Search

An abstract framework for constructing stable decompositions of the spaces corresponding to general symmetric positive definite problems into "local" subspaces and a global "coarse" space is developed. Particular applications of this abstract framework include practically important problems in porous media applications such as: the scalar elliptic (pressure) equation and the stream function formulation of its mixed form, Stokes' and Brinkman's equations. The constant in the corresponding abstract energy estimate is shown to be robust with respect to mesh parameters as well as the contrast, which is defined as the ratio of high and low values of the conductivity (or permeability). The derived stable decomposition allows to construct additive overlapping Schwarz iterative methods with condition numbers uniformly bounded with respect to the contrast and mesh parameters. The coarse spaces are obtained by patching together the eigenfunctions corresponding to the smallest eigenvalues of certain local problems. A detailed analysis of the abstract setting is provided. The proposed decomposition builds on a method of Efendiev and Galvis, Multiscale Model. Simul., 8 (2010), pp. 1461--1483, developed for second order scalar elliptic problems with high contrast. Applications to the finite element discretizations of the second order elliptic problem in Galerkin and mixed formulation, the Stokes equations, and Brinkman's problem are presented. A number of numerical experiments for these problems in two spatial dimensions are provided.

Magneto-optical imaging and magnetization measurements were applied to investigate local formation of superconducting phase effected by a random neck synthesis in Y-Ba-Cu-O system. Polished pellets of strongly inhomogeneous ceramic samples show clearly the appearance of superconducting material in the intergrain zones of binary primary particles reacted under different conditions. Susceptibility measurements allows evaluation of superconducting critical temperature, which turned out to be close to that of optimally doped YBCO., Comment: 6 pages, 11 figures

We present a magnetization study of low density YBCO ceramics carried out in magnetic fields 0.5 Oe < H < 50 kOe. It was demonstrated that superconducting links between grains may be completely suppressed either by a magnetic field of the order of 100 Oe (at low temperatures) or by an increase of temperature above 70 K. This property of present samples allowed to evaluate the ratio between an average grain size and the magnetic field penetration depth lambda. Furthermore, at temperatures T > 85 K, using low-field magnetization measurements, we could evaluate the temperature dependence of lambda, which turned out to be very close to predictions of the conventional Ginzburg-Landau theory. Although present samples consisted of randomly oriented grains, specifics of magnetization measurements allowed for evaluation of lambda_ab(T). Good agreement between our estimation of the grain size with the real sample structure provides evidence for the validity of this analysis of magnetization data. Measurements of equilibrium magnetization in high magnetic fields were used for evaluation of Hc2(T). At temperatures close to T_c, the Hc2(T) dependence turned out to be linear in agreement with the Ginzburg-Landau theory. The value of temperature, at which Hc2 vanishes, coincides with the superconducting critical temperature evaluated from low-field measurements., Comment: 10 pages, 12 figures

The major focus of the Phase II effort described herein is to develop and demonstrate an aircraft capable of autonomously sailing (i.e., to cruise without propulsion or external assistance), and thereby prove that the dual-aircraft platform (DAP) atmospheric satellite concept is potentially viable. This sailing mode of flight was identified as the number-1 enabling technology required for the stratospheric DAP concept (also known as Stratosat) in the NIAC (NASA Innovative Advanced Concept) Phase I effort. No scientific demonstration of this technology has ever been done or documented to our knowledge. This report describes efforts to take a major step towards the sailing mode of flight capability using a single aircraft connected by cable to a moving ground vehicle which uses sufficient crosswind to cruise without propulsion while "pulling" the ground vehicle forward (i.e., without external assistance). The development of a prototype aircraft is described in terms of novel and key hardware and software elements. A specialized prototype aircraft is described, including a novel cable release mechanism, novel "lateron" control surfaces, and a highly-accurate onboard wind measurement system. Additionally, a novel means to safely connect the aircraft to the moving ground vehicle is described involving a fishing rod/reel and integrated load cell. All of these devices were designed and developed in-house and validated in flight testing. Software is developed to provide look-up tables that give the flight condition targets (i.e., 3-D position relative to ground vehicle, forward speed, aircraft orientation, etc.), based on current wind speed and direction. These tables are successfully validated in flight simulation and used onboard the aircraft. High fidelity analysis of the aircraft aerodynamics are described - required to produce accurate target sailing flight conditions. A novel wind tunnel measurement technique is developed to accurately assess the aerodynamics of the ultra-thin cable. A new specialized flight simulator is described which is utilized to develop and verify the flight software required onboard the aircraft, and to support training of pilots for flying the aircraft while tethered to a ground vehicle. The DAP flight simulator was developed within the Matlab-Simulink framework and included detailed treatment of aircraft/cable aerodynamics, cable dynamics, experimentally-derived propeller-motor thrust curves, actuator responsiveness, and realistic air turbulence. The specialized formation flight controller algorithm, developed using this flight simulator, and onboard the aircraft is described. Finally, a novel auto-tuning software is described and verified within the flight simulator that is shown to refine the sailing flight condition targets during flight using an optimization technique involving doublet maneuvers. Virtual flights using the auto-tuning software indicate that the prototype aircraft should be able to reach and hold sailing conditions despite moderate levels of turbulence provided there is sufficient mean wind available. An overview of the flight testing program is provided. Hundreds of short flights were conducted, primarily using a “dead” short runway at Deland Municipal Airport which permitted use of a moving ground vehicle. Additional flight tests at Space Florida’s Shuttle Landing Facility are also described. First year results from these tests in which the aircraft is controlled manually, demonstrated that excessive flight testing would be required for a pilot to learn to sail with visual cues. However, second year results from autonomous flight these tests included successful demonstration of the closed-loop autonomous formation flight capability (i.e., autonomously determine, reach, and hold the required 3-D location relative to the ground vehicle required for sailing). The next step of using the auto-tune software to autonomously refine the aircraft orientation targets to finally achieve sailing remains the primary goal of future work.