The Lattice-Boltzmann-model is analyzed with regard to application to numerical solution of flow acoustic problems. In the first part of this study the description of sound wave propagation by common variants of the Lattice-Boltzmann-model is examined by calculation of phase velocity and effective viscosity for sound waves. Schemes with nine velocities in two dimensions and nineteen velocities in three dimensions are considered. For each of these a single relaxation time model (LBGK-model) and a multiple relaxation time model (MRT) is investigated. All schemes exhibit an almost isotropic error in phase speed of sound waves. With a spatial resolution of 10 or 30 grid spacings per wavelength the deviation of phase speed is less than 1 % or 0.1 %, respectively. The dissipation of sound waves is not simulated correctly by LBGK-models since there the bulk viscosity is fixed to the shear viscosity. Apart from that there is only very little numerical dissipation. The dissipation error therefor is negligible in the audible frequency range in air as long as the simulation volumes do not become very large, i.e. much more than some hundred wavelengths. The MRT-models allow to adjust the bulk viscosity by a suitable choice of relaxation parameters. However, if the bulk viscosity is set to a realistic value, stability of the scheme requires free relaxation parameter values which are close to the relaxation parameters that determine the viscosities. Then the gain in stability of MRT-models compared to LBGK-models is lost to some extent. All schemes considered here are able to reproduce the effect of sound wave convection in homogeneous background flows. Although additional numerical errors arise in transport coefficients, the overall errors are of the same order of magnitude as in the case with zero background flow and are not critical in practical applications. In the second part of the work numerical experiments are described which demonstrate the coupling of the flow- and sound field. Three test cases are considered: Sound generation by a single vortex interaction with the leading edge of a semi-infinite flat plate, sound generation by a grazing flow over a partially covered cavity and instationary flow around a half-cylinder with an attached wedge tail. The first test case is simulated in two dimensions with a self-written program. The sound calculated directly is compared to prediction based on an acoustic analogy. The observed amplitudes of the radiated sound agree quantitatively well for all flow and eddy velocities considered here. This implies, that the coupling of the sound and flow field is correct. In the case of the cavity the flow is computed in two dimensions with a self-written program as well as in three dimensions with the commercially available program PowerFLOW. The simulated pressure fluctuations in the cavity are compared to results of a wind tunnel experiment. Good agreement between simulation and wind tunnel experiment is found. The instationary flow around a half cylinder with an attached wedge tail is simulated in three dimensions using PowerFLOW. The radiated sound cannot be captured with PowerFLOW because of insufficient quantization of fluid density. However, pressure fluctuations on the surface of the body exhibit good agreement with the result of a wind tunnel test. Summarizing the results of this work it can concluded, that the Lattice-Boltzmann-model is well suited to numerical solutions of flow acoustic problems.

The Lattice-Boltzmann-model is analyzed with regard to application to numerical solution of flow acoustic problems. In the first part of this study the description of sound wave propagation by common variants of the Lattice-Boltzmann-model is examined by calculation of phase velocity and effective viscosity for sound waves. Schemes with nine velocities in two dimensions and nineteen velocities in three dimensions are considered. For each of these a single relaxation time model (LBGK-model) and a multiple relaxation time model (MRT) is investigated. All schemes exhibit an almost isotropic error in phase speed of sound waves. With a spatial resolution of 10 or 30 grid spacings per wavelength the deviation of phase speed is less than 1 % or 0.1 %, respectively. The dissipation of sound waves is not simulated correctly by LBGK-models since there the bulk viscosity is fixed to the shear viscosity. Apart from that there is only very little numerical dissipation. The dissipation error therefor is negligible in the audible frequency range in air as long as the simulation volumes do not become very large, i.e. much more than some hundred wavelengths. The MRT-models allow to adjust the bulk viscosity by a suitable choice of relaxation parameters. However, if the bulk viscosity is set to a realistic value, stability of the scheme requires free relaxation parameter values which are close to the relaxation parameters that determine the viscosities. Then the gain in stability of MRT-models compared to LBGK-models is lost to some extent. All schemes considered here are able to reproduce the effect of sound wave convection in homogeneous background flows. Although additional numerical errors arise in transport coefficients, the overall errors are of the same order of magnitude as in the case with zero background flow and are not critical in practical applications. In the second part of the work numerical experiments are described which demonstrate the coupling of the flow- and sound field. Three test cases are considered: Sound generation by a single vortex interaction with the leading edge of a semi-infinite flat plate, sound generation by a grazing flow over a partially covered cavity and instationary flow around a half-cylinder with an attached wedge tail. The first test case is simulated in two dimensions with a self-written program. The sound calculated directly is compared to prediction based on an acoustic analogy. The observed amplitudes of the radiated sound agree quantitatively well for all flow and eddy velocities considered here. This implies, that the coupling of the sound and flow field is correct. In the case of the cavity the flow is computed in two dimensions with a self-written program as well as in three dimensions with the commercially available program PowerFLOW. The simulated pressure fluctuations in the cavity are compared to results of a wind tunnel experiment. Good agreement between simulation and wind tunnel experiment is found. The instationary flow around a half cylinder with an attached wedge tail is simulated in three dimensions using PowerFLOW. The radiated sound cannot be captured with PowerFLOW because of insufficient quantization of fluid density. However, pressure fluctuations on the surface of the body exhibit good agreement with the result of a wind tunnel test. Summarizing the results of this work it can concluded, that the Lattice-Boltzmann-model is well suited to numerical solutions of flow acoustic problems.

The linear Boltzmann equation describes neutron transport in nuclear systems. We consider discretization methods for the time-independent mono-energetic transport equation, and focus on mixed-hybrid primal and dual formulations obtained through an even- and odd-parity flux decomposition. A finite element technique discretizes the spatial variable, and a PN spherical harmonic technique discretizes the angular variable. Mixed-hybrid methods combine attractive features of both mixed and hybrid methods, namely the simultaneous approximation of even- and odd-parity fluxes (thus of flux and current) and the use of Lagrange multipliers to enforce interface regularity constraints. While their study provides insight into purely mixed and purely hybrid methods, mixed-hybrid methods can also be used as such. Mixed and mixed-hybrid methods, so far restricted to diffusion theory, are here generalized to higher order angular approximations. We first adapt existing second-order elliptic mixed-hybrid theory to the lowest-order spherical harmonic approximation, i.e., the P1 approximation. Then, we introduce a mathematical setting and provide well-posedness proofs for the general PN spherical harmonic approximation. Well-posedness theory in the transport case has thus far been restricted to the first-order (integro-differential) form of the transport equation. Proceeding from P1 to PN , the primal/dual distinction related to the spatial variable is supplemented by an even-/odd-order PN distinction in the expansion of the angular variable. The spatial rank condition is supplemented by an angular rank condition satisfied using interface angular expansions corresponding to the Rumyantsev conditions, for which we establish a new derivation using the Wigner coefficients. Demonstration of the practical use of even-order PN approximations is in itself a significant achievement. Our numerical results exhibit an interesting enclosing property when both even- and odd-order PN approximations are employed.

Abstract : This thesis tackles the problem of the possible phase transitions in the presence of a magnetic field, and of the transport properties of quasi-one-dimensional (quasi-1D) superconductors like Bechgaard salts. In the framework of the quasi-1D electron-gas model, the renormalization group (RG) method is used for studying the effect of Zeeman coupling to a magnetic field on the structure of the phase diagram of the quasi-1D electron gas model. For the transport theory, a combination of linearized Boltzmann equation and renormalization group method is used to investigate the electrical resistivity and the Seebeck coefficient of quasi-1D correlated organic metals like the Bechgaard salts near their quantum critical point that joins antiferromagnetism and superconductivity. The thesis is organized in four chapters. In the first chapter, an introduction to the Bechgaard and Fabre salts is given and properties of their generic temperature-pressure phase diagram are explained. These compounds are considered as the reference systems for the comparison between theory and experiments on the nature and symmetry of the superconducting phase in a magnetic field and the anomalous transport properties in the normal phase. The problem of the observed anomalously high value of the upper critical field of Bechgaard salts is the main issue of chapter two. We approach this problem with the aid of the weak coupling renormalization group technique in the presence of Zeeman coupling, for an extended quasi-1D electron-gas model, which includes inter-chain hopping, nesting deviations along with both intrachain and inter-chain repulsive interactions. This allows us to study the efect of quasi-1D spin fluctuations originating from constructive interference between unconventional superconductivity (SC) and density-wave instabilities on the magnetic field vs temperature phase diagram of these quasi-1D superconductors. Our results support the existence of a crossover from d-wave to an inhomogeneous d-wave FFLO superconducting state under field. In the third chapter, we introduce the semi-classical Boltzmann equation for transport in its linearized form. The Boltzmann theory is coupled to the RG method for the calculation of the renormalized umklapp scattering amplitude for the anisotropic scattering time. We then study the temperature and pressure variation of the electrical resistivity and the Seebeck coefficient of the Bechgaard salts quasi-one-dimensional organic superconductors in the quantum critical domain of their normal phase. We demonstrate that momentum and temperature dependence of umklapp scattering strongly affects the temperature behavior of transport in the metallic state, as a function of nesting deviations that simulate the influence of pressure in the actual phase diagram. This defines a characteristic quantum critical region where significant deviations from the Fermi-liquid behavior are seen, either as an anomalous power law of electrical resistivity or sign reversal of the Seebeck coefficient. / Cette thèse aborde le problème des transitions de phase possibles, en présence d'un champ magnétique, et des propriétés de transport dans des supraconducteurs quasi-unidimensionnels (quasi-1D) comme les sels de Bechgaard. Dans le cadre du modèle d'un gaz d'électrons quasi-1D, on utilise la méthode du groupe de renormalisation (GR) pour étudier l'effet du couplage Zeeman sur le diagramme de phase ce système. Pour la théorie du transport, une combinaison de l'équation de Boltzmann linéarisée et de la méthode de groupe de renormalisation est utilisée pour étudier la résistivité électrique et le coefficient de Seebeck de métaux organiques comme les sels de Bechgaard au voisinage de leur point critique quantique joignant l'antiferromagnétisme et la supraconductivité. La thèse est organisée en quatre chapitres. Dans le chapitre un, une introduction aux sels de Bechgaard et de Fabre est donnée et les propriétés de leur diagramme de phase générique en température-pression sont expliquées. Ces composés sont considérés comme des systèmes de référence pour la comparaison entre la théorie et les expériences sur la nature et la symétrie de la phase supraconductrice sous un champ magnétique et les propriétés anormales de transport dans la phase normale. Le problème de la valeur anormalement élevée du champ critique supérieur observée dans les sels de Bechgaard est la question principale traitée au chapitre deux. Nous abordons ce problème à l'aide de la technique de couplage faible du groupe de renormalisation, pour le modèle du gaz d'électrons quasi-1D étendu, qui contient le saut inter-chaînes, les déviations par rapport à l'emboitement parfait, ainsi que les interactions intra-chaînes et inter-chaînes répulsives. Ceci nous permet d'étudier l'effet des fluctuations de spin quasi-1D provenant d'une interférence constructive entre la supraconductivité non conventionnelle (SC) et les instabilités d'onde de densité sur le diagramme de phase en champ magnétique et en température de ces supraconducteurs quasi-1D. Grâce à notre approche, nous examinons les instabilités possibles dans la partie basse température/champ élevé du diagramme de phase. Dans le troisième chapitre, nous introduisons l'équation semi-classique de Boltzmann pour le transport dans sa forme linéarisée. La théorie de Boltzmann est couplée à la méthode du GR pour le calcul de l'amplitude de diffusion umklapp renormalisée entrant dans l'évaluation du temps de diffusion anisotrope. Nous étudions ensuite la variation en température et en pression de la résistivité électrique et le coefficient de Seebeck pour les supraconducteurs organiques quasi-1D, les sels de Bechgaard, dans le domaine critique quantique de leur phase métallique. Nous démontrons que la variation en quantité du mouvement et en température de la diffusion umklapp sur la surface de Fermi affecte fortement le comportement thermique du transport dans l'état métallique, en fonction des déviations à l'emboîtement parfait. Dans notre modèle, ces déviations simulent l'influence de la pression dans le diagramme de phase réel. Ceci définit une région critique quantique caractéristique où des écarts significatifs par rapport au comportement du liquide de Fermi sont observés, soit comme une loi de puissance anormale de la résistivité électrique, soit comme un changement de signe du coefficient de Seebeck.

<div> Underlying physics in bubble coalescence is critical for understanding bubble transportation. It is one of the major mechanisms of microfluidics. Understanding the mechanism has benefits in the design, development, and optimization of microfluidics for various applications. The underlying physics in bubble coalescence is investigated numerically using the free energy-based lattice Boltzmann method by massive parametrization and classification.</div><div><br></div><div> Firstly, comprehensive GPU (Graphics Processing Unit) parallelization, convergence check, and validation are carried out to ensure the computational efficiency and physical accuracy for the numerical simulations.</div><div><br></div><div> Then, the liquid-gas system is characterized by an Ohnesorge number (Oh). Two distinct coalescence phenomena with and without oscillation, are separated by a critical Oh (~0.477)number. For the oscillation cases(Oh<0.477), the mechanism of damped oscillation in microbubble coalescence is explored in terms of the competition between driving and resisting forces. Through an analogy to the conventional damped harmonic oscillator, the saddle-point trajectory over the entire oscillation can be well predicted analytically. Without oscillation in the range of 0.50r^-n </div><div><br></div><div> After that, the liquid-gas-solid interface is taken into consideration in the liquid-gas system. Six cases based on the experiment set-ups are simulated first for validation of the computational results. Based on these, a hypothesis is established about critical factors to determine if coalescence-induced microbubble detachment (CIMD) will occur. From the eighteen experimental and computational cases, we conclude that when the radius ratio is close to 1 and the father bubble is larger, then it will lead to CIMD.</div><div><br></div><div> Lastly, the effects of initial conditions on the coalescence of two equal-sized air microbubbles (R₀) in water are investigated. In both initial scenarios, the neck bridge evolution exhibits a half power-law scaling, r/R₀=A₀(t/t_i)^1/2 after development time. The development time is caused by the significant bias between the capillary forces contributed by the meniscus curvature and the neck bridge curvature. Meanwhile, the physical mechanism behind each behavior has been explored.</div>

Thesis advisor: David A. Broido / A theory is presented for describing the lattice thermal conductivities of graphene and single-walled carbon nanotubes. A phonon Boltzmann transport equation approach is employed to describe anharmonic phonon-phonon, crystal boundary, and isotopic impurity scattering. Full quantum mechanical phonon scattering is employed and an exact solution for the linearized Boltzmann transport equation is determined for each system without use of common relaxation time and long-wavelength approximations. The failures of these approximations in describing the thermal transport properties of nanotubes is discussed. An efficient symmetry based dynamical scheme is developed for carbon nanotubes and selection rules for phonon-phonon scattering in both graphene and nanotubes are introduced. The selection rule for scattering in single-walled carbon nanotubes allows for calculations of the thermal conductivities of large-diameter and chiral nanotubes that could not be previously studied due to computational limitations. Also due to this selection rule, no acoustic-only umklapp scattering can occur, thus, acoustic-optic scattering must be included in order to have thermal resistance from three-phonon processes. The graphene selection rule severely restricts phonon-phonon scattering of out-of-plane modes. This restriction leads to large contributions to the total thermal conductivity of graphene from the acoustic, out-of-plane modes which have been previously neglected. Empirical potentials used to model interactions in carbon-based materials are optimized to better describe the lattice dynamics of graphene-derived systems. These potentials are then used to generate the interatomic force constants needed to make calculations of the thermal conductivities of graphene and carbon nanotubes. Calculations of the thermal conductivities of single-walled carbon nanotubes and graphene for different temperatures and lengths are presented. The thermal conductivities of SWCNTs saturate in the diffusive regime when the effects of higher-order scattering processes are estimated and correctly reproduce the ballistic limit for short-length nanotubes at low temperatures. The effects of isotopic impurity scattering on the thermal conductivities of graphene and SWCNTs are explored. Isotopic impurities have little effect in the low (high) temperature regime where boundary (umklapp) scattering dominates the behavior of the thermal conductivities. In the intermediate temperature regime, modest reductions in the thermal conductivities, 15-20%, occur due to impurities. The thermal conductivities of a wide-range of SWCNTs are explored. The thermal conductivities of successively larger-diameter, one-dimensional nanotubes approach the thermal conductivity of two-dimensional graphene. / Thesis (PhD) — Boston College, 2010. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

In multi-agent Markov Decision Processes, a controllable agent must perform optimal planning in a dynamic and uncertain environment that includes another unknown and uncontrollable agent. Given a task specification for the controllable agent, its ability to complete the task can be impeded by an inaccurate model of the intent and behaviors of other agents. In this work, we introduce an active policy inference algorithm that allows a controllable agent to infer a policy of the environmental agent through interaction. Active policy inference is data-efficient and is particularly useful when data are time-consuming or costly to obtain. The controllable agent synthesizes an exploration-exploitation policy that incorporates the knowledge learned about the environment's behavior. Whenever possible, the agent also tries to elicit behavior from the other agent to improve the accuracy of the environmental model. This is done by mapping the uncertainty in the environmental model to a bonus reward, which helps elicit the most informative exploration, and allows the controllable agent to return to its main task as fast as possible. Experiments demonstrate the improved sample efficiency of active learning and the convergence of the policy for the controllable agents.

Heat dissipation is a critical bottleneck for microelectronic device performance and longevity. At micrometer and nanometer length scales heat carriers scatter at the boundaries of the material reducing its thermal conductivity. Additionally, thermal boundary conductance across dissimilar material interfaces becomes a dominant factor due to the increase in surface area relative to the volume of device layers. Therefore, techniques for monitoring spatially varying temperature profiles, and methods to improve thermal performance are critical to future device design and optimization. The first half of this thesis focused on frequency domain thermoreflectance (FDTR) to measure thermal transport in nanometer-thick polymer films and across an organic-inorganic interface. Hybrid structures of organic and inorganic materials are widely used in devices such as batteries, solar cells, transistors, and flexible electronics. The Langmuir-Blodgett (LB) technique was used to fabricate nanometer-thick polymer films ranging from 2 - 30 nm. FDTR was then used to experimentally determine the thermal boundary conductance between the polymer and solid substrates. The second half of the thesis focused on developing a fundamental understanding of thermal transport in wide-bandgap (WBG) materials, such as GaN, and ultrawide-bandgap (UWBG) materials, such as diamond, to improve thermal dissipation in power electronic devices. Improvements in WBG materials and device technologies have slowed as thermal properties limit their performance. UWBG materials can provide a dramatic leap in power electronics technologies while temporarily sidestepping the problems associated with their WBG cousins. However, for power electronic devices based on WBG- and UWBG-materials to reach their full potential the thermal dissipation issues in these hard-driven devices must be understood and solved. FDTR provides a comprehensive pathway towards fully understanding the physics governing phonon transport in WBG- and UWBG-based devices. By leveraging FDTR imaging and measuring samples as a function of temperature, defect concentration, and thickness, in conjunction with transport models, a well-founded understanding of the dominant thermal-carrier scattering mechanisms in these devices was achieved. With this knowledge we developed pathways for their mitigation.

Orientador: Augusto Agostinho Neto / Orientador: Elso Drigo Filho / Coorientador: Tereza Pereira de Souza / Banca: Iolanda Midea Cuccovia / Banca: Marcelo Andres Fossey / Resumo: Proteínas e peptídeos são constituídos por subunidades estruturalmente mais imples chamadas aminoácidos. Uma importante propriedade destes é que, dependendo das características do meio (tais como pH e concentração iônica), os seus grupos onizáveis podem ceder prótons e, assim, adquirir carga elétrica não nula. Tal carga nfluenciará na eficiência da formação de ligações peptídicas e em interações proteína- igante, por exemplo. Partindo da hipótese de que a diferença entre os valores de pK dos rupos ionizáveis isolados e destes como partes constituintes de um aminoácido é devida, principalmente, à interação eletrostática adicional que se atribui à presença de rupos vizinhos, elaborou-se um modelo que emprega a forma linearizada da equação de Poisson-Boltzmann para o estudo de propriedades físico-químicas de moléculas com rês grupos ionizáveis. Neste trabalho tal modelo foi aplicado aos aminoácidos: Aspartato, Glutamato, Cisteína, Tirosina, Arginina, Lisina e Histidina. Calcularam-se os valores de pK e as respectivas cargas elétricas médias de tais moléculas. Como os esultados obtidos concordaram com aqueles oriundos de trabalhos experimentais, o modelo teórico foi expandido para tratar de di, tetra, pentapeptídeos e de resíduos de isina e glutamato da proteína Staphylococcal Nuclease. Os valores do Fator de Correlação de Pearson calculados para ambos proteínas e peptídeos são superiores a 0,99, fato este que evidencia a eficiência e versatilidade do modelo ao reproduzir alores de pK reportados por outros autores / Abstract: Proteins and peptides are composed of subunits structurally simpler called amino acids. An important property of these is that, depending on the medium characteristics (such pH and ionic concentration), its ionizable groups may provide protons and thereby acquire a nonzero electric charge. Such charge will affect the formation of peptide bond and protein-ligand interactions, for example. Assuming that the difference between pK values of the isolates ionizable groups and of these as constituents parts of an amino acid is mainly due to the extra electrostatic interaction attributed to the presence of neighboring groups, was developed a structure-based model that employs the linearized form of the Poisson-Boltzmann equation for the study of physicochemical properties of molecules with three ionizable groups. In this work it was applied to the amino acids: aspartate, glutamate, cysteine, tyrosine, arginine, lysine and histidine. The pK values and respective mean electric charges were calculated. As the calculated values agreed with those from experimental studies, the theoretical model has been expanded to the treatment of di, tetra, pentapeptides and Staphylococcal Nuclease residues. The Pearson Correlation Factor calculated for both proteins and peptides are above 0.99, what points to the effectiveness and versatility of the model to reproduce pK values reported by other works / Mestre

Neste trabalho, estuda-se uma abordagem de caráter analítico para problemas bidimensionais de transporte de nêutrons que são descritos pela equação linear de Boltzmann. Neste sentido, aplica-se o método ADO, método Anal tico de Ordenadas Discretas, para resolver as equações unidimensionais nodais, obtidas a partir da integração da formulação bidimensional. Nesta derivação, necessita-se de equações auxiliares para os fluxos desconhecidos no contorno. Assim, duas propostas são apresentadas: na primeira, relações entre o fluxo integrado e o fluxo desconhecido são introduzidas e na segunda, os termos desconhecidos são tratados como fonte do problema. Resultados numéricos são apresentados e comparados com resultados existentes na literatura. / In this work, an analytical approach for two dimensional transport problems, describeb by the linear Boltzmann Equation, is proposed. In this sense, the ADO method, Analytical Discrete Ordinates, is applied to solve the one dimensional equations obtained by the application of a nodal scheme. In this derivation, auxiliary equations are needed for the unknown uxes at the boundary. So two proposals are presented: rst, relations between the integrated ux and the unknown ux are introduced and the second, the unknown terms are treated as source of the problem. Numerical results are presented and compared with available results in the literature.