The practical application of a finite difference method for analyzing transonic flow over oscillating airfoils and wings

Separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances was performed. The steady velocity potential was obtained first from the well known nonlinear equation for steady transonic flow. The unsteady velocity potential was then obtained from a linear differential equation in complex form with spatially varying coefficients. Since sinusoidal motion is assumed, the unsteady equation is independent of time. The results of an investigation into the relaxation-solution-instability problem was discussed. Concepts examined include variations in outer boundary conditions, a coordinate transformation so that the boundary condition at infinity may be applied to the outer boundaries of the finite difference region, and overlapping subregions. The general conclusion was that only a full direct solution in which all unknowns are obtained at the same time will avoid the solution instabilities of relaxation. An analysis of the one-dimensional form of the unsteady transonic equation was studied to evaluate errors between exact and finite difference solutions. Pressure distributions were presented for a low-aspect-ratio clipped delta wing at Mach number of 0.9 and for a moderate-aspect-ratio rectangular wing at a Mach number of 0.875

Computation of the transonic perturbation flow fields around two- and three-dimensional oscillating wings

Analytical and empirical studies of a finite difference method for the solution of the transonic flow about an harmonically oscillating wing are presented along with a discussion of the development of a pilot program for three-dimensional flow. In addition, some two- and three-dimensional examples are presented

A user's guide for V174, a program using a finite difference method to analyze transonic flow over oscillating wings

The design and usage of a pilot program using a finite difference method for calculating the pressure distributions over harmonically oscillating wings in transonic flow are discussed. The procedure used is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The steady velocity potential which must be obtained from some other program, is required for input. The unsteady differential equation is linear, complex in form with spatially varying coefficients. Because sinusoidal motion is assumed, time is not a variable. The numerical solution is obtained through a finite difference formulation and a line relaxation solution method

Further investigation of a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings

Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. The steady velocity potential is obtained first from the well-known nonlinear equation for steady transonic flow. The unsteady velocity potential is then obtained from a linear differential equation in complex form with spatially varying coefficients. Since sinusoidal motion is assumed, the unsteady equation is independent of time. An out-of-core direct solution procedure was developed and applied to two-dimensional sections. Results are presented for a section of vanishing thickness in subsonic flow and an NACA 64A006 airfoil in supersonic flow. Good correlation is obtained in the first case at values of Mach number and reduced frequency of direct interest in flutter analyses. Reasonable results are obtained in the second case. Comparisons of two-dimensional finite difference solutions with exact analytic solutions indicate that the accuracy of the difference solution is dependent on the boundary conditions used on the outer boundaries. Homogeneous boundary conditions on the mesh edges that yield complex eigenvalues give the most accurate finite difference solutions. The plane outgoing wave boundary conditions meet these requirements

Doping, European Law and the Implications of Meca-Medina

The ruling of the European Court of Justice in the anti-doping case of Meca Medina v. The Commission has important implications for athletes, domestic governing bodies, international federations and supra-national actors such as WADA and the Court of Arbitration for Sport. Meca-Medina has been criticised as an unwelcome interference by the courts in the legitimate activities of sporting organisations, but after Bosman it was fanciful to argue that those organisations should be ‘above the law’ and the courts should have no jurisdiction over their activities. That said, there is a stark difference between the courts having jurisdiction over sports’ decisions and being willing to overturn them - the courts have been, and remain, willing to defer to the expertise of sporting organisations. However, the ECJ’s ruling in MOTOE confirms that the courts will intervene in appropriate circumstances. In order to avoid sanction on competition law grounds sports organisations must thus be able to justify their provisions on (for example) what is an unacceptable level of nandrolone, show that athletes’ fundamental rights such as the right to a fair hearing have been respected, and ensure that any sanctions imposed upon athletes who fall foul of doping regulations are proportionate to the offence committed

Modelling and testing the x-ray performance of CCD and CMOS APS detectors using numerical finite element simulations

Pixellated monolithic silicon detectors operated in a photon-counting regime are useful in spectroscopic imaging applications. Since a high energy incident photon may produce many excess free carriers upon absorption, both energy and spatial information can be recovered by resolving each interaction event. The performance of these devices in terms of both the energy and spatial resolution is in large part determined by the amount of diffusion which occurs during the collection of the charge cloud by the pixels. Past efforts to predict the X-ray performance of imaging sensors have used either analytical solutions to the diffusion equation or simplified monte carlo electron transport models. These methods are computationally attractive and highly useful but may be complemented using more physically detailed models based on TCAD simulations of the devices. Here we present initial results from a model which employs a full transient numerical solution of the classical semiconductor equations to model charge collection in device pixels under stimulation from initially Gaussian photogenerated charge clouds, using commercial TCAD software. Realistic device geometries and doping are included. By mapping the pixel response to different initial interaction positions and charge cloud sizes, the charge splitting behaviour of the model sensor under various illuminations and operating conditions is investigated. Experimental validation of the model is presented from an e2v CCD30-11 device under varying substrate bias, illuminated using an Fe-55 source

Three-photon electromagnetically induced transparency using Rydberg states

We demonstrate electromagnetically induced transparency in a four-level cascade system where the upper level is a Rydberg state. The observed spectral features are sub-Doppler and can be enhanced due to the compensation of Doppler shifts with AC Stark shifts. A theoretical description of the system is developed that agrees well with the experimental results, and an expression for the optimum parameters is derived

Analytical investigation of correlated charge collection in CCDs

Correlated charge collection phenomena in CCD sensors are presently of interest due to their potentially major implications in space and ground based astronomy missions. These effects may manifest as a signal dependent Point Spread Function (PSF), or as a nonlinearity in the Photon Transfer Curve (PTC). We present the theoretical background to a simple analytical model based on previously published solutions of Poisson's equation which aims to aid conceptual understanding of how various device parameters relate to the magnitude of correlated charge collection. We separate correlated charge collection into two components - firstly excess diffusion caused by increasing drift time as the electric field in the device decreases, which is isotropic, and secondly anisotropic pixel boundary shifting as the fringing field in the parallel transfer direction collapses. Equations are presented which can be solved numerically to give reasonable detail, or solved analytically using simplifying approximations

Piezoelectrically actuated time-averaged atomic microtraps

We present a scheme for creating tight and adiabatic time-averaged atom-traps through the piezoelectric actuation of nanomagnetic structures. We show that potentials formed by the circular translation of magnetic structures have several advantages over conventional rotating-field techniques, particularly for high trap frequencies. As the magnitude of the actuation is changed, the trapping potential can be changed adiabatically between harmonic 3D confinement and a toroidal trap