634 research outputs found
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
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
Graded Hecke algebras for disconnected reductive groups
We introduce graded Hecke algebras H based on a (possibly disconnected)
complex reductive group G and a cuspidal local system L on a unipotent orbit of
a Levi subgroup M of G. These generalize the graded Hecke algebras defined and
investigated by Lusztig for connected G.
We develop the representation theory of the algebras H. obtaining complete
and canonical parametrizations of the irreducible, the irreducible tempered and
the discrete series representations. All the modules are constructed in terms
of perverse sheaves and equivariant homology, relying on work of Lusztig. The
parameters come directly from the data (G,M,L) and they are closely related to
Langlands parameters.
Our main motivation for considering these graded Hecke algebras is that the
space of irreducible H-representations is canonically in bijection with a
certain set of "logarithms" of enhanced L-parameters. Therefore we expect these
algebras to play a role in the local Langlands program. We will make their
relation with the local Langlands correspondence, which goes via affine Hecke
algebras, precise in a sequel to this paper.Comment: Theorem 3.4 and Proposition 3.22 in version 1 were not entirely
correct as stated. This is repaired in a new appendi
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