The algebra of rack and quandle cohomology

In this paper we describe methods for computing rack and quandle cohomology. We illustrate these methods by completely determining the cohomology of prime dihedral quandles

The adjoint group of an Alexander quandle

We show that the adjoint group of the Alexander quandle associated to an abelian group M and an automorphism T has a nice description in terms of M and T

Photoelectron spectrometer with means for stabilizing sample surface potential

An improved X-ray photoelectron spectrometer is disclosed, which includes circuit means to determine the surface potential of a sample, e.g., an insulator. The circuit means comprise an electron gun, whose potential is modulated at a preselected frequency above and below a selected potential with respect to the spectrometer common potential, e.g., ground. The beam of electrons is directed to the sample surface. The sample's surface potential is offset by an offset power supply with respect to the spectrometer common potential until the ac current which flows through the sample reaches a peak amplitude. A lock-in amplifier is included to measure the ac current in phase with the modulating frequency

Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities

The interaction of a plane weak shock wave with a single discrete gaseous inhomogeneity is studied as a model of the mechanisms by which finite-amplitude waves in random media generate turbulence and intensify mixing. The experiments are treated as an example of the shock-induced Rayleigh-Taylor instability. or Richtmyer-Meshkov instability, with large initial distortions of the gas interfaces. The inhomogeneities are made by filling large soap bubbles and cylindrical refraction cells (5 cm diameter) whose walls are thin plastic membranes with gases both lighter and heavier than the ambient air in a square (8.9 cm side shock-tube text section. The wavefront geometry and the deformation of the gas volume are visualized by shadowgraph photography. Wave configurations predicted by geometrical acoustics, including the effects of refraction, reflection and diffraction, are compared to the observations. Departures from the predictions of acoustic theory are discussed in terms of gasdynamic nonlinearity. The pressure field on the axis of symmetry downstream of the inhomogeneity is measured by piezoelectric pressure transducers. In the case of a cylindrical or spherical volume filled with heavy low-sound-speed gas the wave which passes through the interior focuses just behind the cylinder. On the other hand, the wave which passes through the light high-sound-speed volume strongly diverges. Visualization of the wavefronts reflected from and diffracted around the inhomogeneities exhibit many features known in optical and acoustic scattering. Rayleigh-Taylor instability induced by shock acceleration deforms the initially circular cross-section of the volume. In the case of the high-sound-speed sphere, a strong vortex ring forms and separates from the main volume of gas. Measurements of the wave and gas-interface velocities are compared to values calculated for one-dimensional interactions and for a simple model of shock-induced Rayleigh-Taylor instability. The circulation and Reynolds number of the vortical structures are calculated from the measured velocities by modeling a piston vortex generator. The results of the flow visualization are also compared with contemporary numerical simulations