Tendency of spherically imploding plasma liners formed by merging plasma jets to evolve toward spherical symmetry

Three dimensional hydrodynamic simulations have been performed using smoothed particle hydrodynamics (SPH) in order to study the effects of discrete jets on the processes of plasma liner formation, implosion on vacuum, and expansion. The pressure history of the inner portion of the liner was qualitatively and quantitatively similar from peak compression through the complete stagnation of the liner among simulation results from two one dimensional radiationhydrodynamic codes, 3D SPH with a uniform liner, and 3D SPH with 30 discrete plasma jets. Two dimensional slices of the pressure show that the discrete jet SPH case evolves towards a profile that is almost indistinguishable from the SPH case with a uniform liner, showing that non-uniformities due to discrete jets are smeared out by late stages of the implosion. Liner formation and implosion on vacuum was also shown to be robust to Rayleigh-Taylor instability growth. Interparticle mixing for a liner imploding on vacuum was investigated. The mixing rate was very small until after peak compression for the 30 jet simulation.Comment: 28 pages, 16 figures, submitted to Physics of Plasmas (2012

Homotopy liftings and Hochschild cohomology of some twisted tensor products

The Hochschild cohomology of a tensor product of algebras is isomorphic to a graded tensor product of Hochschild cohomology algebras, as a Gerstenhaber algebra. A similar result holds when the tensor product is twisted by a bicharacter. We present new proofs of these isomorphisms, using Volkov's homotopy liftings that were introduced for handling Gerstenhaber brackets expressed on arbitrary bimodule resolutions. Our results illustrate the utility of homotopy liftings for theoretical purposes.Comment: 14 pages, minor reference corrections, added Section 4 with example

Multi-chord fiber-coupled interferometer with a long coherence length laser

This paper describes a 561 nm laser heterodyne interferometer that provides time-resolved measurements of line-integrated plasma electron density within the range of 10^15-10^18 cm^(-2). Such plasmas are produced by railguns on the Plasma Liner Experiment (PLX), which aims to produce \mu s-, cm-, and Mbar-scale plasmas through the merging of thirty plasma jets in a spherically convergent geometry. A long coherence length, 320 mW laser allows for a strong, sub-fringe phase-shift signal without the need for closely-matched probe and reference path lengths. Thus only one reference path is required for all eight probe paths, and an individual probe chord can be altered without altering the reference or other probe path lengths. Fiber-optic decoupling of the probe chord optics on the vacuum chamber from the rest of the system allows the probe paths to be easily altered to focus on different spatial regions of the plasma. We demonstrate that sub-fringe resolution capability allows the interferometer to operate down to line-integrated densities of order 10^15 cm^(-2).Comment: submitted to Rev. Sci. Instrum. (2011

Cohomology of finite dimensional pointed Hopf algebras

We prove finite generation of the cohomology ring of any finite dimensional pointed Hopf algebra, having abelian group of grouplike elements, under some mild restrictions on the group order. The proof uses the recent classification by Andruskiewitsch and Schneider of such Hopf algebras. Examples include all of Lusztig's small quantum groups, whose cohomology was first computed explicitly by Ginzburg and Kumar, as well as many new pointed Hopf algebras. We also show that in general the cohomology ring of a Hopf algebra in a braided category is braided commutative. As a consequence we obtain some further information about the structure of the cohomology ring of a finite dimensional pointed Hopf algebra and its related Nichols algebra.Comment: 36 pages, references adde

Color Lie rings and PBW deformations of skew group algebras

We investigate color Lie rings over finite group algebras and their universal enveloping algebras. We exhibit these universal enveloping algebras as PBW deformations of skew group algebras: Every color Lie ring over a finite group algebra with a particular Yetter-Drinfeld structure has universal enveloping algebra that is a quantum Drinfeld orbifold algebra. Conversely, every quantum Drinfeld orbifold algebra of a particular type arising from the action of an abelian group is the universal enveloping algebra of some color Lie ring over the group algebra. One consequence is that these quantum Drinfeld orbifold algebras are braided Hopf algebras

Reexamining Roe: Nineteenth-Century Abortion Statutes and the Fourteenth Amendment.

Abstract Forthcoming