In this work we study vertical, acoustic propagation in a non-homogeneous media for a spatially-compact, time-harmonic source. An analytical, 2-layer model is developed representing the acoustic pressure disturbance propagating in the atmosphere. The validity of the model spans the distance from the Earth's surface to 30,000 meters. This includes the troposphere (adiabatic), ozone layer (isothermal), and part of the stratosphere (isothermal). The results of the model derivation in the adiabatic region yield pressure solutions as Bessel functions of the First (J) and Second (Y) Kind of order $-\frac{7}{2}$ with an argument of $2 \Omega \tau$ (where $\Omega$ represents a dimensionless frequency and $\tau$ is a dimensionless vertical height in z (vertical coordinate)). For an added second layer (isothermal region), the pressure solution is a decaying sinusoidal, exponential function above the first layer. In particular, the vertical, acoustic propagation is examined for various configurations. These are divided into 2 basic classes. The first class consists of examining the pressure response function when the source is located on boundary interfaces, while the second class consists of situations where the source is arbitrarily located within a finite layer. In all instances, a time-harmonic, compact source is implicitly understood. However, each class requires a different method of solution. The first class conforms to a general boundary value problem, while the second requires the use of Green's functions method. In investigating problems of the first class, 3 different scenarios are examined. In the first case, we apply our model to a semi-infinite medium with a time-harmonic source ($e^{-i \omega t}$) located on the ground. In the next 2 cases, a semi-infinite medium is overlain on the previous medium at a height of z=13,000 meters. Thus, there exist two boundaries: the ground and the layer interface between the 2 media. Sources placed at these interfaces represent the 2nd and 3rd scenarios, respectively. The solutions to all 3 cases are of the form $A \frac{J_{-\frac{7}{2}}(2 \Omega \tau)}{{\tau}^{-\frac{7}{2}}} + B \frac{Y_{-\frac{7}{2}}(2 \Omega \tau)}{{\tau}^{-\frac{7}{2}}}$, where \textit{A} and \textit{B} are constants determined by the boundary conditions. For the 2nd class, we examine the application to a time-harmonic, compact source placed arbitrarily within the 1st layer. The method of Green's functions is used to obtain a particular solution for the model equations. This result is compared with a Fast Field Program (FFP) which was developed to test these solutions. The results show that the response given by the Green's function compares favorably with that of the FFP. Keywords: Linear Acoustics, Inhomogeneous Medium, Layered Atmosphere, Boundary Value Problem, Green's Function Method

The impact of the spin degree of freedom on the transport properties of electrons traveling through magnetic materials has been known since the pioneer work of Mott [1]. Since then it has been demonstrated that the spin angular momentum plays a key role in the scattering process of electrons in magnetic multilayers. This role has been emphasized by the discovery of the Giant Magnetoresistance in 1988 by Fert and Grunberg [2, 3]. Among the numerous applications and effects that emerged in mesoscopic devices two mechanisms have attracted our attention during the course of this thesis: the spin transfer torque and the spin Hall effects. The former consists in the transfer of the spin angular momentum from itinerant carriers to local magnetic moments [4]. This mechanism results in the current-driven magnetization switching and excitations, which has potential application in terms of magnetic data storage and non-volatile memories. The latter, spin Hall effect, is considered as well to be one of the most fascinating mechanisms in condensed matter physics due to its ability of generating non-equilibrium spin currents without the need for any magnetic materials. In fact the spin Hall effect relies only on the presence of the spin-orbit interaction in order to create an imbalance between the majority and minority spins. The objective of this thesis is to investigate the impact of disorder on spin dependent transport phenomena. To do so, we identified three classes of systems on which such disorder may have a dramatic influence: (i) antiferromagnetic materials, (ii) impurity-driven spin-orbit coupled systems and (iii) two dimensional semiconducting electron gases with Rashba spin-orbit coupling. Antiferromagnetic materials - We showed that in antiferromagnetic spin-valves, spin transfer torque is highly sensitive to disorder, which prevents its experimental observation. To solve this issue, we proposed to use either a tunnel barrier as a spacer or a local spin torque using spin-orbit coupling. In both cases, we demonstrated that the torque is much more robust against impurities, which opens appealing venues for its experimental observation. Extrinsic spin-orbit coupled systems - In disordered metals accommodating spin orbit coupled impurities, it is well-known that spin Hall effect emerges due to spin dependent Mott scattering. Following a recent prediction, we showed that another effect coexists: the spin swapping effect, that converts an incoming spin current into another spin current by "swapping" the momentum and spin directions. We showed that this effect can generate peculiar spin torque in ultrathin magnetic bilayers. Semiconductors spintronics - This last field of research has attracted a massive amount of hope in the past fifteen years, due to the ability of coherently manipulating the spin degree of freedom through interfacial, so-called Rashba, spin-orbit coupling. However, numerical simulations failed reproducing experimental results due to coherent interferences between the very large number of modes present in the system. We showed that spin-independent disorder can actually wash out these interferences and promote the conservation of the spin signal. In the course of this PhD, we showed that while disorder-induced dephasing is usually detrimental to the transmission of spin information, in selected situation, it can actually promote spin transport mechanisms and participate to the enhancement of the desired spintronics phenomenon.

Gaseous pollution has become a global issue and its presence above certain limits is hazardous to human health and environment. Detection of such gases is an immediate need and researchers around the world are trying to solve this problem. Metal oxides are being used as sensing materials for a long time, but a high operating temperature limits applications in many areas. On the other hand, two-dimensional (2D) materials with high surface-to-volume ratio and chemical stability are promising candidates in the field of gas sensing. This includes monolayer transition metal dichalcogenides, such as MoS2 and WS2, which are direct band gap materials. While few layer transition metal dichalcogenides are indirect band gap materials, they are easier to synthesize than monolayers. Therefore, it is important to understand whether few layer transition metal dichalcogenides possess the same sensing behavior as the corresponding monolayers. For this reason the first part of this dissertation compares the sensing behavior of monolayer and few layer MoS2 and WS2. Two dimensional hexagonal boron nitride is a highly stable structural analogue of graphene. However, its insulating behavior with large band gap is not suitable for sensing. Recently, monolayer Si2BN has been proposed to exist. As the presence of Si makes this material reactive, the second part of this dissertation addresses its application as sensing material. In the _nal part of this dissertation, in search of a metal free, non-toxic, and earth abundant sensor material, further structural analogues of graphene are considered, namely monolayer C3N, monolayer C3Si, and monolayer C6BN. In particular, different theoretical approaches for studying the sensing performance of materials are compared to each other.

<div>The widely accepted Non-equilibrium Greens functions (NEGF) method and the Self-Consistent Born Approximation, to include scattering, is employed. Due to the large matrix sizes typically needed when solving Greens functions, an efficient recursive algorithm is typically utilized. However, the current state of the art of this so-called recursive Greens function algorithm only allows the inclusion of local scattering or non-locality within a limited range. Most scattering mechanisms are Coulombic and are therefore non-local. Recently, we have developed an addition to the recursive Greens function algorithm that can handle arbitrary non-locality. Validation and performance will be assessed for nanowires.</div><div><br></div><div>The second half of this work discusses the modeling of an active ingredient in a liquid environment. The state of the art is outlined with options for different modeling approaches - mainly the implicit and the explicit solvation model. Extensions of the explicit model to include an open, quantum environment is the main work of the second half. First results for an extension of the commonly used molecular dynamics with thermodynamic integration are also presented.</div>

The spin filter capability of a (0,8) armchair graphene nanoribbon with Fe atoms at substitutional sites is investigated by density functional theory in combination with the non-equilibrium Green's function technique. For specific arrangements, a high degree of spin polarisation is achieved. These include a single substitution at an edge position or double substitution in the central sector of the transmission element. The possibility of switching between majority and minority spin polarisation by changing the double substitution geometry is predicted. Including the bias dependence of the transmission function proves to be essential for correct representation of the spin-resolved current-voltage profiles.

The spin-dependent transmission properties of (0,8) graphene nanoribbons (GNRs) with two substitutional Fe atom impurities (2Fe-aGNRs) have been studied by the non-equilibrium Green's function (NEGF) method in conjunction with density functional theory (DFT). Emphasis is placed on the spin-filtering activity of current transmission elements derived from these structures. In particular, it is shown that devices based on 2Fe-aGNR approach the limit of half-metallicity, where the magnitude and the sign of the current spin polarization is controlled by the bias across the device as well as the spin state of the 2Fe subsystem. This effect is rationalized by electronic structure and partial-density-of-states (PDOS) analysis of the transmission element. An occupied spin minority state, induced by the Fe-atom moiety and close to the Fermi energy of 2Fe-aGNR, accounts for the predominance of minority spin polarization. Comparison with nanosystems obtained from 2Fe-aGNR, involving vacancies rather than impurities, or both types of defects, reveals that substantial degrees of current spin polarization prevail across a wide variety of device types.

The application of the Hershcel-Quincke (HQ) tube as a noise reduction device for one-dimensional plane-wave sound fields has been studied in great detail in previous years. In this thesis, an analytical technique is developed to investigate the potential of the HQ tube concept to control higher-order duct modes. This analytical method involves modeling the tube-duct interfaces as finite piston sources, which couple the acoustic field inside the main duct with the acoustic field within the HQ tube(s). The acoustic field within the HQ tube is modeled as plane-waves and the acoustic field within the main duct is modeled by expanding the sound field in terms of the higher-order modes. This model is then used to investigate the noise reduction mechanisms behind the attenuation of higher-order modes. These mechanisms involve both the reflection of the incident wave as well as the reconstruction and recombination of the modal content of the incident disturbance into other modes. The effects of the modal content of the disturbance along with the HQ tube geometric parameters, such as tube axial position, length, distance between interfaces, and cross-sectional area, are studied with respect to the frequencies of attenuation and the reduction obtained. These results show the potential of the Herschel-Quincke tube concept to reduce higher-order modes in ducts. / Master of Science

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. / QC 20101118

Heating and cooling needs have been highly demanded as the extreme weathers become increasingly frequent and global warming becomes well-founded. Because ground temperature keeps relatively constant at 20-30 feet below the surface, using the earth as a thermal mass for temperature conditioning and thermal management creates an energy-efficient and environmentally beneficial approach to surface heating and cooling, which has been used in self-heated pavement, greenhouse, and building integrated photovoltaic thermal systems. Inspired by the human body wherein a blood circulation system keeps skin nearly at a constant temperature under environmental changes, a thermal fluid circulation system is introduced to the geothermal well system. Through bi-directional heat exchange between surface space with the ground, heat harvested at high temperatures can be stored underground for utilization at low temperatures, so that the surface temperature variations can be significantly reduced for daily and yearly cycles minimizing the heating/cooling needs. Understanding the heat transfer under the ground and thermal stress of the heat exchange systems induced by the temperature changes is critical for system design, performance prediction and optimization, and system control and operation. This dissertation studies heat transfer and thermomechanical problems for different geothermal systems. The temperature field of the earth can be calculated given the heat source and ambient temperature. Due to nonuniform thermal expansion caused by temperature differences or material mismatches, thermal stress will be induced. Its interaction with surface mechanical load and displacement constraint will be investigated for the design and failure analysis of the fluid circulation and heat exchange system. In the theoretical study, the earth is approximated as a semi-infinite domain. Green's function technique has been used in the analysis of heat conduction, elastic, and thermoelastic problems respectively. The semi-infinite domain with a surface boundary condition can be considered a special case of two semi-infinite domains with a perfectly bonded interface, which forms an infinite bi-material domain. For a Dirichlet boundary value problem with a constant temperature or displacement, the top semi-infinite domain can be considered with infinitely large conductivity or stiffness, respectively; for a Neumann boundary value problem with zero flux or traction, the top semi-infinite domain can be considered with a zero conductivity or stiffness, respectively. The general Green's functions of an infinite bi-material domain can recover the classic solutions for Boussinesq's problem, Mindlin's problem, Kelvin's problem, etc. The three-dimensional (3D) problems can be used to recover the corresponding two-dimensional (2D) problems by an integral of Green's function in one dimension through the Hadamard regularization. Firstly, the heat transfer problem in an infinite bi-material is introduced and the Green's function is formulated for the temperature change caused by a point heat source in the material. It is used to simulate heat transfer for a spherical heat exchanger embedded underground in geothermal energy applications. The temperature field of the spherical inhomogeneity embedded in an infinite bi-material subjected to a uniform far-field steady-state or sinusoidal heat flux is determined by solving the boundary value problem. Eshelby’s equivalent inclusion method (EIM) is used to consider the mismatch of the thermal conductivities of the particle from the matrix, which is simulated by a prescribed temperature gradient. When the material of one semi-infinite domain exhibits zero or infinite thermal conductivity, the above solution can be used for a semi-infinite domain containing a heat source with heat insulation or constant temperature on the boundary, respectively. The analytical solution has been verified with the finite element method. The formulation is used to simulate a spherical heat source embedded in a semi-infinite domain. The method can be immediately applied to the design of geothermal energy systems for heat storage and harvesting. When the heat exchanger is a long horizontal pipe, a similar procedure can be conducted for the corresponding 2D problem. If the temperature exhibits a cyclic change, such as daily variation, the formulation is extended to the harmonic transient heat conduction problems. Secondly, a similar formulation has been introduced for the elastic problem of an infinite bi-material. The Green's function is formulated for the displacement caused by a point force in the bi-material. It is used to simulate the stress transfer for a spherical heat exchanger embedded underground in geothermal energy applications. The formulation of the heat transfer problem is extended to the corresponding elastic problem. How a surface mechanical load is transferred to the underground heat exchanger is illustrated. The interactions between a heat exchanger and the surface load are investigated. Finally, the thermoelastic problem of an infinite bi-material is introduced and the Green's function is formulated for the displacement field caused by a point heat source in the material. It can be straightforwardly used to derive the thermoelastic stress caused by a distributed heat source by volume integrals. However, when the thermal conductivity and elasticity of the heat exchanger are different from the earth in actual geothermal energy applications, the Green's function cannot be directly used. By analogy to Eshelby's equivalent inclusion method, a dual equivalent inclusion method (DEIM) is introduced to address the dual material mismatch in thermal and elastic properties. The fundamental solutions of a bi-material for thermal, elastic, and thermoelastic problems are versatile and recover the ones of the single material domain for both 2D and 3D problems. The equivalent inclusion method is successfully extended to the thermoelastic problems to simulate the material mismatch. The formulation can be used in designing a geothermal heat exchanger for heat storage and supply for energy-efficient buildings as well as other geothermal applications. Future work will extend the fundamental solutions to time-dependent thermomechanical load and investigate the daily and seasonal heat exchange with the ground using different configurations of the pipelines. The algorithms will be integrated into the inclusion-based boundary element method (iBEM) for geothermal system design and analysis.

Quantum dot infrared photodetectors (QDIPs) have emerged as a promising technology in the mid- and far-infrared (3-25 μm) for medical and environmental sensing that have a lot of advantages over current technologies based on Mercury Cadmium Telluride (MCT) and quantum well (QW) infrared photodetectors (QWIPs). In addition to the uniform and stable surface growth of III/V semiconductors suitable for large area focal plane applications and thermal imaging, the three dimension confinement in QDs allow sensitivity to normal incidence, high responsivity, low darkcurrent and high operating temperature. The growth, processing and characterizations of these detectors are costly and take a lot of time. So, developing theoretical models based on the physical operating principals will be so useful in characterizing and optimizing the device performance. Theoretical models based on non-equilibrium Green's functions have been developed to electrically and optically characterize different structures of QDIPs. The advantage of the model over the previous developed classical and semiclassical models is that it fairly describes quantum transport phenomenon playing a significant role in the performance of such nano-devices and considers the microscopic device structure including the shape and size of QDs, heterostructure device structure and doping density. The model calculates the density of states from which all possible energy transitions can be obtained and hence obtains the operating wavelengths for intersubband transitions. The responsivity due to intersubband transitions is calculated and the effect of having different sizes and different height-to-diameter ratio QDs can be obtained for optimization. The dark and photocurrent are calculated from the quantum transport equation provided by the model and their characteristics at different design parameter are studied. All the model results show good agreement with the available experimental results. The detectivity has been calculated from the dark and photocurrent characteristics at different design parameters. The results shows a trade off between the responsivity and detectivity and what determines the best performance is how much the rate of increase of the photocurrent and dark current is affected by changing the design parameters. Theoretical modeling developed in the thesis give good description to the QDIP different characteristics that will help in getting good estimation to their physical performance and hence allow for successful device design with optimized performance and creating new devices, thus saving both time and money. / Thesis / Doctor of Philosophy (PhD)