Aurorae often break down into elongated filaments parallel to the geomagnetic field lines (B) with cylindrically symmetric structures. The object of this thesis is to study the ion distribution function and transport properties in response to the sudden introduction of a radial electric field (E) in such a cylindrical geometry. Both collision-free and collisional situations are considered.<p> The thesis starts by solving a collision-free problem where the electric field is constant in time but increases linearly with radius, while the initial ion density is uniform in space. The attendant Boltzmann equation is solved by tracking the ions back in time, thereby using the temporal link between the initial position and velocity of an ion and its position and velocity at an arbitrary time and place. Complete analytical solutions show that the ion distribution function is a pulsating Maxwellian in time, and all transport parameters (e.g., bulk speed, temperature, etc.) oscillate in time but independent of radius. If the ion-neutral collisions are taken into account by employing a simple relaxation model, analytical solutions are also obtained. In this case, the ion distribution function can be driven to horseshoe shapes which are symmetric with respect to the ExB direction. The bulk parameters evolve in a transition period of the order of one collision time as they go from oscillating to the non-oscillating steady state.<p> In more realistic electric field structures which are spatially inhomogeneous but still constant in time, a generalized semi-numerical code is developed under collision-free conditions. This code uses a backmapping approach to calculate the ion velocity distribution and bulk parameters. With arbitrarily selected electric field rofiles, calculations reveal various shapes of ion velocity distribution functions (e.g., tear-drop, core-halo, ear-donut, etc). The associated transport properties are also obtained and discussed.<p> Under both collision-free and collisional conditions, the effect of the density inhomogeneities at the initial time is studied in an electric field which is proportional to radius and constant in time. With two profiles of the initial ion density for the collision-free case, and one profile for the collisional case, complete analytical solutions are obtained. The results reveal that the distribution function and the bulk properties are now strongly dependent on radial position.<p> If the radial electric field is unable to stay constant with time but modulated by in-coming charged particles, a fluid formalism is used to study the excitation of several plasma waves under different kinds of initial conditions. These identified waves include the ion cyclotron oscillation, the ion and electron upper-hybrid oscillations, and the lower-hybrid oscillation.<p> The results of this thesis are expected to be applicable to high-resolution observations. Future work should also include the mirror effect and the formation of conics in velocity space. Finally, the velocity distributions obtained in this thesis could trigger various plasma instabilities, and this topic should also be looked at in the future.

No description available.

Thesis (Ph.D.). / Written for the Computational Acoustic Modeling Laboratory, School of Music. Title from title page of PDF (viewed 2008/01/12). Includes bibliographical references.

Frankfurt (Main), Univ., Diss., 2009

Chemnitz-Zwickau, Techn. Univ., Diss., 1996.

Techn. University, Diss., 2004--Berlin.

The motion of microorganisms presents interesting and diffcult problems ranging from mechanisms of propulsion to collective effects. Experimentally, some of the complicating factors, such as death, reproduction, chemotaxis, etc., can be suppressed through genetic manipulation or environmental control. Nonequilibrium statistical mechanics has been used to study simple models, however proceeding analytically is extremely challenging. Thus simulations, where one has total control over and knowledge of the system, are a compelling method for examining models of their behaviour. In this work I present simulations of minimal, self-propelled particles, while ensuring realistic hydrodynamic behaviour using the lattice Boltzmann method (LBM), a well-studied method for simulating fluid flows that scales linearly in computational effort with the system volume. The derivation of the LBM is reviewed, including the addition of forces in a consistent, accurate manner as well as thermal fluctuations that satisfy the fluctuation-dissipation theorem. It is extended to include singular forces via a regularization of the Dirac δ-function. This is implemented and extensively tested for agreement with low Reynolds number hydrodynamics. The regularized singularities are used to develop an effcient algorithm for pointlike particles which move under the influence of an external force, such as gravity, or thermal fluctuations of the fluid. The method is compared to theoretical results and simulations using a well-studied algorithm that resolves the particle, finding good agreement in the dilute limit and significantly reduced computational requirements. Using the singular forces, we then construct a minimal model for self-propelled particles, that may also experience forces or undergo random changes of orientation (modelling the “run-and-tumble” dynamics observed in swimming bacteria such as E. coli). The collective behaviour of these model swimmers is studied in three situations: sedimentation under gravity; in a central, harmonic trap; and in a Poiseuille flow between parallel plates. For sedimentation, the behaviour is not very different from that expected of non-interacting run-and-tumble particles, except that total collapse to the container bottomwhen the weight of the particles equals the propelling force is prevented by the velocity fluctuations caused by the particles’ activity. The trapped particles, for runlengths comparable to the trap size, self-assemble into a pump-like structure, while for short run-lengths an approximately Gaussian distribution seenwithout hydrodynamic interactions, is maintained. In Poiseuille flows we find the particles orient upstream; forweak flows this results in a net upstreamcurrent. We find significant hydrodynamic effects, in the dilute limit, only when there is some mechanism that causes alignment of the particles.

Liquid water management in the cathode of polymer electrolyte membrane fuel cells (PEMFC) is crucial to efficient transport of gases and to maintaining electrochemical activity in the catalyst layer. Cracks and interfacial voids are typical of catalyst layers in operating cells, and are thought to affect water management and other transport properties such as gas diffusion and conductivity. This thesis investigates the effect of such morphological imperfections on liquid water transport using a combination of numerical techniques. Both the catalyst layer and microporous layer parts of the cathode are considered. The layers are first numerically reconstructed using data from advanced microscopy, and cracks, perforations and interfacial voids are created. Lattice Boltzmann simulations of the dynamics liquid water imbibition process are performed to study the effect of characterizing features of the cracks and interfacial voids such as aperture area, degree of protrusion, and tortuosity. The resulting liquid water distributions were then input into a pore scale model to characterize the effect of the morphological features on other transport properties, such as effective diffusivities and conductivities. Larger crack apertures were found to increase liquid water uptake, and elongated cracks allowed for faster breakthrough at lower saturation levels. A notable observation is that short and large interfacial cracks have a higher liquid water uptake potential due to the lower effective capillary pressures. It was also found that elongated cracks aligned with the pressure gradient provide preferential pathway, and a capillary pressure increase that favours liquid water transport towards the membrane and mitigates flooding. The effective diffusivity increased for all crack protrusion depths, even for the wet catalyst layer, likely due to low liquid water saturation. The geometry with the most elongated crack showed a significant increase in gas diffusion under wet conditions, indicating that enhanced gas transport is achievable when liquid water removal is effective. Protonic and electrical conductivities decreased for all crack shapes due to higher contact resistance. / Graduate / 0548 / vlosier@uvic.ca

Doctor en Ciencias de la Ingeniería, Mención Modelación Matemática / En la mecánica estadística, la ecuación de Boltzmann espacialmente homogénea (en honor de Ludwig Eduard Boltzmann, quien introdujo la primera versión en 1872) describe a nivel macroscópico la evolución temporal de la distribución de las velocidades de una enorme cantidad de moléculas de un gas en R³, las cuales obedecen las leyes de la mecánica clásica y están sujetas a colisiones a nivel microscópico. Ecuaciones de similares características han sido introducidas recientemente en variadas situaciones; por ejemplo, para modelar la redistribución de riqueza en una población, en el contexto de la Econofísica. Con el fin de validar matemáticamente la ecuación de Boltzmann y a la vez deducir propiedades de la misma, en 1956 Kac propuso estudiar un sistema de partículas, el cual es un proceso estocástico a valores en (R³)^N que representa las velocidades de N partículas que evolucionan continuamente en el tiempo y cambian su estado mediante saltos aleatorios correspondientes a las colisiones entre ellas. Es sabido que este sistema aproxima a la ecuación, en el sentido que se cumple la propiedad de propagación de caos: la medida empírica del sistema converge débilmente a la solución de la ecuación en el límite cuando N → ∞. En los últimos años ha habido gran interés por cuantificar esta convergencia, con dependencia explícita en N y en el tiempo t, e idealmente uniforme en t, pues esto validaría plenamente a la distribución estacionaria de la ecuación como el estado del gas en equilibrio termodinámico. En la presente tesis se estudia la propagación de caos para algunos sistemas de partículas, incluyendo a los modelos recién descritos. En el Capítulo 2 se trabaja con un sistema a valores en un espacio general, y se obtiene un resultado de propagación de caos en convergencia débil en el espacio de trayectorias. En el Capítulo 3 se estudia una clase de sistemas de partículas en R que incluye a algunos modelos de redistribución de riqueza y a una versión simplificada de la ecuación de Boltzmann, introducida por Kac. Se desarrolla una técnica de coupling que permite obtener resultados de propagación de caos con tasas polinomiales moderadas en N y t. Finalmente, en el Capítulo 4 se utiliza esta técnica en el contexto de la ecuación de Boltzmann y se obtiene el resultado principal de la tesis (el cual mejora significativamente la tasa uniforme obtenida por Mischler y Mouhot en 2013): Teorema. Para la ecuación de Boltzmann espacialmente homogénea en el caso de las moléculas de Maxwell, se tiene una tasa uniforme de propagación de caos, en distancia de Wasserstein 2 al cuadrado, de orden casi N^{−1/6}.

In this thesis, two numerical modeling methods are used to investigate the thermal conductivity of the polymer electrolyte membrane (PEM) fuel cell gas diffusion layer (GDL). First, an analytical model is used to study the through-plane thermal conductivity from representative physical GDL models informed by microscale computed tomography imaging of four commercially available GDL materials. The effect of the heterogeneity of the through-plane porosity of the GDL and polytetrafluoroethylene (PTFE) treatment is studied and it is noted that the high porosity surface transition regions have a dominating effect over the addition of PTFE in impacting the overall thermal conductivity. Next, the lattice Boltzmann method (LBM) is employed to study both the in-plane and through-plane thermal conductivity of stochastic numerically generated GDL modeling domains. The effect of GDL compression, binder content, PTFE treatment, addition of a microporous layer (MPL), heterogeneous porosity distributions, and water saturation on the thermal conductivity are investigated.