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.     

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.     

XHSTT: an XML archive for high school timetabling problems in different countries

We present the progress on the benchmarking project for high school timetabling that was introduced at PATAT 2008. In particular, we announce the High School Timetabling Archive XHSTT-2011 with 21 instances from 8 countries and an evaluator capable of checking the syntax of instances and evaluating the solutions.     

Theory of reflectance measurements in quantitative evaluation in TLC and HPTLC. 1. Multilayer model of reflectance and transmittance

In the approach described in this paper, the layer of adsorbent is divided into n sublayers. The radiation density in each sublayer is given by the sum of the transmittance and the reflectance of the adjacent sublayers. Absorption of light by the layer or the substance will diminish this radiation density. Depending upon the factors of reflectance and transmittance some light will pass to the adjacent sublayers. Two polynomials are derived from this readily understood formulation to calculate the reflectance or the transmittance of a layer of finite thickness. The algorithms given describe the reflectance and transmittance encountered in practical measurements with large amounts of substance per spot, as well as with small amounts. There are no restrictions with respect to nonideal scattering or reflection by the adsorbent layer support.     

The combined effect of cations and anions on the dynamics of water

We studied the orientational relaxation of the OD-stretch vibration of HDO molecules in concentrated solutions of alkali-halide salts (NaCl, NaI, CsCl and KI) in isotopically diluted water (4% D(2)O in H(2)O), using polarization-resolved femtosecond infrared pump-probe spectroscopy (fs-IR). We were able to distinguish the orientational dynamics of the water molecules solvating the halide ions from the dynamics of the bulk water and the water solvating the cations. We found that the reorientation of the halide-bound molecules shows two strongly different components (2.0 ± 0.3 ps and 9 ± 1 ps), related to a wiggling motion of the OD group hydrogen-bonded to the anion, and rotational diffusion of the molecule over the charged anion surface, respectively. The relative amplitudes of the two components are dependent on the nature of both the anion and cation, and on the concentration. These results show that cations can have a profound effect on the solvation shell dynamics of their counter-ions.     

A localized hybrid method of stress analysis: A combination of moiré interferometry and FEM

A method of combining moiré interferometry and the finite-element method to effect localized stress analysis is presented. The displacement data from local regions of interest in the optical experiment are used as boundary conditions for the finite-element stress analysis. The stability of the method is examined with data from simple numerical models one of which corresponded to the stress analysis of a pin-loaded plate with friction. These studies show that the method requires the sensivity of moiré interferometry for successful implementation, i.e., displacement data accuracy within 0.1 μm or 4 μin. This localized hybrid method of stress analysis provides a powerful and efficient method for the reduction of experimental data.     

An algebraic interpretation of the multivariate <Emphasis Type="Italic">q</Emphasis>-Krawtchouk polynomials

The multivariate quantum q-Krawtchouk polynomials are shown to arise as matrix elements of “q-rotations” acting on the state vectors of many q-oscillators. The focus is put on the two-variable case. The algebraic interpretation is used to derive the main properties of the polynomials: orthogonality, duality, structure relations, difference equations, and recurrence relations. The extension to an arbitrary number of variables is presented.     

Corneal studies by photoelasticity

Freshly enucleated andin vivo eyes of cats were analyzed to determine the detailed distribution of birefringence across the cornea and through its thickness, and to determine the change of birefringence with intraocular pressure. Scattered light and oblique-incidence photoelasticity were used. The experiments are summarized and special considerations are discussed. These include the necessity for a laser-light source; diffraction limitation in producing a narrow ribbon of light; rotation of the plane of polarization; inequalities in reflected components of polarized light.     

Photoelastic-fringe multiplication—For tenfold increase in sensitivity

Slices from three-dimensional frozen-stress models were collected from numerous photoelastic laboratories and these diverse samples were used to demonstrate fringe multiplication. Multiplied isochromatic patterns of excellent clarity and fidelity are presented. Maximum multiplication factors of 9 or 11 are exhibited for most demonstrations, but multiplications by 17 and 25 are exhibited for special cases. Speed, accuracy and simplicity of the method are discussed, and benefits of full-field data retrieval are emphasized.     

New optical methods of moiré fringe multiplication

Photographs or other replicas of relatively coarse specimen screens can be analyzed with sensitivities corresponding to screens of many thousands of lines per inch (lpi). Moiré fringe multiplication is accomplished by collecting specific groups of diffracted beams emanating from two moiré screens in series. Three methods are described and multiplication by factors as high as 30 are demonstrated. Sensitivity and accuracy are increased by the fringe-multiplication factor. Usefulness of full-field mechanical differentiation techniques is extended to cases of correspondingly lower strains. These fringe-multiplication methods apply to both bar-and-space screens and transparent diffraction gratings.