Incidence Hypergraphs: Box Products & the Laplacian

The box product and its associated box exponential are characterized for the categories of quivers (directed graphs), multigraphs, set system hypergraphs, and incidence hypergraphs. It is shown that only the quiver case of the box exponential can be characterized via homs entirely within their own category. An asymmetry in the incidence hypergraphic box product is rectified via an incidence dual-closed generalization that effectively treats vertices and edges as real and imaginary parts of a complex number, respectively. This new hypergraphic box product is shown to have a natural interpretation as the canonical box product for graphs via the bipartite representation functor, and its associated box exponential is represented as homs entirely in the category of incidence hypergraphs; with incidences determined by incidence-prism mapping. The evaluation of the box exponential at paths is shown to correspond to the entries in half-powers of the oriented hypergraphic signless Laplacian matrix.Comment: 34 pages, 23 figures, 4 table

Inclusive charged hadron elliptic flow in Au + Au collisions at sNN\sqrt{s_{NN}} = 7.7 - 39 GeV

A systematic study is presented for centrality, transverse momentum ($p_T$) and pseudorapidity ($\eta$) dependence of the inclusive charged hadron elliptic flow ($v_2$) at midrapidity($|\eta| < 1.0$) in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7, 11.5, 19.6, 27 and 39 GeV. The results obtained with different methods, including correlations with the event plane reconstructed in a region separated by a large pseudorapidity gap and 4-particle cumulants ($v_2{4}$), are presented in order to investigate non-flow correlations and $v_2$ fluctuations. We observe that the difference between $v_2{2}$ and $v_2{4}$ is smaller at the lower collision energies. Values of $v_2$, scaled by the initial coordinate space eccentricity, $v_{2}/\varepsilon$, as a function of $p_T$ are larger in more central collisions, suggesting stronger collective flow develops in more central collisions, similar to the results at higher collision energies. These results are compared to measurements at higher energies at the Relativistic Heavy Ion Collider ($\sqrt{s_{NN}}$ = 62.4 and 200 GeV) and at the Large Hadron Collider (Pb + Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV). The $v_2(p_T)$ values for fixed $p_T$ rise with increasing collision energy within the $p_T$ range studied ($< 2 {\rm GeV}/c$). A comparison to viscous hydrodynamic simulations is made to potentially help understand the energy dependence of $v_{2}(p_{T})$. We also compare the $v_2$ results to UrQMD and AMPT transport model calculations, and physics implications on the dominance of partonic versus hadronic phases in the system created at Beam Energy Scan (BES) energies are discussed.Comment: 20 pages, 12 figures. Version accepted by PR

Strangeness Enhancement in Cu+Cu and Au+Au Collisions at \sqrt{s_{NN}} = 200 GeV

We report new STAR measurements of mid-rapidity yields for the $\Lambda$, $\bar{\Lambda}$, $K^{0}_{S}$, $\Xi^{-}$, $\bar{\Xi}^{+}$, $\Omega^{-}$, $\bar{\Omega}^{+}$ particles in Cu+Cu collisions at \sNN{200}, and mid-rapidity yields for the $\Lambda$, $\bar{\Lambda}$, $K^{0}_{S}$ particles in Au+Au at \sNN{200}. We show that at a given number of participating nucleons, the production of strange hadrons is higher in Cu+Cu collisions than in Au+Au collisions at the same center-of-mass energy. We find that aspects of the enhancement factors for all particles can be described by a parameterization based on the fraction of participants that undergo multiple collisions