When a ferromagnet is heated, it loses its magnetism. Stars and planets have magnetic fields, as does the Earth. But it is known that the center of the Earth is very hot. Therefore, to sustain the large magnetic field of a planet, we cannot look to simple ferromagnetism like that of a bar magnet, but we have to look at the movement of electric charges within the Earth’s molten core to generate magnetic field. This magnetic field sustainment against ohmic dissipation by turbulent flow is referred to as the turbulent dynamo effect. Theoretical research into the mechanisms that create the dynamo has been actively pursued for several decades, culminating recently in massive computer simulations of the Earth’s core. Most of these studies have employed the equations of magnetohydrodynamics (MHD), a nonlinear theory of electrically conducting fluids. The EDQNM (Eddy-Damped Quasi-Normal Markovian) closure is a statistical model designed so that the turbulence equations derived from Navier-Stokes dynamics can be closed and satisfy the realizability condition of positivity of the kinetic energy spectrum. In case of MHD turbulence, realizability requires more work. We have proved in an earlier work that equations analogous to those expected of the EDQNM closure for MHD without mean fields satisfy the appropriate realizability conditions (Turner and Pratt 1999). In this work, we discuss requirements needed to make the MHD equations realizable with mean fields, extending those of neutral fluid turbulence by Turner [1]. Finally, we discuss direct numerical simulations and the correspondence of the statistical theories with simulation results.

archives@tulane.edu / This dissertation utilizes molecular theory and simulations to study thermodynamics of ions in electrolyte solutions of practical interest. The first half of this work focuses on two important electrochemical energy storage systems: Lithium ion batteries and supercapacitors based on carbon nanotube (CNT) forests. In lithium ion batteries, the characteristics of Li+ transport are studied in the solid electrolyte interphase of batteries. This study has potential applications in the design and theoretical testing of novel fast-charging batteries. The work on CNT supercapacitor focuses on the dependence of capacitance on pore spacing and electrode potentials. In the second half, the hydration of halides (fluoride and chloride) are studied using Quasi-chemical theory (QCT). Here, refinements in the implementation of QCT are pursued, leading to free energies that are in excellent agreement with experiments. This advancement should be helpful to address issues such as Hofmeister effects and selectivity in ion channels. / 1 / Ajay Muralidharan

In this thesis we apply the idea of a barcode from persistent homology to four hierarchical clustering methods: single, average, complete, and Ward's linkage. Desirable theoretical properties of dendrograms, the standard tool to visualize the output of hierarchical clustering methods, were described by Carlsson. We define analogous properties for hierarchical clustering quasi-barcodes and prove that average and complete quasi-barcodes possess a property that dendrograms do not. We discuss how to decide where to "cut" the output of hierarchical clustering quasi-barcodes based on the distance between the heights at which clusters merge. We find the best possible matching for calculating the Wasserstein distance between quasi-barcodes built from the same number of data points all born at time 0. We also prove that single, average, and complete quasi-barcodes are stable in the sense that small perturbations in distances between points produce small changes in quasi-barcodes. In order to test the efficiency of quasi-barcodes and the cut-off criteria, we generate datasets of points arranged in blobs or concentric circles and look whether the combination of the quasi-barcode with the cut-off criteria successfully finds the right amount of clusters in the dataset and whether it places points in the correct clusters. Finally, we apply these tools to datasets from New York University and Peking University of typically developed controls and attention hyperactivity deficit disorder subjects between the ages of 7 and 18.

The main subject of this thesis is solitons due to degenerate parametric four-wave mixing. Derivation of the governing equations is carried out for both spatial solitons (slab waveguide) and temporal solitons (optical fibre). Higher-order effects that are ignored in the standard paraxial approximation are discussed and estimated. Detailed analysis of conventional solitons is carried out. This includes discovery of various solitons families, linear stability analysis of fundamental and higher-order solitons, development of theory describing nonlinear dynamics of higher-order solitons. The major findings related to the stationary problem are bifurcation of a two-frequency soliton family from an asymptotic family of infinitely separated one-frequency solitons, jump bifurcation and violation of the bound state principle. Linear stability analysis shows a rich variety of internal modes of the fundamental solitons and existence of a stability window for higher-order solitons. Theory for nonlinear dynamics of higher-order solitons successfully predicts the position and size of the stability window, and various instability scenarios. Equivalence between direct asymptotic approach and invariant based approach is demonstrated. A general analytic approach for description of localised solutions that are in resonance with linear waves (quasi-solitons and embedded solitons) is given. This includes normal form theory and approximation of interacting particles. The main results are an expression for the amplitude of the radiating tail of a quasi-soliton, and a two-fold criterion for existence of embedded solitons. Influence of nonparaxiality on soliton stability is investigated. Stationary instability threshold is derived. The major results are shift and decreasing of the size of the stability window for higher-order solitons. The latter is the first demonstration of the destabilizing influence of nonparaxiality on higher-order solitons. Analysis of different aspects of solitons is based on universal approaches and methods. This includes Hamiltonian formalism, consideration of symmetry properties of the model, development of asymptotic models, construction of perturbation theory, application of general theorems etc. Thus, the results obtained can be extended beyond the particular model of degenerate four-wave mixing. All theoretical predictions are in good agreement with the results of direct numerical modeling.

Le principal résultat de la thèse est un théorème de convexité réel pour les applications moment à valeurs dans un groupe de Lie. Ce théorème est appliqué à la construction de sous-variétés lagrangiennes dans les quotients quasi-hamiltoniens, en particulier dans les espaces de représentations de groupes de surfaces. La notion de représentation décomposable fournit une interprétation géométrique de la sous-variété lagrangienne obtenue.

On présente quelques résultats concernant l'existence ou l'inexistence de décompositions géométriques sur les variétés de dimension 3, compactes ou non.

No description available.

<p>This dissertation presents the first experiments on radio frequency (rf) spectroscopy of a quasi-two dimensional strongly interacting ultracold atomic Fermi gas. A 50-50 mixture of spin-up and spin-down atoms is confined in a series of pancake-shaped traps produced using an optical standing-wave. To make the system quasi-two dimensional, I adjust the Fermi energy in the weakly confined direction to be comparable to the harmonic oscillator energy level spacing in the tightly confined direction.</p><p>For a perfectly two dimensional system, at low enough temperature, spin-up and spin-down atoms should form dimers in the ground state of the tightly confined direction. However, in our quasi-two dimensional system I find that the simple dimer theory does not agree with the measured radio-frequency spectra. Instead, the data can be explained by polaron to polaron transitions, which is a many-body effect. Here, a polaron is a spin-down impurity surrounded by a cloud of particle-hole pairs in a spin-up Fermi sea. With this unique strongly interacting quasi-two dimensional system, I am able to study the interplay between confinement induced two-body pairing and many-body physics in confined mesoscopic systems of several hundred atoms, which has not been previously explored and offers new challenges for predictions.</p> / Dissertation

The use of multiple antennas at the transmitter and/or the receiver promises greatly increased capacity. This can be useful to meet the ever growing demand of wireless connectivity, provided we can find techniques to efficiently exploit the advantages of the Multiple-Input Multiple-Output (MIMO) system. This work explores the MIMO system in a flat quasi-static fading scenario. Such a channel occurs, for example, in packet data systems, where the channel fade is constant for the duration of a codeword and changes independently from one transmission to another. We first show why it is hard to compute the true constrained modulation outage capacity. As an alternative, we present achievable lower bounds to this capacity based on existing space-time codes. The bounds we compute are the fundamental limits to the performance of these space-time codes under maximum-likelihood decoding, optimal outer codes and asymptotically long lengths. These bounds also indicate that MIMO systems have different behavior under Gaussian signaling (unconstrained input) and under the finite alphabet setting. Our results naturally suggest the use of concatenated codes to approach near-capacity performance. However, we show that a system utilizing an iterative decoder has a fundamental limit – it cannot be universal and therefore it cannot perform arbitrarily close to its outage limit. Next, we propose two different transceiver structures that have good performance. The first structure is based on a novel BCJR-decision feedback decoder which results in performance within a dB of the outage limit. The second structure is based on recursive realizations of space-time trellis codes and uses iterative decoding at the receiver. This recursive structure has impressive performance even when the channel has time diversity. Thus, it forms the basis of a very flexible and robust MIMO transceiver structure.

The Poincare equations, also known as Lagrange's equations in quasi coordinates, are revisited with special attention focused on a diagonal form. The diagonal form stems from a special choice of quasi velocities that were first introduced by Georg Hamel nearly a century ago. The form has been largely ignored because the quasi velocities create so-called Hamel coefficients that appear in the governing equations and are based on the partial derivative of the mass matrix factorization. Consequently, closed-form expressions for the Hamel coefficients can be difficult to obtain and relying on finite-dimensional, numerical methods are unattractive. In this thesis we use a newly developed operator overloading technique to automatically generate the Hamel coefficients through exact partial differentiation together with numerical evaluation. The equations can then be numerically integrated for system simulation. These special Poincare equations are called the Hamel Form and their usefulness in dynamic modeling and control is investigated. Coordinated control algorithms for an automatic retargeting system are developed in an attempt to protect an area against direct assaults. The scenario is for a few weapon systems to suddenly be faced with many hostile targets appearing together. The weapon systems must decide which weapon system will attack which target and in whatever order deemed sufficient to defend the protected area. This must be performed in a real-time environment, where every second is crucial. Four different control methods in this thesis are developed. They are tested against each other in computer simulations to determine the survivability and thought process of the control algorithms. An auction based control algorithm finding targets of opportunity achieved the best results.