PHENIX Studies of the Scaling Properties of Elliptic Flow at RHIC

Recent PHENIX elliptic flow ($v_2$) measurements for identified particles produced in Au+Au and Cu+Cu collisions at $\sqrt{s_{NN}}=200$ GeV are presented and compared to other RHIC measurements. They indicate universal scaling of $v_2$ compatible with partonic collectivity leading to the flow of light, strange and heavy quarks with a common expansion velocity field.Comment: Proceedings, Quark Matter 2006, Shanghai, Chin

Anisotropic Flow Measurements at RHIC

Anisotropic flow measurements in relativistic-heavy ion collisions at RHIC-BNL and LHC-CERN have provided strong evidence for the formation of a strongly coupled Quark-Gluon Plasma (sQGP). In this article, we briefly review and discuss the recent results of anisotropic flow measurements from the STAR and PHENIX experiments at RHIC, such as 1) new measurements at top RHIC energy

Multidimensional threshold matrices and extremal matrices of order 22

The paper is devoted to multidimensional $(0,1)$-matrices extremal with respect to containing a polydiagonal (a fractional generalization of a diagonal). Every extremal matrix is a threshold matrix, i.e., an entry belongs to its support whenever a weighted sum of incident hyperplanes exceeds a given threshold. Firstly, we prove that nonequivalent threshold matrices have different distributions of ones in hyperplanes. Next, we establish that extremal matrices of order $2$ are exactly selfdual threshold Boolean functions. Using this fact, we find the asymptotics of the number of extremal matrices of order $2$ and provide counterexamples to several conjectures on extremal matrices. Finally, we describe extremal matrices of order $2$ with a small diversity of hyperplanes.Comment: v. 2: small correction

Vertices of the polytope of polystochastic matrices and product constructions

A multidimensional nonnegative matrix is called polystochastic if the sum of its entries at each line is equal to $1$. The set of all polystochastic matrices of order $n$ and dimension $d$ is a convex polytope $\Omega_n^d$. In the present paper, we compare known bounds on the number $V(n,d)$ of vertices of the polytope $\Omega_n^d$, propose two constructions of vertices of $\Omega_n^d$ based on multidimensional matrix multiplication, and list all vertices of the polytope $\Omega_3^4$.Comment: v.1: a preliminary version of paper v.2: several typos are corrected; all vertices of 3-dimensional polystochastic matrices of order 4 are listed; still a preliminary versio