Simple solutions of fireball hydrodynamics for rotating and expanding triaxial ellipsoids and final state observables

We present a class of analytic solutions of non-relativistic fireball hydrodynamics for a fairly general class of equation of state. The presented solution describes the expansion of a triaxial ellipsoid that rotates around one of the principal axes. We calculate the hadronic final state observables such as single-particle spectra, directed, elliptic and third flows, as well as HBT correlations and corresponding radius parameters, utilizing simple analytic formulas. We call attention to the fact that the final tilt angle of the fireball, an important observable quantity, is not independent on the exact definition of it: one gets different angles from the single-particle spectra and from HBT measurements. Taken together, it is pointed out that these observables may be sufficient for the determination of the magnitude of the rotation of the fireball. We argue that observing this rotation and its dependence on collision energy would reveal the softness of the equation of state. Thus determining the rotation may be a powerful tool for the experimental search for the critical point in the phase diagram of strongly interacting matter.Comment: 17 pages, 12 figure panel

Stability of a chain of phase oscillators

We study a chain of N + 1 phase oscillators with asymmetric but uniform coupling. This type of chain possesses 2 N ways to synchronize in so-called traveling wave states, i.e., states where the phases of the single oscillators are in relative equilibrium. We show that the number of unstable dimensions of a traveling wave equals the number of oscillators with relative phase close to π . This implies that only the relative equilibrium corresponding to approximate in-phase synchronization is locally stable. Despite the presence of a Lyapunov-type functional, periodic or chaotic phase slipping occurs. For chains of lengths 3 and 4 we locate the region in parameter space where rotations (corresponding to phase slipping) are present

A new family of exact and rotating solutions of fireball hydrodynamics

A new class of analytic, exact, rotating, self-similar and surprisingly simple solutions of non-relativistic hydrodynamics are presented for a three-dimensionally expanding, spheroidally symmetric fireball. These results generalize earlier, non-rotating solutions for ellipsoidally symmetric fireballs with directional, three-dimensional Hubble flows. The solutions are presented for a general class of equations of state that includes the lattice QCD equations of state and may feature inhomogeneous temperature and corresponding density profiles.Comment: Dedicated to T. Kodama on the occasion of his 70th birthday. 15 pages, no figures. Accepted for publication at Phys. Rev. C. Minor rewritings from previous versio

Triangle areas in line arrangements

A widely investigated subject in combinatorial geometry, originated from Erd\H{o}s, is the following. Given a point set $P$ of cardinality $n$ in the plane, how can we describe the distribution of the determined distances? This has been generalized in many directions. In this paper we propose the following variants. Consider planar arrangements of $n$ lines. Determine the maximum number of triangles of unit area, maximum area or minimum area, determined by these lines. Determine the minimum size of a subset of these $n$ lines so that all triples determine distinct area triangles. We prove that the order of magnitude for the maximum occurrence of unit areas lies between $\Omega(n^2)$ and $O(n^{9/4})$. This result is strongly connected to both additive combinatorial results and Szemer\'edi--Trotter type incidence theorems. Next we show a tight bound for the maximum number of minimum area triangles. Finally we present lower and upper bounds for the maximum area and distinct area problems by combining algebraic, geometric and combinatorial techniques.Comment: Title is shortened. Some typos and small errors were correcte

Anomalous diffusion of pions at RHIC

After pointing out the difference between normal and anomalous diffusion, we consider a hadron resonance cascade (HRC) model simulation for particle emission at RHIC and point out, that rescattering in an expanding hadron resonance gas leads to a heavy tail in the source distribution. The results are compared to recent PHENIX measurements of the tail of the particle emitting source in Au+Au collisions at RHIC. In this context, we show, how can one distinguish experimentally the anomalous diffusion of hadrons from a second order QCD phase transition.Comment: 12 pages, 26 figures. Presented by T. Csorgo at the 2nd Workshop on Particle Femtoscopy and Correlations - WPCF in Sao Paulo, sept 2006. Brazilian Journal of Physics in press, minor misprints fixe