On the effect of leading edge blowing on circulation control airfoil aerodynamics

In the present context the term circulation control is used to denote a method of lift generation that utilizes tangential jet blowing over the upper surface of a rounded trailing edge airfoil to determine the location of the boundary layer separation points, thus setting an effective Kutta condition. At present little information exists on the flow structure generated by circulation control airfoils under leading edge blowing. Consequently, no theoretical methods exist to predict airfoil performance under such conditions. An experimental study of the flow field generated by a two dimensional circulation control airfoil under steady leading and trailing edge blowing was undertaken. The objective was to fundamentally understand the overall flow structure generated and its relation to airfoil performance. Flow visualization was performed to define the overall flow field structure. Measurements of the airfoil forces were also made to provide a correlation of the observed flow field structure to airfoil performance. Preliminary results are presented, specifically on the effect on the flow field structure of leading edge blowing, alone and in conjunction with trailing edge blowing

An experimental study of airfoil-spoiler aerodynamics

The steady/unsteady flow field generated by a typical two dimensional airfoil with a statically deflected flap type spoiler was investigated. Subsonic wind tunnel tests were made over a range of parameters: spoiler deflection, angle of attack, and two Reynolds numbers; and comprehensive measurements of the mean and fluctuating surface pressures, velocities in the boundary layer, and velocities in the wake. Schlieren flow visualization of the near wake structure was performed. The mean lift, moment, and surface pressure characteristics are in agreement with previous investigations of spoiler aerodynamics. At large spoiler deflections, boundary layer character affects the static pressure distribution in the spoiler hingeline region; and, the wake mean velocity fields reveals a closed region of reversed flow aft of the spoiler. It is shown that the unsteady flow field characteristics are as follows: (1) the unsteady nature of the wake is characterized by vortex shedding; (2) the character of the vortex shedding changes with spoiler deflection; (3) the vortex shedding characteristics are in agreement with other bluff body investigations; and (4) the vortex shedding frequency component of the fluctuating surface pressure field is of appreciable magnitude at large spoiler deflections. The flow past an airfoil with deflected spoiler is a particular problem in bluff body aerodynamics is considered

Correcting for selection bias via cross-validation in the classification of microarray data

There is increasing interest in the use of diagnostic rules based on microarray data. These rules are formed by considering the expression levels of thousands of genes in tissue samples taken on patients of known classification with respect to a number of classes, representing, say, disease status or treatment strategy. As the final versions of these rules are usually based on a small subset of the available genes, there is a selection bias that has to be corrected for in the estimation of the associated error rates. We consider the problem using cross-validation. In particular, we present explicit formulae that are useful in explaining the layers of validation that have to be performed in order to avoid improperly cross-validated estimates.Comment: Published in at http://dx.doi.org/10.1214/193940307000000284 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Higher-order splitting algorithms for solving the nonlinear Schr\"odinger equation and their instabilities

Since the kinetic and the potential energy term of the real time nonlinear Schr\"odinger equation can each be solved exactly, the entire equation can be solved to any order via splitting algorithms. We verified the fourth-order convergence of some well known algorithms by solving the Gross-Pitaevskii equation numerically. All such splitting algorithms suffer from a latent numerical instability even when the total energy is very well conserved. A detail error analysis reveals that the noise, or elementary excitations of the nonlinear Schr\"odinger, obeys the Bogoliubov spectrum and the instability is due to the exponential growth of high wave number noises caused by the splitting process. For a continuum wave function, this instability is unavoidable no matter how small the time step. For a discrete wave function, the instability can be avoided only for \dt k_{max}^2{<\atop\sim}2 \pi, where $k_{max}=\pi/\Delta x$.Comment: 10 pages, 8 figures, submitted to Phys. Rev.

Any-order propagation of the nonlinear Schroedinger equation

We derive an exact propagation scheme for nonlinear Schroedinger equations. This scheme is entirely analogous to the propagation of linear Schroedinger equations. We accomplish this by defining a special operator whose algebraic properties ensure the correct propagation. As applications, we provide a simple proof of a recent conjecture regarding higher-order integrators for the Gross-Pitaevskii equation, extend it to multi-component equations, and to a new class of integrators.Comment: 10 pages, no figures, submitted to Phys. Rev.

Dimension-adaptive bounds on compressive FLD Classification

Efficient dimensionality reduction by random projections (RP) gains popularity, hence the learning guarantees achievable in RP spaces are of great interest. In finite dimensional setting, it has been shown for the compressive Fisher Linear Discriminant (FLD) classifier that forgood generalisation the required target dimension grows only as the log of the number of classes and is not adversely affected by the number of projected data points. However these bounds depend on the dimensionality d of the original data space. In this paper we give further guarantees that remove d from the bounds under certain conditions of regularity on the data density structure. In particular, if the data density does not fill the ambient space then the error of compressive FLD is independent of the ambient dimension and depends only on a notion of ‘intrinsic dimension'