Continuity properties of the integrated density of states on manifolds

We first analyze the integrated density of states (IDS) of periodic Schrödinger operators on an amenable covering manifold. A criterion for the continuity of the IDS at a prescribed energy is given along with examples of operators with both continuous and discontinuous IDS. Subsequently, alloy-type perturbations of the periodic operator are considered. The randomness may enter both via the potential and the metric. A Wegner estimate is proven which implies the continuity of the corresponding IDS. This gives an example of a discontinuous “periodic” IDS which is regularized by a random perturbation.     

Deposition and Characterization of Metastable Cu3N Layers for Applications in Optical Data Storage

 Cu₃N films for optical data storage were deposited on Si(100) wafers and 0.6 mm thick polycarbonate DVD base material discs at a temperature of 50 °C by reactive magnetron sputtering. A copper target was sputtered in rf mode in a nitrogen plasma. For basic investigations concerning the composition and structure of Cu₃N, Si wafers were used as substrate material. To study the suitability of Cu₃N as an optical data storage medium under technical conditions, Cu₃N/Al bilayers were deposited on polycarbonate discs. The composition and structure of the films were investigated by X-ray photoelectron spectroscopy (XPS) and X-ray diffraction (XRD). The decomposition of Cu₃N into metallic copper and nitrogen was induced and characterized with a dynamic tester consisting of an optical microscope with an integrated high power laser diode. The change in reflectivity induced by the laser pulses was measured by a high sensitivity photo detector. Optimized Cu₃N films could be decomposed into metallic copper at pulse lengths of 200 ns. The reflectivity change from 3.2% to 33.2% for completely transformed areas and to 12% for single bits as well as the maximum write data rate of 3.3 Mbit/s demonstrated the suitability of Cu₃N for write once optical data storage. Especially the carrier to noise ratio of 41 dB shows an increase of a factor of 3 for this novel material as compared to conventional optical data storage media.     

Two-color particle-imaging velocimetry using a single argon-ion laser

A swept-beam, two-color particle-imaging velocimetry (PIV) technique has been developed which utilizes a single argon-ion laser for illuminating the seed particles in a flowfield. In previous two-color PIV techniques two pulsed lasers were employed as the different-color light sources. In the present experiment the particles in a two-dimensional shear-layer flow were illuminated using arotating mirror to sweep the 488.0-nm (blue) and 514·5-nm (green) lines of the argon-ion laser through a test section. The blue- and greenparticle positions were recorded on color film with a 35-mm camera. The unique color coding eliminates the directional ambiguities associated with single-color techniques because the order in which the particle images are produced is known. Analysis of these two-color PIV images involved digitizing the exposed film to obtain the blue and green-particle image fields and processing the digitized images with velocity-displacement software. Argon-ion lasers are available in many laboratories; with the addition of a rotating mirror and a few optical components, it is possible to conduct flow-visualization experiments and make quantitative velocity measurements in many flow facilities.List of symbols d length of displacement vector - d _m distance between rotating mirror and concave mirror - n _f number of facets on rotating mirror - R seed-particle radius - v velocity in x, y plane - v _s sweep velocity of laser beams, assumed to be in y direction from top to bottom of field of view - v _x, v _y, v _z x, y, and z components of velocity - x ₁, y ₁ color-1 particle coordinates - x ₂, y ₂ color-2 particle coordinates - y _max y dimension of field of view, assumed to be the long dimension - s spatial separation of beams as they approach rotating mirror - t time separation of laser sheets or of swept beams passing fixed point - t _b time between successive sweeps through test section by same beam - t _s time required for both beams to sweep through test section - angular separation of beams reflecting from rotating mirror - fluid viscosity - v angular velocity of rotating mirror in cycles per second - seed-particle density - seed-particle response time - _v, _d, _t standard deviation of velocity, displacement, and time - vorticity This work was supported, in part, by the Aero Propulsion and Power Directorate of Wright Laboratory under Contract No. F33615-90-C-2033.