Brazing and soldering, as advanced manufacturing processes, are of significant importance to industrial applications. It is widely accepted that joining by brazing or soldering is possible if a liquid metal wets the solids to be joined. Wetting, hence spreading and capillary action of liquid metal (often called filler) is of significant importance. Good wetting is required to distribute liquid metal over/between the substrate materials for a successful bonding. Topographically altered surfaces have been used to exploit novel wetting phenomena and associated capillary actions, such as imbibitions (a penetration of a liquid front over/through a rough, patterned surface). Modification of surface roughness may be considered as a venue to tune and control the spreading behavior of the liquids. Modeling of spreading of liquids on rough surface, in particular liquid metals is to a large extent unexplored and constitutes a cutting edge research topic. In this dissertation the imbibitions of liquid metal has been considered as pertained to the metal bonding processes involving brazing and soldering fillers. First, a detailed review of fundamentals and the recent progress in studies of non-reactive and reactive wetting/capillary phenomena has been provided. An imbibition phenomenon has been experimentally achieved for organic liquids and molten metals during spreading over topographically modified intermetallic surfaces. It is demonstrated that the kinetics of such an imbibition over rough surfaces follows the Washburn-type law during the main spreading stage. The Washburn-type theoretical modeling framework has been established for both isotropic and anisotropic non-reactive imbibition of liquid systems over rough surfaces. The rough surface domain is considered as a porous-like medium and the associated surface topographical features have been characterized either theoretically or experimentally through corresponding permeability, porosity and tortuosity. Phenomenological records and empirical data have been utilized to verify the constructed model. The agreement between predictions and empirical evidence appears to be good. Moreover, a reactive wetting in a high temperature brazing process has been studied for both polished and rough surfaces. A linear relation between the propagating triple line and the time has been established, with spreading dominated by a strong chemical reaction.

abstract: Scattering from random rough surface has been of interest for decades. Several methods were proposed to solve this problem, and Kirchho approximation (KA) and small perturbation method (SMP) are among the most popular. Both methods provide accurate results on rst order scattering, and the range of validity is limited and cross-polarization scattering coecient is zero for these two methods unless these two methods are carried out for higher orders. Furthermore, it is complicated for higher order formulation and multiple scattering and shadowing are neglected in these classic methods. Extension of these two methods has been made in order to x these problems. However, it is usually complicated and problem specic. While small slope approximation is one of the most widely used methods to bridge KA and SMP, it is not easy to implement in a general form. Two scale model can be employed to solve scattering problems for a tilted perturbation plane, the range of validity is limited. A new model is proposed in this thesis to deal with cross-polarization scattering phenomenon on perfect electric conducting random surfaces. Integral equation is adopted in this model. While integral equation method is often combined with numerical method to solve the scattering coecient, the proposed model solves the integral equation iteratively by analytic approximation. We utilize some approximations on the randomness of the surface, and obtain an explicit expression. It is shown that this expression achieves agreement with SMP method in second order. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2017

In this study, the properties of the reflected paths and scattering phenomena were investigated in the LMDS band (28 GHz). We used the newly developed sampling swept time delay short pulse (SSTDSP) sounder to collect field data in certain locations on the Virginia Tech campus. The sounder collected the channel impulse response analog waveform, sampled, digitized and reconstructed it. The stored data were used to produce the power delay profile and other channel parameters. In particular, we collected scattered and reflected data regarding the channel response with different incident angle and distance set-ups from brick and limestone walls. We used the reflected pulse width and maximum excess delay derived from each power delay profile to analyze the rough surface scattering phenomena. We found that limestone and brick walls exhibited some diffuse scattering. The reflected pulse of a limestone wall had more maximum excess delay spread than did a brick wall at -15dB power threshold. The mean maximum excess delay for the reflected pulse of the limestone wall measurement set-ups was more than two times that of the brick wall. With equal transmitter and receiver distances to the wall, we found that as the incident angle increased, the maximum excess delay decreased but the perpendicular reflection coefficient increased. It is recommended that for future study, a second generation SSTDSP sounder will replicate the measurement with larger distance and angle set-ups as well as in non-line-of-sight areas. / Master of Science

No description available.

No description available.

We study the spontaneous edge current of chiral superconductors with high chirality both in the absence and presence of Meissner screening. We compute the edge current from a self-consistent solution to a set of coupled equations: quasiclassical Eilenberger equation, superconducting gap equation, and Maxwell equation. We find that the spatial dependent chiral edge current is largely suppressed and has more nodes for higher chirality pairings. In the absence of Meissner screening, the integrated current at T=0 is zero for all higher chirality pairings; while it is substantial for chiral p-wave. This conclusion is consistent with previous studies. In contrast, at finite T, the integrated current is non-zero even for higher chiral pairings. It turns out that the spatial varying order parameter is crucial to understand this finite T behavior of the edge current. When Meissner screening is included, the magnitude of the edge currents is reduced for all chiral pairings; however, the reduction is much weaker in higher chirality cases. We conclude that the Meissner effect is not that important for higher chiral pairings. We also consider the effect of the rough surface on the edge current. The edge current of even chiral pairings is inverted by the strong surface roughness; however, that of the odd chiral pairings is not. The sub-dominant order parameters, induced by the surface, are the key to understanding this current inversion. / Thesis / Master of Science (MSc)

The aerodynamic flow and fluctuating surface pressure of a plane, turbulent, two-dimensional wall jet flow into still air over smooth and rough surfaces has been investigated in a recently constructed wall jet wind tunnel testing facility. The facility has been shown to produce a wall jet flow with Reynolds numbers based on the momentum thickness, Re<SUB>&delta</SUB> = &deltaU<SUB>m</SUB>/&nu, of between 395 and 1100 and nozzle exit Reynolds numbers, Re<SUB>j</SUB> = U<SUB>m</SUB>b/&nu, of between 16000 and 45000. The wall jet flow properties (&delta, &delta<SUP>*</SUP>, &theta, y<SUB>1/2</SUB>, U<SUB>m</SUB>, u<SUP>*</SUP>, etc.) were measured and characterized over a wide range of initial flow conditions and measurement locations relative to the wall jet source. These flow properties were measured for flow over a smooth flow surface and for flow over roughness patches of finite extent. The patches used in the current study varied in length from 305 mm to 914 mm (between 24 and 72 times the nozzle height, b) and were placed so that the leading edge of the patch was fixed at 1257 mm (x/b = 99) downstream of the wall jet source. These roughness patches were of a random sand grain roughness type and the roughness grain size was varied throughout this experiment. The tests covered roughness Reynolds numbers (k<SUP>+</SUP>) ranging from less than 2 to over 158 (covering the entire range of rough wall flow regimes from hydrodynamically smooth to fully rough). For the wall jet flows over 305 mm long patches of roughness, the displacement and momentum thicknesses were found to vary noticeably with the roughness grain size, but the maximum velocity, mixing layer length scale, y<SUB>/2</SUB>, and the boundary layer thickness were not seen to vary in a consistent, determinable way. Velocity spectra taken at a range of initial flow conditions and at several distinct heights above the flow surface showed a limited scaling dependency on the skin friction velocity near the flow surface. The spectral density of the surface pressure of the wall jet flow, which is not believed to have been previously investigated for smooth or rough surfaces, showed distinct differences with that seen in a conventional boundary layer flow, especially at low frequencies. This difference is believed to be due to the presence of a mixing layer in the wall jet flow. Both the spectral shape and level were heavily affected by the variation in roughness grain size. This effect was most notable in overlap region of the spectrum. Attempts to scale the wall jet surface pressure spectra using outer and inner variables were successful for the smooth wall flows. The scaling of the rough wall jet flow surface pressure proved to be much more difficult, and conventional scaling techniques used for ordinary turbulent boundary layer surface pressure spectra were not able to account for the changes in roughness present during the current study. An empirical scaling scheme was proposed, but was only marginally effective at scaling the rough wall surface pressure. / Ph. D.

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

Les propriétés de surface, particulièrement microgéométriques, jouent un rôle essentiel dans tous les systèmes tribologiques. L’analyse de la répartition des efforts de contact dans l’interface entre surfaces rugueuses est indispensable à la prédiction du frottement, de l'usure, de l'adhérence, des résistances de contact électrique et thermique… De nombreux modèles ont été proposés ces dernières décennies pour prédire les efforts entre aspérités de surfaces rugueuses. Parmi ces modèles, les modèles statistiques sont majoritairement développés en considérant le contact ente une surface rugueuse équivalente, la surface somme - qui tient compte des microgéométries des deux surfaces en contact ainsi que de leur matériau - et un plan lisse. Cependant la validité de cette modélisation n’a pas été clairement démontrée. L’objectif de notre étude a été de développer un modèle statistique de contact entre deux surfaces rugueuses isotropes aléatoires puis de comparer les résultats obtenus pour ces deux surfaces avec ceux obtenus en considérant la surface somme définie classiquement à partir des deux surfaces rugueuses et un plan lisse. Les différences entre les résultats nous ont amenés à proposer une nouvelle modélisation de la surface somme. / Surface properties, particularly micro-geometry, play a key role in all tribological systems. The analysis of the distribution of contact forces in the interface between rough surfaces is essential for the prediction of friction, wear, adhesion, electrical and thermal contact resistance... Many models have been proposed during the last decades to predict the forces between asperities of rough surfaces. Among these models, statistical models are mainly based on the contact between an equivalent rough surface, the sum surface - which combines micro-geometry of the two surfaces in contact and their material - and a smooth plane. However, the validity of this model has not been clearly demonstrated. The aim of our study was to develop a statistical model of the contact between two random isotropic rough surfaces and then compare the results with those obtained by considering the classical sum surface. The differences between the results have led us to propose a new definition for the sum surface.