteins. This has involved aligning phospholipid bilayer nanodiscs at the lipid interface and subsequent characterization through neutron reflectometry.

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The Method of Ordered Multiple Interactions provides a numerical solution to the integral<br />equations describing surface scattering which is both computationally efficient and reliably<br />convergent. The method has been applied in a variety of ways to solving the electromagnetic<br />scattering from perfectly-conducting rough surfaces. A desire to more accurately predict<br />the scattering from natural terrain has led to the representation of the surface material as<br />penetrable instead of conductive.<br /><br />For this purpose, the Method of Ordered Multiple Interactions is applied to numerically<br />solve the electromagnetic scattering from randomly-rough dielectric surfaces. A primary<br />consequence of the penetrable surface material is the introduction of a pair of coupled integral equations in place of the single integral equation used to solve the problem with a perfectly conducting surface. The method is tested and analyzed by developing independent scattering solutions for canonical cases in a transform domain and by comparing results with solutions from other techniques.<br /><br />The dielectric implementation of the Method of Ordered Multiple Interactions is used to solve<br />the electromagnetic scattering from a class of randomly-rough dielectric surfaces. This allows<br />for the characterization of the effect of a number of transmitter and surface parameters in the<br />scattering problem, observing bistatically and also specifically in the backscatter direction.<br /><br />MOMI is then applied as a method to examine subsurface penetration characteristics from<br />a similar family of rough surfaces. Characteristics of the environment parameters and the<br />scattered field itself are examined, and the numerical challenges associated with observing<br />beneath the surface are identified and addressed.<br /><br />The Method of Ordered Multiple Interactions is then incorporated as a major component of<br />a larger solution which computes the total scattering when a dielectric object is buried just<br />beneath the rough surface. This hyrid approach uses MOMI and the Method of Moments to<br />iteratively account for multiple interactions between the target and the dielectric interface,<br />enabling the study of scattering from the combined environment of a rough surface and the<br />embedded object, as well as the individual scattering events which combine to form the<br />steady-state solution. / Ph. D.

Radio propagation models provide an estimate of the power loss in a communication link caused by the surface of the ground, atmospheric refraction, foliage, and other environmental factors.  Many of the models rely on digital topographic databases to provide information about the terrain, and generally the databases are sparsely sampled relative to the electromagnetic wavelengths used for communication systems.  This work primarily develops a technique to evaluate the effects of that sparsity on the uncertainty of propagation models. That is accomplished by accurately solving the electromagnetic fields over many randomly  rough surfaces which pass through the sparse topographic data points, many possible communication links, all of which fit the underlying data, are represented.  The power variation caused by the different surface realizations is that due to the sparse sampling. Additionally, to verify that this solution technique is a good model, experimental propagation measurements were taken, and compared to the computations. / Master of Science