Electromagnetic Field Control and Optimization Using Metamaterials

Transformation optics has shown the ability to cloak an object from incident electromagnetic radiation is possible. However, the material parameters are inhomogeneous, anisotropic, and, in some instances, singular at various locations. In order for a cloak to be practically realized, simplified parameter sets are required. However, the simplified parameters result in a degradation in the cloaking function. Constitutive parameters for simplified two-dimensional cylindrical cloaks have been developed with two material property constraints. It was initially believed satisfying these two constraints would result in the simplified cylindrical cloaks having the same wave equation as an ideal cloak. Because of this error, the simplified cloaks were not perfect. No analysis was done to determine all material parameter constraints to enable a perfect two-dimensional cylindrical cloak. This research developed a third constraint on the material parameters. It was shown as the material parameters better satisfy this new equation, a two-dimensional cylindrical cloak\u27s hidden region is better shielded from incident radiation. Additionally, a novel way to derive simplified material parameters for two-dimensional cylindrical cloaks was developed. A Taylor series expansion dictated by the new constraint equation leads to simplified cloaks with significantly improved scattering width performances when compared to previous published results. During the course of this research, it was noted all cloak simulations are performed using finite element method (FEM) based numerical methods. A Green\u27s function was used to accurately calculate scattering widths from a two-dimensional cylindrical cloak with a perfect electrically conducting inner shell. Significant time improvements were achieved using the Green\u27s function compared to an FEM solution particularly as the computational domain size is increased. Finally, cloaks are physically realized using metamaterials. Design of metamaterials has typically been done empirically. Shifts in S-parameter measurements and the resulting extracted constitutive parameters are used to determine the impact to resonant regions due to various geometries. A new way to design and possibly optimize unit cell metamaterials was investigated using an eigendecomposition to identify the cell resonances. Different structures were shown to have different resonances, and control of the resonant locations can lead to optimum designs

Controlling the Transmitted Field into a Cylindrical Cloak\u27s Hidden Region

Constitutive parameters for simplified cylindrical cloaks have been developed such that εzµθ and εzµr match those of the ideal cylindrical cloak. Although they are not perfect, simplified cylindrical cloaks have been shown to inherit many of the power-bending properties of the ideal cloak. However, energy is transmitted into simplified cloaks\u27 hidden regions. Here, we develop a constraint equation that can be used to determine how closely field behavior within the simplified cylindrical cloak matches that of the ideal cloak. The deviation from this controlling equation can be reduced by controlling the cloak\u27s parameter value, μθ As the deviation from our constraint equation is decreased, the field transmitted into the cloak\u27s hidden region is reduced, resulting in less energy impinging on the cloaked object. This results in a smaller scattered field due to the presence of the cloaked object. However, the resulting impedance mismatch at r = b results in a significant scattered field by the cloak itself. Thus, we have found when using cylindrical cloaks that satisfy the ideal values of εzµθ and εzµr for scattering width reduction, it is more important to have a matched impedance at r = b than to have a smaller field transmitted into the cloak\u27s hidden region. However, such cloaks\u27 scattering widths can vary significantly as a function of the object in the hidden region. A cloak with a matched impedance at r = b and that satisfies specific values for εzµθ and μ′θ performs reasonably well in terms of scattering width reduction in certain angular regions while being independent of the object in the hidden region. © 2008 Optical Society of America

Gravitational Instantons and Fluxes from M/F-theory on Calabi-Yau fourfolds

We compactify four-dimensional N=1 gauged supergravity theories on a circle including fluxes for shift-symmetric scalars. Four-dimensional Taub-NUT gravitational instantons universally correct the three-dimensional superpotential in the absence of fluxes. In the presence of fluxes these Taub-NUT instanton contributions are no longer gauge-invariant. Invariance can be restored by gauge instantons on top of Taub-NUT instantons. We establish the embedding of this scenario into M-theory. Circle fluxes and gaugings arise from a restricted class of M-theory four-form fluxes on a resolved Calabi-Yau fourfold. The M5-brane on the base of the elliptic fourfold dualizes into the universal Taub-NUT instanton. In the presence of fluxes this M5-brane is anomalous. We argue that anomaly free contributions arise from involved M5-brane geometries dual to gauge-instantons on top of Taub-NUT instantons. Adding a four-dimensional superpotential to the gravitational instanton corrections leads to three-dimensional Anti-de Sitter vacua at stabilized compactification radius. We comment on the possibility to uplift these M-theory vacua, and to tunnel to four-dimensional F-theory vacua.Comment: 47 pages, 2 figure

On Some Geometry of Graphs

In this thesis we study the intrinsic geometry of graphs via the constants that appear in discretized partial differential equations associated to those graphs. By studying the behavior of a discretized version of Bochner\u27s inequality for smooth manifolds at the cone point for a cone over the set of vertices of a graph, a lower bound for the internal energy of the underlying graph is obtained. This gives a new lower bound for the size of the first non-trivial eigenvalue of the graph Laplacian in terms of the curvature constant that appears at the cone point and the size of the vertex set for the underlying graph. For the sake of completeness, the main analysis for cones is actually done for cones over subsets of the vertex set. We follow this analysis up by studying which types of functions can achieve equality in the discrete Bochner inequality, in particular functions which yield the largest possible curvature bound at the cone point come with a dynamical definition. We are then able to classify the space of all such functions via spectral graph theory and recast the regularity of a graph in terms of the dimension of this space of functions

Superfluid vs Ferromagnetic Behaviour in a Bose Gas of Spin-1/2 Atoms

We study the thermodynamic phases of a gas of spin-1/2 atoms in the Hartree-Fock approximation. Our main result is that, for repulsive or weakly-attractive inter-component interaction strength, the superfluid and ferromagnetic phase transitions occur at the same temperature. For strongly-attractive inter-component interaction strength, however, the ferromagnetic phase transition occurs at a higher temperature than the superfluid phase transition. We also find that the presence of a condensate acts as an effective magnetic field that polarizes the normal cloud. We finally comment on the validity of the Hartree-Fock approximation in describing different phenomena in this system.Comment: 10 pages, 2 figure

LES of unsteady vortex aerodynamics in complex geometry gas-turbine fuel injectors

LES of unsteady vortex aerodynamics in complex geometry gas-turbine fuel injector

Normal-superfluid interaction dynamics in a spinor Bose gas

Coherent behavior of spinor Bose-Einstein condensates is studied in the presence of a significant uncondensed (normal) component. Normal-superfluid exchange scattering leads to a near-perfect local alignment between the spin fields of the two components. Through this spin locking, spin-domain formation in the condensate is vastly accelerated as the spin populations in the condensate are entrained by large-amplitude spin waves in the normal component. We present data evincing the normal-superfluid spin dynamics in this regime of complicated interdependent behavior.Comment: 5 pages, 4 fig

Role of Anti Thymocyte Globulin (ATG) Prior to Unrelated Donor Stem Cell Transplantation (URD SCT) in Patients with Hematologic Malignancies: A Single Center Experience

15 juillet 19461946/07/15 (N16)