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Articles 1 - 9 of 9
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Electromagnetic Resonant Scattering In Layered Media With Fabrication Errors, Emily Anne Mchenry
Electromagnetic Resonant Scattering In Layered Media With Fabrication Errors, Emily Anne Mchenry
LSU Doctoral Dissertations
In certain layered electromagnetic media, one can construct a waveguide that supports a harmonic electromagnetic field at a frequency that is embedded in the continuous spectrum. When the structure is perturbed, this embedded eigenvalue moves into the complex plane and becomes a “complex resonance” frequency. The real and imaginary parts of this complex frequency have physical meaning. They lie behind anomalous scattering behaviors known collectively as “Fano resonance”, and people are interested in tuning them to specific values in optical devices. The mathematics involves spectral theory and analytic perturbation theory and is well understood [16], at least on a theoretical …
Information Theoretic Study Of Gaussian Graphical Models And Their Applications, Ali Moharrer
Information Theoretic Study Of Gaussian Graphical Models And Their Applications, Ali Moharrer
LSU Doctoral Dissertations
In many problems we are dealing with characterizing a behavior of a complex stochastic system or its response to a set of particular inputs. Such problems span over several topics such as machine learning, complex networks, e.g., social or communication networks; biology, etc. Probabilistic graphical models (PGMs) are powerful tools that offer a compact modeling of complex systems. They are designed to capture the random behavior, i.e., the joint distribution of the system to the best possible accuracy. Our goal is to study certain algebraic and topological properties of a special class of graphical models, known as Gaussian graphs. First, …
On Braids, Branched Covers And Transverse Invariants, Jose Hector Ceniceros
On Braids, Branched Covers And Transverse Invariants, Jose Hector Ceniceros
LSU Doctoral Dissertations
In this work, we present a brief survey of knot theory supported by contact 3-manifolds. We focus on transverse knots and explore different ways of studying transverse knots. We define a new family of transverse invariants, this is accomplished by considering $n$-fold cyclic branched covers branched along a transverse knot and we then extend the definition of the BRAID invariant $t$ defined in cite{BVV} to the lift of the transverse knot. We call the new invariant the lift of the BRAID invariant and denote it by $t_n$. We then go on to show that $t_n$ satisfies a comultiplication formula and …
Manifestations Of Symmetry In Polynomial Link Invariants, Kyle Istvan
Manifestations Of Symmetry In Polynomial Link Invariants, Kyle Istvan
LSU Doctoral Dissertations
The use and detection of symmetry is ubiquitous throughout modern mathematics. In the realm of low-dimensional topology, symmetry plays an increasingly significant role due to the fact that many of the modern invariants being developed are computationally expensive to calculate. If information is known about the symmetries of a link, this can be incorporated to greatly reduce the computation time. This manuscript will consider graphical techniques that are amenable to such methods. First, we discuss an obstruction to links being periodic, developed jointly with Dr. Khaled Qazaqzeh at Kuwait University, using a model developed by Caprau and Tipton. We will …
Reduced Order Models For Beam-Wave Interaction In High Power Microwave Sources, Lokendra Singh Thakur
Reduced Order Models For Beam-Wave Interaction In High Power Microwave Sources, Lokendra Singh Thakur
LSU Doctoral Dissertations
We apply an asymptotic analysis to show that corrugated waveguides can be represented as cylindrical waveguides with smooth metamaterial coatings when the corrugtions are subwavelength. Here the metamaterial delivers an effective anisotropic surface impedance, effective dielectric constant, and imparts novel dispersive effects on signals traveling inside the waveguide. These properties arise from the subwavelength resonances of the metamaterial. For sufficiently deep corrugations, the waveguide exhibits backward wave propagation, which can be understood in the present context as a multi-scale phenomenon resulting from local resonances inside the subwavelength geometry. Our approach is well suited to numerical computation and we provide a …
On The Skein Theory Of 0-Framed Surgery Along The Trefoil Knot, Andrew Robert Holmes
On The Skein Theory Of 0-Framed Surgery Along The Trefoil Knot, Andrew Robert Holmes
LSU Doctoral Dissertations
In this dissertation, we will give a generating set of the Kauffman bracket skein module over the field Q(A) of 0-framed surgery along the trefoil knot. This generating set is described as a certain subset of a known basis for the skein module over Z[A^±1] of the trefoil exterior.
Moduli Spaces Of Flat Gsp-Bundles, Neal David Livesay
Moduli Spaces Of Flat Gsp-Bundles, Neal David Livesay
LSU Doctoral Dissertations
A classical problem in the theory of differential equations is the classification of first-order singular differential operators up to gauge equivalence. A related algebro-geometric problem involves the construction of moduli spaces of meromorphic connections. In 2001, P. Boalch constructed well-behaved moduli spaces in the case that each of the singularities are diagonalizable. In a recent series of papers, C. Bremer and D. Sage developed a new approach to the study of the local behavior of meromorphic connections using a geometric variant of fundamental strata, a tool originally introduced by C. Bushnell for the study of p-adic representation theory. Not only …
Asymptotic Formulae For Restricted Unimodal Sequences, Richard Alexander Frnka
Asymptotic Formulae For Restricted Unimodal Sequences, Richard Alexander Frnka
LSU Doctoral Dissertations
Additive enumeration problems, such as counting the number of integer partitions, lie at the intersection of various branches of mathematics including combinatorics, number theory, and analysis. Extending partitions to integer unimodal sequences has also yielded interesting combinatorial results and asymptotic formulae, which form the subject of this thesis. Much like the important work of Hardy and Ramanujan proving the asymptotic formula for the partition function, Auluck and Wright gave similar formulas for unimodal sequences. Following the circle method of Wright, we provide the asymptotic expansion for unimodal sequences with odd parts. This is then generalized to a two-parameter family of …
Extraction Of Displacement Fields In Heterogeneous Media Using Optimal Local Basis Functions, Paul Derek Sinz
Extraction Of Displacement Fields In Heterogeneous Media Using Optimal Local Basis Functions, Paul Derek Sinz
LSU Doctoral Dissertations
The Multiscale Spectral Generalized Finite Element Method (MS-GFEM) was developed in recent work by Babuska and Lipton. The method uses optimal local shape functions, optimal in the sense of the Kolmogorov n-width, to approximate solutions to a second order linear elliptic partial differential equation with L-infinity coefficients. In this dissertation an implementation of MS-GFEM over a two subdomain partition of unity is outlined and several numerical experiments are presented. The method is applied to compute local fields inside high contrast particle suspensions. The method's performance is evaluated for various examples with different contrasts between reinforcement particles and matrix material. The …