Technical background for a demonstration magnetic levitation system

A preliminary technical assessment of the feasibility of a demonstration Magnetic Levitation system, required to support aerodynamic models with a specified clear air volume around them, is presented. Preliminary calculations of required sizes of electromagnets and power supplies are made, indicating that the system is practical. Other aspects, including model position sensing and controller design, are briefly addressed

On Vertically Global, Horizontally Local Models for Astrophysical Disks

Disks with a barotropic equilibrium structure, for which the pressure is only a function of the density, rotate on cylinders in the presence of a gravitational potential, so that the angular frequency of such a disk is independent of height. Such disks with barotropic equilibria can be approximately modeled using the shearing box framework, representing a small disk volume with height-independent angular frequency. If the disk is in baroclinic equilibrium, the angular frequency does generally depend on height, and it is thus necessary to go beyond the standard shearing box approach. In this paper, we show that given a global disk model, it is possible to develop approximate models that are local in horizontal planes without an expansion in height with shearing-periodic boundary conditions. We refer to the resulting framework as the vertically global shearing box (VGSB). These models can be non-axisymmetric for globally barotropic equilibria but should be axisymmetric for globally baroclinic equilibria. We provide explicit equations for this VGSB which can be implemented in standard magnetohydrodynamic codes by generalizing the shearing-periodic boundary conditions to allow for a height-dependent angular frequency and shear rate. We also discuss the limitations that result from the radial approximations that are needed in order to impose height-dependent shearing periodic boundary conditions. We illustrate the potential of this framework by studying a vertical shear instability and examining the modes associated with the magnetorotational instability.Comment: 24 pages, 8 figures, updated to match published versio

Approaches to control of the large angle magnetic suspension test fixture

The Large Angle Magnetic Suspension Test Fixture is a five degree-of-freedom system, developed and built at NASA Langley Research Center. It is intended for study of control techniques in magnetic suspension systems with large angular capabilities. In this study, steps have been taken to prove the system in practice, using the existing hardware. A classical control approach, using dual phase advance compensators, is applied in simulation and hardware. A single decoupled degree-of-freedom of the system is stabilized and controlled in simulation. The procedure is then employed for all five degrees-of-freedom. The design and implementation of an analog and a digital controller are described. Results from simulation and the actual system are compared and analyzed. The ability to the system to sustain suspension over a large angular range has been proven in hardware

Generalized Quantum Search with Parallelism

We generalize Grover's unstructured quantum search algorithm to enable it to use an arbitrary starting superposition and an arbitrary unitary matrix simultaneously. We derive an exact formula for the probability of the generalized Grover's algorithm succeeding after n iterations. We show that the fully generalized formula reduces to the special cases considered by previous authors. We then use the generalized formula to determine the optimal strategy for using the unstructured quantum search algorithm. On average the optimal strategy is about 12% better than the naive use of Grover's algorithm. The speedup obtained is not dramatic but it illustrates that a hybrid use of quantum computing and classical computing techniques can yield a performance that is better than either alone. We extend the analysis to the case of a society of k quantum searches acting in parallel. We derive an analytic formula that connects the degree of parallelism with the optimal strategy for k-parallel quantum search. We then derive the formula for the expected speed of k-parallel quantum search.Comment: 14 pages, 2 figure