6,821 research outputs found
The Steinberg torus of a Weyl group as a module over the Coxeter complex
Associated to each irreducible crystallographic root system , there is
a certain cell complex structure on the torus obtained as the quotient of the
ambient space by the coroot lattice of . This is the Steinberg torus. A
main goal of this paper is to exhibit a module structure on (the set of faces
of) this complex over the (set of faces of the) Coxeter complex of . The
latter is a monoid under the Tits product of faces. The module structure is
obtained from geometric considerations involving affine hyperplane
arrangements. As a consequence, a module structure is obtained on the space
spanned by affine descent classes of a Weyl group, over the space spanned by
ordinary descent classes. The latter constitute a subalgebra of the group
algebra, the classical descent algebra of Solomon. We provide combinatorial
models for the module of faces when is of type or .Comment: 36 pages, 23 figures. Extended abstract of this work appeared in
proceedings of FPSAC 25 (Paris): DMTCS proceedings AS, 2013, p. 277-28
Event-by-event analysis of ultra-relativistic heavy-ion collisions in smoothed particle hydrodynamics
The method of smoothed particle hydrodynamics (SPH) is applied for
ultra-relativistic heavy-ion collisions. The SPH method has several advantages
in studying event-by-event fluctuations, which attract much attention in
looking for quark gluon plasma (QGP) formation, because it gives a rather
simple scheme for solving hydrodynamical equations. Using initial conditions
for Au+Au collisions at RHIC energy produced by NeXus event generator, we solve
the hydrodynamical equation in event-by-event basis and study the fluctuations
of hadronic observables such as dN/dy due to the initial conditions. In
particular, fluctuations of elliptic flow coefficient v2 is investigated for
both the cases, with and without QGP formation. This can be used as an
additional test of QGP formation.Comment: LaTeX, 16 figures, 3 tables, 23 pages. Talk presented at 6th
International Workshop on Relativistic Aspects of Nuclear Physics(RANP2000),
Caraguatatuba, Tabatinga Beach, Sao Paulo, Brazil, October 17-20, 2000. To be
published in the proceedings (World Scientific, Singapore
Event-by-event fluctuations in hydrodynamical description of heavy-ion collisions
Effects caused by the event-by-event fluctuation of the initial conditions in
hydrodynamical description of high-energy heavy-ion collisions are
investigated. Non-negligible effects appear for several observable quantities,
even for a fixed impact parameter . They are sensitive to the equation
of state, being the dispersions of the observable quantities in general smaller
when the QGP phase appears at the beginning of hydrodynamic evolution than when
the fluid remains hadron gas during whole the evolution.Comment: 4 pages, 4 figures, talk presented to Quark Matter 2001 Conferenc
NeXSPheRIO results on elliptic flow at RHIC and connection with thermalization
Elliptic flow at RHIC is computed event-by-event with NeXSPheRIO. Reasonable
agreement with experimental results on is obtained. Various effects
are studied as well: reconstruction of impact parameter direction, freeze out
temperature, equation of state (with or without crossover), emission mecanism.Comment: Contribution to the Proceedings of the Quark-Gluon Plasma
Thermalization workshop. Content slightly increase
The effect of shear and bulk viscosities on elliptic flow
In this work, we examine the effect of shear and bulk viscosities on elliptic
flow by taking a realistic parameterization of the shear and bulk viscous
coefficients, and , and their respective relaxation times,
and . We argue that the behaviors close to ideal fluid
observed at RHIC energies may be related to non-trivial temperature dependence
of these transport coefficients.Comment: 6 pages, 4 figures, to appear in the proceedings of Strange Quark
Matter 2009 (SQM09
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