Fung Shui Cheung. / Thesis (M. Phil.)--Chinese University of Hongkong. / Bibliography: leaves 177-188.

This thesis studies the Bar-Natan skein module of the solid torus with a particular boundary curve system, and in particular a diagrammatic presentation of it due to Russell. This module has deep connections to topology and categorification: it is isomorphic to both the total homology of the (n,n)-Springer variety and the 0th Hochschild homology of the Khovanov arc ring H^n. We can also view the Bar-Natan--Russell skein module from a representation-theoretic viewpoint as an extension of the Frenkel--Khovanov graphical description of the Lusztig dual canonical basis of the nth tensor power of the fundamental U_q(sl_2)-representation. One of our primary results is to extend a dualization construction of Khovanov using Jones--Wenzl projectors from the Lusztig basis to the Russell basis. We also construct and explore several deformations of the Russell skein module. One deformation is a quantum deformation that arises from embedding the Russell skein module in a space that obeys Kauffman--Lins diagrammatic relations. Our quantum version recovers the original Russell space when q is specialized to -1 and carries a natural braid group action that recovers the symmetric group action of Russell and Tymoczko. We also present an equivariant deformation that arises from replacing the TQFT algebra A used in the construction of the rings H^n by the equivariant homology of the two-sphere with the standard action of U(2) and taking the 0th Hochschild homology of the resulting deformed arc rings. We show that the equivariant deformation has the expected rank. Finally, we consider the Khovanov two-functor F from the category of tangles. We show that it induces a surjection from the space of cobordisms of planar (2m, 2n)-tangles to the space of (H^m, H^n)-bimodule homomorphisms and give an explicit description of the kernel. We use our result to introduce a new quotient of the Russell skein module.

We provide a new relative trace formula approach to the theorem of Waldspurger on toric periods for GL₂, with possible applications to the global Gross-Prasad conjecture for orthogonal groups.

Um dos teoremas conhecidos de Poincaré afirma: Seja f um homeomorfismo do círculo que preserva orientação. Se p/q, com mdc(p, q) = 1, é o número de rotação de f, então f possui um ponto periódico de período q. Quando o conceito de número de rotação para um homeomorfismo do círculo é generalizado para um homeomorfismo f : T2 ? T2 homotópico à identidade, o resultado é um subconjunto convexo do plano R2, chamado conjunto de rotação e é denotado por ½(F) onde F é um levantamento de f. No caso que ½(F) tem interior não vazio, J. Franks obteve resultados análogos ao Teorema de Poincaré. Nesta dissertação estudamos um resultado análogo, obtido por Jonker e Zhang, quando ½(F) não tem interior. Mais precisamente: assumimos que ½(F) é um segmento de reta com inclinação irracional e mostramos que se 1 n(p1, p2) ? ½(F), com mdc(p1, p2, n) = 1, então f possui um ponto periódico de período n / One of the well know results of Poincaré state: Let f be an orientation preserving circle homeomorphism. If p/q, with mdc(p, q) = 1, is the rotation number of f, then there is a periodic point for f whose period is q. When the concept of rotations number, for orientation preserving circle homeomorphism, is generalized for torus homeomorphism f : T2 ? T2 that are homotopic to the identity, it results in a convex subset of R2, called rotation set and is denoted by ½(F) where F is a lifting of f. In the case that ½(F) has non-empty interior, J. Franks proved similar results to the Poincaré Theorem. In this work, when ½(F) has empty interior, we study an similar result obtained by Jonker and Zhang. More precisely: they suppose that the rotation set ½(F) is a line segment with irrational slope and demonstrate that if 1 n(p1, p2) ? ½(F), with mdc(p1, p2, n) = 1, then f has a periodic point of period n

Bibliography : leaves 184-188. / vi, 188 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.)--University of Adelaide, Dept. of Pure Mathematics, 1994

No description available.

Phenols are priority pollutants that are commonly found in a large number of industrial wastewaters. Different processes are currently available for the elimination of phenol from wastewater but present some disadvantages like low efficiency, high energy-consumption, the necessity of acclimatisation of the sludges or the limitation of the treatment capacity. The need to find alternatives has made the enzymatic processes a good option. In the last two decades, several processes were implemented with different enzymes from plants and microorganisms, including peroxidases from several sources, as the horseradish peroxidase.Also, different enzyme configurations, free or immobilised enzyme and different supports for immobilisation have been studied. Substantial attention has been devoted to the covalent immobilisation of enzymes on porous insoluble supports such as glass, alumina, silica, and chitosan.The main novelty of this work is the utilisation of a torus reactor for the removal of organic contaminants from wastewaters. This reactor, which can be considered as a loop reactor, presents some advantages over other stirred tank reactors.The goal of this work is the study of the hydrodynamics of a torus reactor for its further application in the enzymatic elimination of phenol and the coupling of the kinetics and the modelisation.In a first step, the enzymatic elimination of phenol was experimentally studied in the torus reactor. In order to compare the performances, several assays were also carried out with a stirred reactor. A high degree of conversion was obtained for the enzymatic elimination of phenol in both reactors with the tested quantities of phenol. It was concluded that, keeping a ratio of 1:1 between the phenol and the H2O2 initial molar quantities, the highest final reaction conversion was obtained. Using the torus reactor was obtained 97% of phenol conversion when the optimal concentrations of substrates were usedIn order to improve economically the process, the enzyme should be used in a continuous regime over a long time period to exploit it completely. For this reason it was necessary to immobilise the enzyme. This work presents a new configuration that has never been tested: the horseradish peroxidase supported on Eupergit.In a second step, the characterisation using the CFD of the flow-field in a torus reactor of 100 ml, similar to the experimental reactor, was carried out for two different configurations, batch and continuous operating modes. Moreover, the scale-up of the volume of the torus reactor was carried out using CFD for a 300 ml reactor.Finally, the enzymatic reaction of phenol with the HRP was modelled using the CFD coupled to the kinetic model of the enzymatic reaction to the flow simulation. These results allowed the possibility of optimising and scaling-up the process using the CFD modelisation. / Los compuestos fenólicos son contaminantes prioritarios que se encuentran comúnmente en una gran cantidad de efluentes industriales. Diferentes procesos están disponibles actualmente para la eliminación de fenol desde dicho efluentes pero los mismos presentan algunas desventajas como pueden ser una baja eficiencia, un mayor consumo de energía, la producción de lodos conteniendo hierro o limitaciones en la capacidad de tratamiento. La necesidad de encontrar alternativas a estos problemas ha hecho del proceso enzimático una buena opción. En las últimas dos décadas, varios procesos han sido implementados utilizando diferentes enzimas extraídas de plantas y microorganismos como pueden ser las peroxidasas de diversas fuentes, incluyendo la horseradish peroxidasa.Diferentes configuraciones de enzimas, libre e inmovilizada y diferentes soportes para la inmovilización han sido también estudiados. Sustancial atención ha sido dedicada a la inmovilización de enzimas por enlace covalente sobre soportes porosos insolubles tales como vidrio, aluminio, sílice y chitosan. El objetivo de este trabajo es el estudio de la hidrodinámica dentro de un reactor tórico para su posterior aplicación en la eliminación enzimática de fenol y el acople entre las cinéticas y la modelización.En una primera etapa, la eliminación enzimática de fenol es estudiada experimentalmente en el reactor tórico. Con el objetivo de comparar el rendimiento de dicho reactor, varios ensayos se realizaron en un reactor agitado tradicional. Un alto grado de conversión de fenol ha sido obtenido para la eliminación enzimática de fenol en ambos reactores para las cantidades estudiadas de fenol. Ha sido observado que es necesario mantener una relación de 1:1 entre la concentración inicial de fenol y la de peróxido de hidrógeno para lograr la mayor conversión de fenol. Usando el reactor tórico ha sido obtenido un 97% de conversión de fenol cuando las concentraciones óptimas de substratos y enzimas fueron utilizados. Con el objetivo de mejorar económicamente el proceso y hacerlo factible para su uso a escala industrial, la enzima debería ser utilizada en un proceso en continuo sobre un largo período de tiempo para explotarla completamente. Por esta razón, ha sido necesario inmovilizar la enzima. Este trabajo muestra una nueva configuración que no ha sido aún probada: la horseradish peroxidase soportada en Eupergit. Asimismo, la caracterización usando CFD del campo de flujo de un reactor tórico similar al experimental de 100 ml ha sido realizada para un reactor trabajando de forma batch y continua. Un escalado en el volumen del reactor tórico ha sido realizado utilizando CFD para un reactor de 300 ml. Finalmente, la reacción enzimática de fenol con HRP has sido modelada acoplando el modelo cinético obtenido experimentalmente con las simulaciones del campo de flujo dentro del reactor. Estos resultados permitirán la optimización y el escalado del proceso usando CFD.

Io has one of the most dynamic atmospheres in the solar system due in part to an orbital resonance with Europa and Ganymede that causes intense tidal heating and volcanism. The volcanism serves to create a myriad of volcanic plumes across Io's surface that sustain temporally varying local atmospheres. The plumes primarily eject sulfur dioxide (SO₂) that condenses on Io's surface during the relatively cold night. During the day, insolation warms the surface to temperatures where a global partially collisional atmosphere can be sustained by sublimation from SO₂ surface frosts. Both the volcanic and sublimation atmospheres serve as the source for the Jovian plasma torus which flows past Io at ~57 km/s. The high energy ions and electrons in the Jovian plasma torus interact with Io's atmosphere causing atmospheric heating, chemical reactions, as well as altering the circumplanetary winds. Energetic ions which impact the surface can sputter material and create a partially collisional atmosphere. Simulations suggest that energetic ions from the Jovian plasma cannot penetrate to the surface when the atmospheric column density is greater than 10¹⁵ cm⁻². These three mechanisms for atmospheric support (volcanic, sublimation, and sputtering) all play a role in supporting Io's atmosphere but their relative contributions remain unclear. In the present work, the Direct Simulation Monte Carlo (DSMC) method is used to simulate the interaction of Io's atmosphere with the Jovian plasma torus and the results are compared to observations. These comparisons help constrain the relative contributions of atmospheric support as well as highlight the most important physics in Io's atmosphere. These rarefied gas dynamics simulations improve upon earlier models by using a three-dimensional domain encompassing the entire planet computed in parallel. The effects of plasma heating, planetary rotation, inhomogeneous surface frost, molecular residence time of SO₂ on the exposed non-frost surface, and surface temperature distribution are investigated. Circumplanetary flow is predicted to develop from the warm dayside toward the cooler nightside. Io's rotation leads to a highly asymmetric frost surface temperature distribution (due to the frost's high thermal inertia) which results in circumplanetary flow that is not axi-symmetric about the subsolar point. The non-equilibrium thermal structure of the atmosphere, specifically vibrational and rotational temperatures, is also examined. Plasma heating is found to significantly inflate the atmosphere on both the dayside and nightside. The plasma energy flux causes high temperatures at high altitudes, but plasma energy depletion through the dense gas column above the warmest frost permits gas temperatures cooler than the surface at low altitudes. A frost map (Douté et al., 2001) is used to control the sublimated flux of SO₂ which can result in inhomogeneous column densities that vary by nearly a factor of four for the same surface temperature. A short residence time for SO₂ molecules on the non-frost component is found to smooth lateral atmospheric inhomogeneities caused by variations in the surface frost distribution, creating an atmosphere that looks nearly identical to one with uniform frost coverage. A longer residence time is found to agree better with mid-infrared observations (Spencer et al., 2005) and reproduce the observed anti-Jovian/sub-Jovian column density asymmetry. The computed peak dayside column density for Io agrees with those suggested by Lyman-[alpha] observations (Feaga et al., 2009) assuming a surface frost temperature of 115 K. On the other hand, the peak dayside column density at 120 K is a factor of five larger and is higher than the upper range of observations (Jessup et al., 2004; Spencer et al., 2005). The results of the original DSMC simulations of Io's atmosphere show that the most important and sensitive parameter is the SO₂ surface frost temperature. To improve upon the original surface temperature model, we constrain Io's surface thermal distribution by a parametric study of its thermophysical properties. Io's surface thermal distribution is represented by three thermal units: sulfur dioxide (SO₂) frosts/ices, non-frosts (probably sulfur allotropes and/or pyroclastic dusts), and hot spots. The hot spots included in the thermal model are static high temperature surfaces with areas and temperatures based on Keck infrared observations. Elsewhere, over frosts and non-frosts, the thermal model solves the one-dimensional heat conduction equation in depth into Io's surface and includes the effects of eclipse by Jupiter, radiation from Jupiter, and latent heat of sublimation and condensation. The best fit parameters for the SO₂ frost and non-frost units are found by using a least-squares method and fitting to observations of the Hubble Space Telescope's Space Telescope Imaging Spectrograph (HST STIS) mid- to near-UV reflectance spectra and Galileo photo-polarimeter (PPR) brightness temperature. The thermophysical parameters are the frost Bond albedo, and thermal inertia, as well as the non-frost surface Bond albedo, and thermal inertia. The best fit parameters are found to be [equations] for the SO2 frost surface and [equations] for the non-frost surface. These surface thermophysical parameters are then used as boundary conditions in global atmospheric simulations of Io's sublimation-driven atmosphere using DSMC. The DSMC simulations show that the sub-Jovian hemisphere is significantly affected by the daily solar eclipse. The SO₂ surface frost temperature is found to drop ~5 K during eclipse but the column density falls by a factor of 20 compared to the pre-eclipse column due to the exponential dependence of the SO₂ vapor pressure on the SO₂ surface frost temperature. Supersonic winds exist prior to eclipse but become subsonic during eclipse because the collapse of the atmosphere significantly decreases the day-to-night pressure gradient that drives the winds. Prior to eclipse, the supersonic winds condense on and near the cold nightside and form a highly non-equilibrium oblique shock near the dawn terminator. In eclipse, no shock exists since the gas is subsonic and the shock only reestablishes itself an hour or more after egress from eclipse. Furthermore, the excess gas that condenses on the non-frost surface during eclipse leads to an enhancement of the atmosphere near dawn. The dawn atmospheric enhancement drives winds that oppose those that are driven away from the peak pressure region above the warmest area of the SO₂ frost surface. These opposing winds meet and are collisional enough to form stagnation point flow. The simulations are compared to Lyman-[alpha] observations in an attempt to explain the asymmetry between the dayside atmospheres of the anti-Jovian and sub-Jovian hemispheres. A composite "average dayside atmosphere" is formed from a collisionless simulation of Io's atmosphere throughout an entire orbit. The composite "average dayside" atmosphere without the effect of global winds indicates that the sub-Jovian hemisphere should have lower average column densities than the anti-Jovian hemisphere (with the strongest effect at the sub-Jovian point) due entirely to the diurnally averaged effect of eclipse. Lastly, a particle description of the plasma is coupled with the sophisticated surface thermal model and a final set of global DSMC atmospheric simulations are performed. The particle description of energetic ions from the Jovian plasma torus allows for momentum transfer from the ions to the neutral atmosphere. Also, the energetic ions (or solar photons) can dissociate the neutral atmosphere and cause sputtering of SO₂ on the surface. SO₂ remains the dominant dayside species (>90%) despite being dissociated by ions and photons to form O, O₂, S, and SO. SO₂ remains the dominant atmospheric species on the nightside between dusk and midnight due to sputtering of SO₂ surface frosts by energetic ions as well as the high thermal inertia of SO₂ frosts that cause the surface temperature to cool slowly and thus sublime a thicker SO₂ atmosphere. O₂ becomes the dominant atmospheric species above coldest areas of the surface because it is non-condensable at Io's surface temperatures and other species are sticking to the surface. SO and O are present in similar gas fractions because they are created together via the same ion and photo-dissociation reactions. Sulfur column densities are the lowest throughout the atmosphere because S is created slowly via direct dissociation of SO₂; it is instead created primarily through dissociation of SO. The momentum transfer from the plasma is found to have substantial effect on the global wind patterns. The interaction between the plasma pressure and day-to-night pressure gradient is highly dependent on Io's subsolar longitude. Similar to previous simulations, the westward winds reach higher Mach numbers and wind speeds than the eastward winds. This is because the westward winds are accelerated by a larger day-to-night pressure gradient due to the very cold surface temperatures that exist prior to dawn. Eastward equatorial winds on the nightside are accelerated by the plasma pressure and condense out near the dawn terminator after traveling ~3/4 of the circumference of Io. O₂ is pushed to the nightside by the circumplanetary winds where it builds-up until it reaches an equilibrium column density. On the nightside, O₂ is destroyed by ion dissociation. On the nightside, a shear layer develops between the equatorial eastward winds and stagnant non-condensable species at mid-latitudes. This shear layer generates lateral vorticity which is especially visible in O₂ streamlines. Large cyclones develop in the northern and southern hemispheres and are most apparent in the O₂ wind patterns because other species condense out on the nightside. / text

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Thesis (Ph. D.)--University of Texas at Austin, 2004. / Supervisor: Philip J. Morrison. Vita. Includes bibliographical references.