Richardson Extrapolation for Linearly Degenerate Discontinuities

In this paper we investigate the use of Richardson extrapolation to estimate the convergence rates for numerical solutions to advection problems involving discontinuities. We use modified equation analysis to describe the expectation of the approach. In general, the results do not agree with a-priori estimates of the convergence rates. However, we identify one particular use case where Richardson extrapolation does yield the proper result. We then demonstrate this result using a number of numerical examples.Comment: 19 pages, 4 figur

On compactness of admissible parameter sets: Convergence and stability in inverse problems for distributed parameter systems

A series of numerical examples is reported and several algorithms compared for estimation of coefficients in differential equation models. Unconstrained, constrained and Tikhonov regularization methods are tested for their behavior with regard to both convergence (of approximation methods for the states and parameters) and stability (continuity of the estimates with respect to perturbations in the data or observed states)

Investigation of trailing-edge-flap, spanwise-blowing concepts on an advanced fighter configuration

The aerodynamic effects of spanwise blowing on the trailing edge flap of an advanced fighter aircraft configuration were determined in the 4 by 7 Meter Tunnel. A series of tests were conducted with variations in spanwise-blowing vector angle, nozzle exit area, nozzle location, thrust coefficient, and flap deflection in order to determine a superior configuration for both an underwing cascade concept and an overwing port concept. This screening phase of the testing was conducted at a nominal approach angle of attack from 12 deg to 16 deg; and then the superior configurations were tested over a more complete angle of attack range from 0 deg to 20 deg at tunnel free stream dynamic pressures from 20 to 40 lbf/sq ft at thrust coefficients from 0 to 2

Thrust-induced effects on low-speed aerodynamics of fighter aircraft

Results of NASA Langley has conducted wind-tunnel investigations of several fighter configurations conducted to determine the effects of both thrust vectoring and spanwise blowing are reviewed. A recent joint NASA/Grumman Aerospace Corporation/U.S. Air Force Wright Aeronautical Laboratory wind-tunnel investigation was conducted to examine the effects of spanwise blowing on the trailing-edge flap system. This application contrasts with the more familiar method of spanwise blowing near the wing leading edge. Another joint program among NASA/McDonnell Aircraft Company/U.S. Air Force Wright Aeronautical Laboratory investigated the effects of reverse thrust on the low-speed aerodynamics of an F-15 configuration. The F-15 model was fitted with a rotating van thrust reverser concept which could simulate both in-flight reversing for approach and landing or full reversing for ground roll reduction. The significant results of these two joint programs are reported

Density of non-residues in Burgess-type intervals and applications

We show that for any fixed \eps>0, there are numbers $\delta>0$ and $p_0\ge 2$ with the following property: for every prime $p\ge p_0$ and every integer $N$ such that p^{1/(4\sqrt{e})+\eps}\le N\le p, the sequence $1,2,...,N$ contains at least $\delta N$ quadratic non-residues modulo $p$. We use this result to obtain strong upper bounds on the sizes of the least quadratic non-residues in Beatty and Piatetski--Shapiro sequences.Comment: In the new version we use an idea of Roger Heath-Brown (who is now a co-author) to simply the proof and improve the main results of the previous version, 14 page

Entropy of gravitating systems: scaling laws versus radial profiles

Through the consideration of spherically symmetric gravitating systems consisting of perfect fluids with linear equation of state constrained to be in a finite volume, an account is given of the properties of entropy at conditions in which it is no longer an extensive quantity (it does not scale with system's size). To accomplish this, the methods introduced by Oppenheim [1] to characterize non-extensivity are used, suitably generalized to the case of gravitating systems subject to an external pressure. In particular when, far from the system's Schwarzschild limit, both area scaling for conventional entropy and inverse radius law for the temperature set in (i.e. the same properties of the corresponding black hole thermodynamical quantities), the entropy profile is found to behave like 1/r, being r the area radius inside the system. In such circumstances thus entropy heavily resides in internal layers, in opposition to what happens when area scaling is gained while approaching the Schwarzschild mass, in which case conventional entropy lies at the surface of the system. The information content of these systems, even if it globally scales like the area, is then stored in the whole volume, instead of packed on the boundary.Comment: 16 pages, 11 figures. v2: addition of some references; the stability of equilibrium configurations is readdresse