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Applied Mathematics

Louisiana State University

2013

Articles 1 - 15 of 15

Full-Text Articles in Physical Sciences and Mathematics

Uncertainty Quantification Of Film Cooling Effectiveness In Gas Turbines, Hessam Babaee Jan 2013

Uncertainty Quantification Of Film Cooling Effectiveness In Gas Turbines, Hessam Babaee

LSU Master's Theses

In this study the effect of uncertainty of velocity ratio on jet in crossflow and particual- rly film cooling performance is studied. Direct numerical simulations have been combined with a stochastic collocation approach where the parametric space is discretized using Multi-Element general Polynomial Chaos (ME-gPC) method. Velocity ratio serves as a bifurcation parameter in a jet in a crossflow and the dynamical system is shown to have several bifurcations. As a result of the bifurcations, the target functional is observed to have low-regularity with respect to the paramteric space. In that sense, ME-gPC is particularly effective in discretizing the parametric …

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Mixed Categories, Formality For The Nilpotent Cone, And A Derived Springer Correspondence, Laura Joy Rider Jan 2013

Mixed Categories, Formality For The Nilpotent Cone, And A Derived Springer Correspondence, Laura Joy Rider

LSU Doctoral Dissertations

Recall that the Springer correspondence relates representations of the Weyl group to perverse sheaves on the nilpotent cone. We explain how to extend this to an equivalence between the triangulated category generated by the Springer perverse sheaf and the derived category of di_x000B_erential graded modules over a dg-ring related to the Weyl group

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Application Of Helmholtz/Hodge Decomposition To Finite Element Methods For Two-Dimensional Maxwell's Equations, Zhe Nan Jan 2013

Application Of Helmholtz/Hodge Decomposition To Finite Element Methods For Two-Dimensional Maxwell's Equations, Zhe Nan

LSU Doctoral Dissertations

In this work we apply the two-dimensional Helmholtz/Hodge decomposition to develop new finite element schemes for two-dimensional Maxwell's equations. We begin with the introduction of Maxwell's equations and a brief survey of finite element methods for Maxwell's equations. Then we review the related fundamentals in Chapter 2. In Chapter 3, we discuss the related vector function spaces and the Helmholtz/Hodge decomposition which are used in Chapter 4 and 5. The new results in this dissertation are presented in Chapter 4 and Chapter 5. In Chapter 4, we propose a new numerical approach for two-dimensional Maxwell's equations that is based on …

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Large Deviations For Stochastic Navier-Stokes Equations With Nonlinear Viscosities, Ming Tao Jan 2013

Large Deviations For Stochastic Navier-Stokes Equations With Nonlinear Viscosities, Ming Tao

LSU Doctoral Dissertations

In this work, a Wentzell-Freidlin type large deviation principle is established for the two-dimensional stochastic Navier-Stokes equations (SNSE's) with nonlinear viscosities. We fi_x000C_rst prove the existence and uniqueness of solutions to the two-dimensionalstochastic Navier-Stokes equations with nonlinear viscosities using the martingale problem argument and the method of monotonicity. By the results of Varadhan and Bryc, the large deviation principle (LDP) is equivalent to the Laplace-Varadhan principle (LVP) if the underlying space is Polish. Then using the stochastic control and weak convergence approach developed by Budhiraja and Dupuis, the Laplace-Varadhan principle for solutions of stochastic Navier-Stokesequations is obtained in appropriate function …

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Refining The Characterization Of Projective Graphs, Perry K. Iverson Jan 2013

Refining The Characterization Of Projective Graphs, Perry K. Iverson

LSU Doctoral Dissertations

Archdeacon showed that the class of graphs embeddable in the projective plane is characterized by a set of 35 excluded minors. Robertson, Seymour and Thomas in an unpublished result found the excluded minors for the class of k-connected graphs embeddable on the projective plane for k = 1,2,3. We give a short proof of that result and then determine the excluded minors for the class of internally 4-connected projective graphs. Hall showed that a 3-connected graph diff_x000B_erent from K5 is planar if and only if it has K3,3 as a minor. We provide two analogous results for projective graphs. For …

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A Semigroup/Laplace Transform Approach To Approximating Flows, Ladorian Nichele Latin Jan 2013

A Semigroup/Laplace Transform Approach To Approximating Flows, Ladorian Nichele Latin

LSU Doctoral Dissertations

It is well known that all flows in a state space O induce a semigroup of linear operators on an appropriately chosen vector space of functions (observables) from O into a vector space Z (observations). After choosing appropriate continuity assumptions on the flow, the associated semigroup will be strongly continuous and will have a linear, infinitesimal generator A. The purpose of this dissertation is to explore approximation methods for linear semigroups and/or Laplace transform inversion methods in order to reconstruct the flow starting with the linear generator A . In preparing for these investigations, we collect some of the essential …

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Higher Algebraic K-Theory And Tangent Spaces To Chow Groups, Sen Yang Jan 2013

Higher Algebraic K-Theory And Tangent Spaces To Chow Groups, Sen Yang

LSU Doctoral Dissertations

In this work, using higher algebraic K-theory, we provide an answer to the following question asked by Green-Griffiths in [13]: Can one define the Bloch-Gersten-Quillen sequence Gj on infinitesimal neighborhoods Xj so that Ker(G1 &rarr G0)= TG0, Here TG0 should be the Cousin resolution of TKm(OX) and X is any n-dimensional smooth projective variety over a field k, chark=0. Our main results are as follows. The existence of Gj is discussed in chapter 3, following [8] and [18]. The main theorems are theorem5.2.5, theorem 5.2.6 and theorem …

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Extra Structures On Three-Dimensional Cobordisms, Xuanye Wang Jan 2013

Extra Structures On Three-Dimensional Cobordisms, Xuanye Wang

LSU Doctoral Dissertations

A Topological Quantum Field Theory (TQFT) is a functor from a cobordism category to the category of vector spaces, satisfying certain properties. An important property is that the vector spaces should be finite dimensional. For the WRT TQFT, the relevant 2 + 1-cobordism category is built from manifolds which are equipped with an extra structure such as a p1-structure, or an extended manifold structure. In chapter 1, we perform the universal construction of [3] on a cobordism category without this extra structure and show that the resulting quantization functor assigns an infinite dimensional vector space to the torus. In chapter …

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Finite Element Methods For Fourth Order Variational Inequalities, Yi Zhang Jan 2013

Finite Element Methods For Fourth Order Variational Inequalities, Yi Zhang

LSU Doctoral Dissertations

In this work we study finite element methods for fourth order variational inequalities. We begin with two model problems that lead to fourth order obstacle problems and a brief survey of finite element methods for these problems. Then we review the fundamental results including Sobolev spaces, existence and uniqueness results of variational inequalities, regularity results for biharmonic problems and fourth order obstacle problems, and finite element methods for the biharmonic problem. In Chapter 2 we also include three types of enriching operators which are useful in the convergence analysis. In Chapter 3 we study finite element methods for the displacement …

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Adaptive Stochastic Conjugate Gradient Optimization For Temporal Medical Image Registration, Huanhuan Xu Jan 2013

Adaptive Stochastic Conjugate Gradient Optimization For Temporal Medical Image Registration, Huanhuan Xu

LSU Master's Theses

We propose an Adaptive Stochastic Conjugate Gradient (ASCG) optimization algorithm for temporal medical image registration. This method combines the advantages of Conjugate Gradient (CG) method and Adaptive Stochastic Gradient Descent (ASGD) method. The main idea is that the search direction of ASGD is replaced by stochastic approximations of the conjugate gradient of the cost function. In addition, the step size of ASCG is based on the approximation of the Lipschitz constant of the stochastic gradient function. Thus, this algorithm could maintain the good properties of the conjugate gradient method, meanwhile it uses less gradient computation time per iteration and adjusts …

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Skein Theory And Topological Quantum Field Theory, Xuanting Cai Jan 2013

Skein Theory And Topological Quantum Field Theory, Xuanting Cai

LSU Doctoral Dissertations

Skein modules arise naturally when mathematicians try to generalize the Jones polynomial of knots. In the first part of this work, we study properties of skein modules. The Temperley-Lieb algebra and some of its generalizations are skein modules. We construct a bases for these skein modules. With this basis, we are able to compute some gram determinants of bilinear forms on these skein modules. Also we use this basis to prove that the Mahler measures of colored Jones polynomial of a sequence of knots converges to the Mahler measure of some two variable polynomial. The topological quantum field theory constructed …

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Multiplicity Formulas For Perverse Coherent Sheaves On The Nilpotent Cone, Myron Minn-Thu-Aye Jan 2013

Multiplicity Formulas For Perverse Coherent Sheaves On The Nilpotent Cone, Myron Minn-Thu-Aye

LSU Doctoral Dissertations

Arinkin and Bezrukavnikov have given the construction of the category of equivariant perverse coherent sheaves on the nilpotent cone of a complex reductive algebraic group. Bezrukavnikov has shown that this category is in fact weakly quasi-hereditary with Andersen--Jantzen sheaves playing a role analogous to that of Verma modules in category O for a semi-simple Lie algebra. Our goal is to show that the category of perverse coherent sheaves possesses the added structure of a properly stratified category, and to use this structure to give an effective algorithm to compute multiplicities of simple objects in perverse coherent sheaves. The algorithm is …

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Statistical Classification Problems In Assessment Of Teachers, Xuan Wang Jan 2013

Statistical Classification Problems In Assessment Of Teachers, Xuan Wang

LSU Master's Theses

Classification and regression trees form an important and indispensable tool in data analysis and classification problems. Class trees are described in detail with examples. The method is applied to a data set pertaining to evaluation of teachers. In addition, two other classification methods, bagging and AdaBoost are explained. These methods improve existing classifiers to nearly optimal classifiers.

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The Ring Theory And The Representation Theory Of Quantum Schubert Cells, Joel Benjamin Geiger Jan 2013

The Ring Theory And The Representation Theory Of Quantum Schubert Cells, Joel Benjamin Geiger

LSU Doctoral Dissertations

In recent years the quantum Schubert cell algebras, introduced by Lusztig and De Concini--Kac, and Procesi, have garnered much interest as this versatile class of objects are furtive testing grounds for noncommutative algebraic geometry. We unify the two main approaches to analyzing the structure of the torus-invariant prime spectra of quantum Schubert cell algebras, a ring theoretic one via Cauchon's deleting derivations and a representation theoretic characterization of Yakimov via Demazure modules. As a result one can combine the strengths of the two approaches. In unifying the theories, we resolve two questions of Cauchon and Mériaux, one of which involves …

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A Characterization Of Almost All Minimal Not Nearly Planar Graphs, Kwang Ju Choi Jan 2013

A Characterization Of Almost All Minimal Not Nearly Planar Graphs, Kwang Ju Choi

LSU Doctoral Dissertations

In this dissertation, we study nearly planar graphs, that is, graphs that are edgeless or have an edge whose deletion results in a planar graph. We show that all but finitely many graphs that are not nearly planar and do not contain one particular graph have a well-understood structure based on large Möbius ladders.

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