Petroleum leakage from storage tanks, underground pipelines during exploration and production facilities is the reason of hydrocarbon migration into the groundwater. Petroleum companies use various LNAPL (Light Non-Aqueous Phase Liquids) recovery techniques to prevent lateral migration of hydrocarbon through the offsite of a facility. A petroleum refinery facility in the Gulf Coast region of South Texas was selected to evaluate ongoing LNAPL recovery system. Three analyses were carried out in this study. First, hydrogeologic conditions were determined using DGP (Diagnostic Gauge Plots). The concept of why ANT (Apparent LNAPL Thickness) is not a good metric to estimate recovery rates was explained based on hydrogeologic conditions of LNAPL. LNAPL and groundwater surface contour maps were built to have information about the direction of flow. All map illustrations were created using ArcGIS software. Well configurations were used to determine hydrogeologic condition in case of lack sufficient data for DGP. Second, LNAPL transmissivity were estimated using API (American Petroleum Institute) LNAPL Transmissivity Workbook. LNAPL condition was required in estimating LNAPL transmissivity values with API workbook, where methods of analysis are dependent of LNAPL condition. Total fluids recovery data were also used to estimate transmissivity values in the study wells. 0.08 ft2/d transmissivity value was arbitrarily chosen to determine the endpoint of recovery. Third, LNAPL recovery rates were predicted using LDRM (LNAPL Distribution and Recovery Model) for 11 recovery wells in the study region. Single phase –water- extraction method was used for LNAPL recovery under atmospheric conditions. Soil and fluid properties along with recovery system data were required for LNAPL recovery estimation. Some of these data were available from the dataset provided by oil company and some of them were estimated using API and Rosetta databases. Soil properties, radius of recovery values, and water production rates were calibrated in order to fit the LDRM recovery and transmissivity results with the actual field data. The modeled recovery rates and transmissivity values were consistent with actual data. Projections for future in a well were made. The model can be used for the endpoint of recovery projections. / text

In this thesis, we set up a framework to define knot invariants for each choice of a symmetric space. In order to address this task, we start by defining appropriate notions of singular bundles and singular connections for a given symmetric space. We can associate a moduli space to any singular bundle defined over a compact 4-manifold with possibly non-empty boundary. We study these moduli spaces and show that they enjoy nice properties. For example, in the case of the symmetric space SU(n)/SO(n) the moduli space can be perturbed to an orientable manifold. Although this manifold is not necessarily compact, we introduce a comapctification of it. We then use this moduli space for singular bundles defined over 4-manifolds of the form YxR to define knot invariants. In another direction we mimic the construction of Donaldson invariants to define polynomial invariants for closed 4-manifolds equipped with smooth action of Z/2Z. / Mathematics

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In this thesis, we study two problems focusing on the interplay between geometric properties of differential equations and their invariants. / For the first project, we study the validity of the principle of symmetric criticality (PSC) in the context of invariant gauge fields over the four-dimensional non-reductive pseudo-Riemannian homogeneous spaces G/K recently classified by Fels & Renner (2006). Given H compact semi-simple, classification results are obtained for principal H-bundles over G/K admitting: (1) a G-action (by bundle automorphisms) projecting to left multiplication on the base, and (2) at least one G-invariant connection. There are two cases which admit nontrivial examples of such bundles and all G-invariant connections on these bundles are Yang--Mills. Using the invariant criteria obtained by Anderson--Fels--Torre, the validity of PSC is investigated for the bundle of connections and is shown to fail for all but one of the Fels--Renner cases. This failure arises from degeneracy of the scalar product on pseudo-tensorial forms restricted to the space of symmetric variations of an invariant connection. In the exceptional case where PSC is valid, there is a unique G-invariant connection which is moreover universal, i.e. it is a solution of the Euler--Lagrange equations associated to any G-invariant Lagrangian on the bundle of connections. This solution is a canonical connection associated with a weaker notion of reductivity which we introduce. / The second project is a study of the contact geometry of scalar second order hyperbolic equations in the plane of generic type. Following a derivation of parametrized contact-invariants to distinguish Monge--Ampere (class 6-6), Goursat (class 6-7) and generic (class 7-7) hyperbolic equations, we use Cartan's equivalence method to study the generic case. An intriguing feature of this class of equations is that every generic hyperbolic equation admits at most a nine-dimensional contact symmetry algebra. The nine-dimensional bound is sharp: normal forms for the contact-equivalence classes of these maximally symmetric equations are derived and explicit symmetry algebras are presented. Moreover, all such equations are Darboux integrable. An enumeration of several submaximally symmetric (eight and seven-dimensional) structures is also given.

6d (2, 0) theory on M5 branes is investigated by considering its KK modes on a 2d space. Selecting KK modes on different 2d spaces amounts to choosing different set of selfdual strings as the perturbative degrees of freedom thus will give the 6d theories related to each other by U-duality. The 4d effective theory for the KK modes is studied via the M5-D3 duality. Except for the (p, q) open strings, which is the KK mode arising from the selfdual strings, the 3-string junction should also be added since it is the bound state of the (p, q) open strings. The quantization of the 3-string junctions gives the fields, which, when lifted to 6d, may account for the conformal anomaly of the 6d (2, 0) theory. The interaction between the open strings and the 3-string junctions is also considered. The Lagrangian and the corresponding N=4 supersymmetry transformation is obtained up to some additional terms to be added. Although the original 6d (2, 0) theory is not constructed directly, the 4d effective theory for the KK modes gives an equivalent description, from which the 6d S-matrix can be calculated.

We compute the electrical conductivity and shear viscosity at leading order in hot Quantum Electrodynamics. Starting from the Kubo relation for electrical conductivity and shear viscosity, we use diagrammatic methods to write down the appropriate integral equations for bosonic and fermionic effective vertices. We also show how Ward identities can be used to put constraints on these integral equations. One of our main results is an equation relating the kernels of the integral equations with functional derivatives of the full self-energy; it is similar to what is obtained with two-particle-irreducible effective action methods. However, since we use Ward identities as our starting point, gauge invariance is preserved. Using these constraints obtained from Ward identities and also power counting arguments, we select the necessary diagrams that must be resummed at leading order. This includes all non-collinear (corresponding to 2 to 2 scatterings) and collinear (corresponding to 1+N to 2+N collinear scatterings) rungs responsible for the Landau-Pomeranchuk-Migdal effect. We also show the equivalence between our integral equations and the linearized Boltzmann equations of Arnold, Moore and Yaffe obtained using effective kinetic theory.

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Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 52-54). Also available via the Internet.

Thesis (Ph.D.)--Michigan State University. Dept. of Mathematics, 2008. / Title from PDF t.p. (viewed on July 6, 2009) Includes bibliographical references (p. 72-74). Also issued in print.