The Steinberg torus of a Weyl group as a module over the Coxeter complex

Associated to each irreducible crystallographic root system $\Phi$, there is a certain cell complex structure on the torus obtained as the quotient of the ambient space by the coroot lattice of $\Phi$. 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 $\Phi$. 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 $\Phi$ is of type $A$ or $C$.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 $\vec b$. 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 $v_2(\eta)$ 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, $\eta$ and $\zeta$, and their respective relaxation times, $\tau_{\pi}$ and $\tau_{\Pi}$. 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