Made available in DSpace on 2014-06-11T19:26:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-01-28Bitstream added on 2014-06-13T20:35:09Z : No. of bitstreams: 1 barros_aap_me_sjrp.pdf: 459604 bytes, checksum: 0a23c4af2e8f9afe3807f0dd603a1237 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O objetivo desse trabalho é estudar problemas de valor de contorno com três pontos lineares e não ineares, também conhecidos como problemas não Isto é feito, usando as funções de Green, usadas para resolver problemas de valor de contorno com dois pontos. / The aim of this work is to study boundary value problems with three points also known as non-classical problems. This is done using the Green's functions, which are used to solve two-point boundary value problems.

Cette thèse se concentre sur l'étude de l'impact de divers défauts de réseau, c'est-à-dire de dislocations, de parois entre phases inversées, de décalages de mailles et de gaps, sur la conductivité thermique de nano-fils par simulation de dynamique moléculaire et les calculs de fonctions de Green atomiques. Tout d'abord, nous calculons la conductivité thermique de nano-fils de silicium orientés <110> incluant une dislocation spirale par la dynamique moléculaire de non-équilibre. Nous constatons qu'avec l'inclusion d'une dislocation, le taux de diffusion phonon-phonon est amélioré de façon significative en raison de l'existence du champ de déformation induit. Ce processus de diffusion anharmonique augmente avec le vecteur de Burger. Par conséquent, la conductivité thermique de nano-fils disloqués est largement réduite et le pourcentage de réduction est proportionnel à la grandeur du vecteur de Burger. Deuxièmement, le concept de nano-fils de super-réseau anti-phase est proposé et leur conductivité thermique est étudiée avec la dynamique moléculaire d'équilibre. On constate que la frontière anti-phase peut diffuser fortement les phonons et réduire la vitesse de groupe des phonons. Le jeu entre le transport cohérent de phonons et la diffusion de surface conduit à une conductivité thermique minimale à une période de longueur spécifique. La combinaison de la diffusion des phonons à l'interface et la diffusion de surface des nanofils réduit la conductivité thermique de SiC de deux ordres de grandeur, ce qui est d'un grand intérêt pour les applications en thermoélectricité. Troisièmement, nous démontrons que le transport des phonons peut être entravé en grande partie dans un nano-fil de Si avec une structure en zig-zag périodique. Une conductivité thermique plus faible est observée du fait d'un pur effet géométrique, qui produit une disparition complète des directions principales de polarisation de phonon à une période de longueur spécifique. La conductivité thermique minimale et la longueur de période correspondante sont dépendantes du diamètre. L'avantage de cette structure est qu'elle supprime en grande partie le transport thermique sans détériorer le transport d'électrons. Enfin, la transition entre la conduction de la chaleur et le rayonnement de champ proche dans un système de chaîne de clusters de SiO2 est étudiée avec la méthode des fonctions de Green. Trois régions de variation de la conductance dans ce domaine de largeur de gap sont identifiées, plus particulièrement, la région liée à la conduction où les électrons des deux corps sont mis en commun au milieu du gap, la région de champ proche prédominée par des interactions de charges de surface, et la région de champ proche prédominée par des interactions dipôle-dipôle de volume. Cette étude fournit finalement une description de la transition entre le rayonnement et la conduction de la chaleur dans les gaps de dimensions inférieures à quelques nanomètres. / This thesis is focused on the investigation of the impact of various lattice defects, i.e., screw dislocations, anti-phase boundaries, twinning boundaries, and vacuum gaps, on the thermal conductivity of nanowires by molecular dynamic simulations and Green's function calculations. We firstly calculated the thermal conductivity of <110> Si nanowires with a screw dislocation in the center through non-equilibrium molecular dynamics.We find that with the inclusion of a dislocation, the phonon-phonon scattering rate is enhanced dramatically due to the dislocation-induced strain field. This anharmonic scattering process increases with the Burger's vector. As a result, the thermal conductivity of dislocated nanowires is largely reduced and the reduction percentage is proportional to the magnitude of Burger's vector. Secondly, the concept of anti-phase superlattice nanowire is proposed and its thermal conductivity is investigated with equilibrium molecular dynamics. It is found that the anti-phase boundary can strongly scatter phonons and reduce the phonon group velocity. The interplay between phonon coherent transport and boundary scattering results in a minimum thermal conductivity at a specific period length. The combination of anti-phase boundary scattering and nanowire surface scattering reduces the thermal conductivity of SiC by two orders of magnitude, which is of great interest for potential thermoelectric applications. Thirdly, we demonstrate that phonon transport can be hindered to a large extent in a Si nanowire with periodically distributed twinning boundaries. A minimum thermal conductivity is observed due to a pure geometrical effect, which produces a thorough disappearance of favored phonon polarization directions at a specific period length. The minimum thermal conductivity and the corresponding period length are diameter dependent. The advantage of this structure is that it largely suppresses the thermal transport without deteriorating the electron transport. Finally, the transition from heat conduction to near field radiation in a SiO2 cluster chain system is investigated with the phonon Green's function. Three conductance variation regions within the studied distances are identified, more specifically, the heat conduction region with shared electrons in the middle of a gap, the near field region predominated by surface charge interactions, and the near field region predominated by volume dipole-dipole interactions. This study finally provides a description of the transition between radiation and heat conduction in gaps smaller than a few nanometers.

We consider the motion of a Brownian particle trapped in an arbitrary bounded two or three-dimensional domain, whose boundary is reflecting except for a small absorbing window through which the particle can escape. We use the method of matched asymptotic expansions to calculate the mean first passage time, defined as the time taken for the Brownian particle to escape from the domain through the absorbing window. This is known as the narrow escape problem. Since the mean escape time diverges as the window shrinks, the calculation is a singular perturbation problem. We extend our results to include N absorbing windows of varying length in two dimensions and varying radius in three dimensions. We present findings in two dimensions for the unit disk, unit square and ellipse and in three dimensions for the unit sphere. The narrow escape problem has various applications in many fields including finance, biology, and statistical mechanics. / Science, Faculty of / Mathematics, Department of / Graduate

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

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