Microwave Electronics

Contains a report on a research project.Lincoln Laboratory (Purchase Order DDL B-00283)United States ArmyUnited States Air Force (Contract AF19(604)-5200)United States Navy, Office of Naval Research (Nonr-1841(49)

A Hybrid Observer for a Distributed Linear System with a Changing Neighbor Graph

A hybrid observer is described for estimating the state of an $m>0$ channel, $n$-dimensional, continuous-time, distributed linear system of the form $\dot{x} = Ax,\;y_i = C_ix,\;i\in\{1,2,\ldots, m\}$. The system's state $x$ is simultaneously estimated by $m$ agents assuming each agent $i$ senses $y_i$ and receives appropriately defined data from each of its current neighbors. Neighbor relations are characterized by a time-varying directed graph $\mathbb{N}(t)$ whose vertices correspond to agents and whose arcs depict neighbor relations. Agent $i$ updates its estimate $x_i$ of $x$ at "event times" $t_1,t_2,\ldots$ using a local observer and a local parameter estimator. The local observer is a continuous time linear system whose input is $y_i$ and whose output $w_i$ is an asymptotically correct estimate of $L_ix$ where $L_i$ a matrix with kernel equaling the unobservable space of $(C_i,A)$. The local parameter estimator is a recursive algorithm designed to estimate, prior to each event time $t_j$, a constant parameter $p_j$ which satisfies the linear equations $w_k(t_j-\tau) = L_kp_j+\mu_k(t_j-\tau),\;k\in\{1,2,\ldots,m\}$, where $\tau$ is a small positive constant and $\mu_k$ is the state estimation error of local observer $k$. Agent $i$ accomplishes this by iterating its parameter estimator state $z_i$, $q$ times within the interval $[t_j-\tau, t_j)$, and by making use of the state of each of its neighbors' parameter estimators at each iteration. The updated value of $x_i$ at event time $t_j$ is then $x_i(t_j) = e^{A\tau}z_i(q)$. Subject to the assumptions that (i) the neighbor graph $\mathbb{N}(t)$ is strongly connected for all time, (ii) the system whose state is to be estimated is jointly observable, (iii) $q$ is sufficiently large, it is shown that each estimate $x_i$ converges to $x$ exponentially fast as $t\rightarrow \infty$ at a rate which can be controlled.Comment: 7 pages, the 56th IEEE Conference on Decision and Contro

Piezoconductivity of gated suspended graphene

We investigate the conductivity of graphene sheet deformed over a gate. The effect of the deformation on the conductivity is twofold: The lattice distortion can be represented as pseudovector potential in the Dirac equation formalism, whereas the gate causes inhomogeneous density redistribution. We use the elasticity theory to find the profile of the graphene sheet and then evaluate the conductivity by means of the transfer matrix approach. We find that the two effects provide functionally different contributions to the conductivity. For small deformations and not too high residual stress the correction due to the charge redistribution dominates and leads to the enhancement of the conductivity. For stronger deformations, the effect of the lattice distortion becomes more important and eventually leads to the suppression of the conductivity. We consider homogeneous as well as local deformation. We also suggest that the effect of the charge redistribution can be best measured in a setup containing two gates, one fixing the overall charge density and another one deforming graphene locally

Shock propagation and stability in causal dissipative hydrodynamics

We studied the shock propagation and its stability with the causal dissipative hydrodynamics in 1+1 dimensional systems. We show that the presence of the usual viscosity is not enough to stabilize the solution. This problem is solved by introducing an additional viscosity which is related to the coarse-graining scale of the theory.Comment: 14 pages, 16 figure

Magnetovac Cylinder to Magnetovac Torus

A method for mapping known cylindrical magnetovac solutions to solutions in torus coordinates is developed. Identification of the cylinder ends changes topology from R1 x S1 to S1 x S1. An analytic Einstein-Maxwell solution for a toroidal magnetic field in tori is presented. The toroidal interior is matched to an asymptotically flat vacuum exterior, connected by an Israel boundary layer.Comment: to appear in Class. Quant. Gra

Two-dimensional shear modulus of a Langmuir foam

We deform a two-dimensional (2D) foam, created in a Langmuir monolayer, by applying a mechanical perturbation, and simultaneously image it by Brewster angle microscopy. We determine the foam stress tensor (through a determination of the 2D gas-liquid line tension, 2.35 $\pm$ 0.4 pJ$\cdot$m$^{-1}$) and the statistical strain tensor, by analyzing the images of the deformed structure. We deduce the 2D shear modulus of the foam, $\mu= 38 \pm 3 \mathrm{nN}\cdot \mathrm{m}^{-1}$. The foam effective rigidity is predicted to be $35 \pm 3 \mathrm {nN}\cdot \mathrm {m}^{- 1}$, which agrees with the value $37.5 \pm 0.8 \mathrm {nN}\cdot \mathrm {m}^{-1}$ obtained in an independent mechanical measurement.Comment: submitted May 12, 2003 ; resubmitted Sept 9, 200

Factors Influencing Collegiate Athletic Department Revenues

One of the primary challenges of Division I Football Bowl Subdivision (FBS) collegiate athletic programs is revenue generation, particularly in light of increasing costs and competition. Surprisingly, a limited number of studies have investigated factors related to athletic department-generated revenues. A statistically significant multiple regression model was created, explaining 76.7 percent of the variance in annual generated revenues among FBS programs. Factors such as conference affiliation, success in football and men’s basketball, enrollment, and time were identified as important in predicting revenue generation. The Revenue Theory of Costs was put forth as a framework for better understanding the financial behavior of intercollegiate athletic programs

On Gravitational Radiation in Quadratic f(R)f(R) Gravity

We investigate the gravitational radiation emitted by an isolated system for gravity theories with Lagrange density $f(R) = R + aR^2$. As a formal result we obtain leading order corrections to the quadrupole formula in General Relativity. We make use of the analogy of $f(R)$ theories with scalar--tensor theories, which in contrast to General Relativity feature an additional scalar degree of freedom. Unlike General Relativity, where the leading order gravitational radiation is produced by quadrupole moments, the additional degree of freedom predicts gravitational radiation of all multipoles, in particular monopoles and dipoles, as this is the case for the most alternative gravity theories known today. An application to a hypothetical binary pulsar moving in a circular orbit yields the rough limit $a \lesssim 1.7\cdot10^{17}\,\mathrm{m}^2$ by constraining the dipole power to account at most for 1% of the quadrupole power as predicted by General Relativity.Comment: 14 Pages, 1 Figur

Four-body Efimov effect

We study three same spin state fermions of mass M interacting with a distinguishable particle of mass m in the unitary limit where the interaction has a zero range and an infinite s-wave scattering length. We predict an interval of mass ratio 13.384 < M/m < 13.607 where there exists a purely four-body Efimov effect, leading to the occurrence of weakly bound tetramers without Efimov trimers.Comment: 4 pages, 2 figure

Polynomial Solutions of Shcrodinger Equation with the Generalized Woods Saxon Potential

The bound state energy eigenvalues and the corresponding eigenfunctions of the generalized Woods Saxon potential are obtained in terms of the Jacobi polynomials. Nikiforov Uvarov method is used in the calculations. It is shown that the results are in a good agreement with the ones obtained before.Comment: 14 pages, 2 figures, submitted to Physical Review