Quasi-isotropic spacecraft antenna system Final report

Spacecraft quasi-isotropic antenna system for space telemetr

Dual-shaped offset reflector antenna designs from solutions of the geometrical optics first-order partial differential equations

In obtaining solutions to the first-order nonlinear partial differential equations (PDEs) for synthesizing offset dual-shaped reflectors, it is found that previously observed computational problems can be avoided if the integration of the PDEs is started from an inner projected perimeter and integrated outward rather than starting from an outer projected perimeter and integrating inward. This procedure, however, introduces a new parameter, the main reflector inner perimeter radius p(o), when given a subreflector inner angle 0(o). Furthermore, a desired outer projected perimeter (e.g., a circle) is no longer guaranteed. Stability of the integration is maintained if some of the initial parameters are determined first from an approximate solution to the PDEs. A one-, two-, or three-parameter optimization algorithm can then be used to obtain a best set of parameters yielding a close fit to the desired projected outer rim. Good low cross-polarization mapping functions are also obtained. These methods are illustrated by synthesis of a high-gain offset-shaped Cassegrainian antenna and a low-noise offset-shaped Gregorian antenna

The Majorization Arrow in Quantum Algorithm Design

We apply majorization theory to study the quantum algorithms known so far and find that there is a majorization principle underlying the way they operate. Grover's algorithm is a neat instance of this principle where majorization works step by step until the optimal target state is found. Extensions of this situation are also found in algorithms based in quantum adiabatic evolution and the family of quantum phase-estimation algorithms, including Shor's algorithm. We state that in quantum algorithms the time arrow is a majorization arrow.Comment: REVTEX4.b4 file, 4 color figures (typos corrected.

Characterizing Entanglement via Uncertainty Relations

We derive a family of necessary separability criteria for finite-dimensional systems based on inequalities for variances of observables. We show that every pure bipartite entangled state violates some of these inequalities. Furthermore, a family of bound entangled states and true multipartite entangled states can be detected. The inequalities also allow to distinguish between different classes of true tripartite entanglement for qubits. We formulate an equivalent criterion in terms of covariance matrices. This allows us to apply criteria known from the regime of continuous variables to finite-dimensional systems.Comment: 4 pages, no figures. v2: Some discussion added, main results unchange

Regularization of geodesics in static spherically symmetric Kerr-Schild spacetimes

Spanish Relativity Meeting: "Almost 100 years after Einstein's revolution". University of Valencia, 1st-5th of September 2014We describe a method to analyze causal geodesics in static and spherically symmetric spacetimes of Kerr-Schild form which, in particular, allows for a detailed study of the geodesics in the vicinity of the central singularity by means of a regularization procedure based on a generalization of the McGehee regularization for the motion of Newtonian point particles moving in a power-law potential. The McGehee regularization was used by Belbruno and Pretorius [1] to perform a dynamical system regularization of the central singularity of the motion of massless test particles in the Schwarzschild spacetime. Our generalization allows us to consider causal (timelike or null) geodesics in any static and spherically symmetric spacetime of Kerr-Schild form. As an example, we apply these results to causal geodesics in the Schwarzschild and Reissner-Nordstrom spacetimes

On the evaluation codes given by simple d-sequences

Plane valuations at infinity are classified in five types. Valuations in one of them determine weight functions which take values on semigroups of Z2. These semigroups are generated by δ-sequences in Z2. We introduce simple δ-sequences in Z2 and study the evaluation codes of maximal length that they define. These codes are geometric and come from order domains. We give a bound on their minimum distance which improves the Andersen–Geil one. We also give coset bounds for the involved codes

Remote Laboratory for Nuclear Security Education

Laboratory experiences for online students are very limited. To fill this gap, educators in the Department of Nuclear Engineering at Texas A&M University developed a series of radiation detection experiments for their remote students. Radiation detection is only one piece of nuclear security. The objective of the current research is to describe the development and execution of three online laboratories that investigate the basic application of physical security sensors that use light, ultrasonics, and heat to detect adversaries. This laboratory complements lecture material from the department’s Nuclear Security System and Design course. Using the Remote Desktop Application, students connect to a laboratory computer at Texas A&M to control the apparatus and record data. The sensors from a LEGO MINDSTORMS EV3 Education Core set were employed because of their ease of connectivity and their ability to show in a simplistic way how more complex security systems use light, ultrasonics, and heat. Additionally, LabVIEW software was used to control ethernet stepper motors for lateral and rotary motion to move sensors and other apparatus. The three laboratories are described in detail in addition to their learning objectives and results

Potentials for which the Radial Schr\"odinger Equation can be solved

In a previous paper$^1$, submitted to Journal of Physics A -- we presented an infinite class of potentials for which the radial Schr\"odinger equation at zero energy can be solved explicitely. For part of them, the angular momentum must be zero, but for the other part (also infinite), one can have any angular momentum. In the present paper, we study a simple subclass (also infinite) of the whole class for which the solution of the Schr\"odinger equation is simpler than in the general case. This subclass is obtained by combining another approach together with the general approach of the previous paper. Once this is achieved, one can then see that one can in fact combine the two approaches in full generality, and obtain a much larger class of potentials than the class found in ref. $^1$ We mention here that our results are explicit, and when exhibited, one can check in a straightforward manner their validity