Stability experiments on the strongest columns and circular arches

Recent theories predict the cross-sectional shapes for the strongest, end-loaded column and the radially loaded arch whose neutral axis is circular. These tapered shapes have higher predicted load-carrying capacities than uniform columns or arches of equal weight and length or span. The purpose of the present experimental investigation was to study the stability of these configurations, modified so that no experimental model had the predicted cross-sectional area of zero where the bending moments vanished. Precise buckling loads were measured on metal models of tapered, pinned-end columns using strain gages and a unique modification of Southwell's method. The dynamic stability of these end-loaded columns under transverse vibrations was observed. Static stability tests were also performed on Plexiglas models of the strongest shaped circular arch and on the uniform circular arch of equal weight and span. The predicted buckling loads for the strongest shapes agreed reasonably well with measurements. The shaped circular arch, however, was found to be an inefficient design for loading applied uniformly across the span rather than in the radial direction.     

An IR study of the adsorption of water on Ru(001)

The strong OH stretch at 3400 cm^?1 (fwhm ～ 230 cm^?1) in the IR reflection absorption spectra of the system $\text{H}{}_2\text{O}\text{Ru(001)}$ at 85 K indicates the presence of hydrogen-bonded clusters. These clusters appear to form even at the lowest coverages. On the clean surface there is a linear relationship between integrated absorption intensity and coverage. The presence of small quantities of preadsorbed oxygen delays, however, the onset of absorption. It is thought that the oxygen atoms “bind” the water molecules, thus preventing cluster formation and in turn eliminating the intensity enhancement due to hydrogen bonding. Flash desorption spectra also indicate a second binding state when oxygen is coadsorbed. The relevance of these results to models of the electric double layer at the metal-electrolyte interface is discussed.     

Attenuation of strain waves in core samples of three types of rock

Dynamic photoelasticity was employed to determine the velocity of longitudinal stress waves, dynamic modulus of elasticity and attenuation coefficients in rockcore samples 1 in. (25 mm) in diameter, 18 in. (0.46 m) long. Birefringent strips bonded to the core samples of Salem limestone, Charcoal granite and Berea sandstone provided all the data needed for the dynamic characterization of these rock types. The rods were dynamically loaded at one end with a lead-azide charge. A multiple-spark-gap camer was used to record the dynamic isochromatic-fringe patterns occurring in the birefringent strip. Of the three rock types investigated, the Berea sandstone exhibited the largest energy losses as characterized by an attenuation coefficient of 0.0910. Salem limestone and Charcoal granite exhibited much smaller losses with attenuation coefficients of 0.0196 and 0.0024, respectively. The extremely low-energy loss associated with Charcoal granite indicates that this material transmits stress waves as well as most metals.     

Support Varieties for Selfinjective Algebras

Support varieties for any finite dimensional algebra over a field were introduced in (Proc. London Math. Soc. 88 (3) (2004) 705–732) using graded subalgebras of the Hochschild cohomology ring. We mainly study these varieties for selfinjective algebras under appropriate finite generation hypotheses. Then many of the standard results from the theory of support varieties for finite groups generalize to this situation. In particular, the complexity of the module equals the dimension of its corresponding variety, all closed homogeneous varieties occur as the variety of some module, the variety of an indecomposable module is connected, the variety of periodic modules are lines and for symmetric algebras a generalization of Webbs theorem is true. As a corollary of a more general result we show that Webbs theorem generalizes to finite dimensional cocommutative Hopf algebras.Received November 2003Mathematics Subject Classifications (2000) Primary: 16E40, 16G10, 16P10, 16P20; Secondary: 16G70.     

A remark on rank varieties for a class of local algebras

We answer a question raised in [9] by showing the equality of two different definitions of rank variety for finitely generated modules over truncated polynomial algebras. We do this by establishing an isomorphism of algebras used in the two definitions of rank variety. Received: 23 April 2007     

Mechanisms of Resonant Infrared Matrix-Assisted Pulsed Laser Evaporation

For the last decade, a variant of pulsed laser ablation, Resonant-Infrared Matrix-Assisted Pulsed Laser Evaporation (RIR-MAPLE), has been studied as a deposition technique for organic and polymeric materials. RIR-MAPLE minimizes photochemical damage from direct interaction with the intense laser beam by encapsulating the polymer in a high infrared-absorption solvent matrix. This review critically examines the thermally-induced ablation mechanisms resulting from irradiation of cryogenic solvent matrices by a tunable free electron laser (FEL). A semi-empirical model is used to calculate temperatures as a function of time in the focal volume and determine heating rates for different resonant modes in two model solvents, based on the thermodynamics and kinetics of the phase transitions induced in the solvent matrices. Three principal ablation mechanisms are discussed, namely normal vaporization at the surface, normal boiling, and phase explosion. Normal vaporization is a highly inefficient polymer deposition mechanism as it relies on collective collisions with evaporating solvent molecules. Diffusion length calculations for heterogeneously nucleated vapor bubbles show that normal boiling is kinetically limited. During high-power pulsed-FEL irradiation, phase explosion is shown to be the most significant contribution to polymer deposition in RIR-MAPLE. Phase explosion occurs when the target is rapidly heated (10⁸ to 10¹⁰ K/s) and the solvent matrix approaches its critical temperature. Spontaneous density stratification (spinodal decay) within the condensed metastable phase leads to rapid homogeneous nucleation of vapor bubbles. As these vapor bubbles interconnect, large pressures build up within the condensed phase, leading to target explosions and recoil-induced ejections of polymer to a near substrate. Phase explosion is a temperature (fluence) threshold-limited process, while surface evaporation can occur even at very low fluences.     

Application of holographic interferometry to a study of wave propagation in rock

Holographic interferometry was utilized to determine the three orthogonal components of displacement in elastic surface waves. A pulsed ruby laser was used as the light source and techniques to improve its coherence properties are described. Procedures for the formation and reconstruction of the hologram, fringe interpretation, and data reduction and presentation are detailed. The elastic-wave velocities and material constants for pink westerly granite were obtained. Solutions for an explosively generated Rayleigh wave in a half space and its reflection from a free edge are presented.     

Enhanced luminescence and degradation of SiO2:Ce,Tb powder phosphors prepared by a sol-gel process

Enhanced green photoluminescence and cathodoluminescence (CL) from Tb³⁺ ions due to co-doping with Ce³⁺ ions were observed from SiO₂:Ce,Tb powder phosphors prepared by a sol-gel technique. Blue emission from the Ce³⁺ ions was completely suppressed by Tb co-doping, presumably due to energy transfer from Ce³⁺ to Tb³⁺. In addition, the green CL intensity from SiO₂:Ce,Tb degraded by ∼50% when the powders were irradiated for 10 h with a 2 keV, 54 mA/cm² beam of electrons in an ultra-high vacuum chamber containing either 1×10⁻⁸ or 1×10⁻⁷ Torr O₂. Desorption of oxygen from the surface was observed during the decrease of CL intensity. The mechanisms for energy transfer from Ce³⁺ ions to Tb³⁺ ions to enhance the green luminescence, and mechanisms for desorption of oxygen from the phosphor surface that would result in decreased CL intensity are discussed.