Homogeneity and projective equivalence of differential equation fields

We propose definitions of homogeneity and projective equivalence for systems of ordinary differential equations of order greater than two, which allow us to generalize the concept of a spray (for systems of order two). We show that the Euler-Lagrange fields of parametric Lagrangians of order greater than one which are regular (in a natural sense that we define) form a projective equivalence class of homogeneous systems. We show further that the geodesics, or base integral curves, of projectively equivalent homogeneous differential equation fields are the same apart from orientation-preserving reparametrization; that is, homogeneous differential equation fields determine systems of paths

Results from computational analysis of a mixed compression supersonic inlet

A numerical study was performed to simulate the critical flow through a supersonic inlet. This flow field has many phenomena such as shock waves, strong viscous effects, turbulent boundary layer development, boundary layer separations, and mass flow suction through the walls, (bleed). The computational tools used were two full Navier-Stokes (FNS) codes. The supersonic inlet that was analyzed is the Variable Diameter Centerbody, (VDC), inlet. This inlet is a candidate concept for the next generation supersonic involved effort in generating an efficient grid geometry and specifying boundary conditions, particularly in the bleed region and at the outflow boundary. Results for a critical inlet operation compare favorably to Method of Characteristics predictions and experimental data

A new camera for high-resolution infrared imaging of works of art

A new camera – SIRIS (scanning infrared imaging system) – developed at the National Gallery in London allows high-resolution images to be made in the near infrared region (900–1700 nm). The camera is based on a commercially available 320 × 256 pixel indium gallium arsenide area array sensor. This relatively small sensor is moved across the focal plane of the camera using two orthogonal translation stages to give images of c. 5000 × 5000 pixels. The main advantages of the SIRIS camera over scanning infrared devices or sequential image capture and mosaic assembly are its comparative portability and rapid image acquisition – making a 5000 × 5000 pixel image takes less than 20 minutes. The SIRIS camera can operate at a range of resolutions; from around 2.5 pixels per millimetre over an area of up to 2 × 2 m to 10 pixels per millimetre when examining an area measuring 0.5 × 0.5 m. The development of the mechanical, optical and electronic components of the camera, including the design of a new lens, is described. The software used to control image capture and to assemble the individual frames into a seamless mosaic image is mentioned. The camera was designed primarily to examine underdrawings in paintings; preliminary results from test targets and paintings imaged in situ are presented and the quality of the images compared with those from other cameras currently used for this application

SIRIS: a high resolution scanning infrared camera for examining paintings

The new SIRIS (Scanning InfraRed Imaging System) camera developed at the National Gallery in London allows highresolution images of paintings to be made in the near infrared region (900–1700 nm). Images of 5000 × 5000 pixels are made by moving a 320 × 256 pixel InGaAs array across the focal plane of the camera using two orthogonal translation stages. The great advantages of this camera over scanning infrared devices are its relative portability and that image acquisition is comparatively rapid – a full 5000 × 5000 pixel image can be made in around 20 minutes. The paper describes the development of the mechanical, optical and electronic components of the camera, including the design of a new lens. The software routines used to control image capture and to assemble the individual 320 × 256 pixel frames into a seamless mosaic image are also mentioned. The optics of the SIRIS camera have been designed so that the camera can operate at a range of resolutions; from around 2.5 pixels per millimetre on large paintings of up to 2000 × 2000 mm to 10 pixels per millimetre on smaller paintings or details of paintings measuring 500 × 500 mm. The camera is primarily designed to examine underdrawings in paintings; preliminary results from test targets and paintings are presented and the quality of the images compared with those from other cameras currently used in this field