Method and apparatus for producing concentric hollow spheres

Hollow spheres with precisely concentric inner and outer spherical surfaces are formed by applying vibrations to a nonconcentric hollow sphere while it is at an elevated temperature at which it is fluid or plastic, the vibrations producing internal flows which cause the inner and outer surfaces to become precisely concentric. Concentric spheres can be mass produced by extruding a material such as glass or metal while injecting a stream of gas into the center of the extrusion to form a gas-filled tube. Vibrations are applied to the extruded tube to help break it up into individual bodies of a desired uniform size, the bodies tending to form spherical inner and outer surfaces by reason of surface tension, and the continuing application of vibrations causing these surfaces to become concentric

Acoustic energy shaping

A suspended mass is shaped by melting all or a selected portion of the mass and applying acoustic energy in varying amounts to different portions of the mass. In one technique for forming an optical waveguide slug, a mass of oval section is suspended and only a portion along the middle of the cross-section is heated to a largely fluid consistency. Acoustic energy is applied to opposite edges of the oval mass to press the unheated opposite edge portions together so as to form bulges at the middle of the mass. In another technique for forming a ribbon of silicon for constructing solar cells, a cylindrical thread of silicon is drawn from a molten mass of silicon, and acoustic energy is applied to opposite sides of the molten thread to flatten it into a ribbon

Magnetic spin excitations in diluted ferromagnetic systems: the case of Ga1−xMnxAsGa_{1-x}Mn_{x}As

We propose a theory which allow to calculate the magnetic excitation spectrum in diluted ferromagnetic systems. The approach is rather general and based on the Self-Consistent local Random Phase Approximation in which disorder (dilution) and thermal fluctuations are properly treated. To illustrate its reliability and accuracy we calculate the magnetic excitation in the diluted III-V magnetic semiconductor $Ga_{1-x}Mn_{x}As$. It is shown that dilution has a drastic effect on the excitation spectrum, indeed well defined magnon excitations exist only in a small region of the Brillouin zone centered around the $\Gamma$ point. We also calculate the spin stiffness in optimally annealed sample as a function of $Mn^{2+}$ concentration. A comparison to available measurements is done. We find a very good agreement for both the Curie temperature and the spin stiffness measured in well annealed samples and provide a plausible explanation for the very small values measured in as grown samples.Comment: The manuscript has been modified, 4 figures are included. Accepted for publication in Eur. Phys. Let

Primitive Cohomology of Hopf algebras

Primitive cohomology of a Hopf algebra is defined by using a modification of the cobar construction of the underlying coalgebra. Among many of its applications, two classifications are presented. Firstly we classify all non locally PI, pointed Hopf algebra domains of Gelfand-Kirillov dimension two; and secondly we classify all pointed Hopf algebras of rank one. The first classification extends some results of Brown, Goodearl and others in an ongoing project to understand all Hopf algebras of low Gelfand-Kirillov dimension. The second generalizes results of Krop-Radford and Wang-You-Chen which classified Hopf algebras of rank one under extra hypothesis. Properties and algebraic structures of the primitive cohomology are discussed

Heat-operated cryogenic electrical generator

Generator operation is based upon unusual hydrodynamic properties exhibited by liquid helium below superfluid critical point. Below that temperature, liquid behaves as though it is mixture of two interpenetrating fluids. When transition takes place between superfluid and normal states, conservation of momentum is always balanced by normal fluid

Acoustic bubble removal method

A method is described for removing bubbles from a liquid bath such as a bath of molten glass to be used for optical elements. Larger bubbles are first removed by applying acoustic energy resonant to a bath dimension to drive the larger bubbles toward a pressure well where the bubbles can coalesce and then be more easily removed. Thereafter, submillimeter bubbles are removed by applying acoustic energy of frequencies resonant to the small bubbles to oscillate them and thereby stir liquid immediately about the bubbles to facilitate their breakup and absorption into the liquid