Collective flow and QCD phase transition

In the first part I discuss the sensitivity of collective matter expansion in ultrarelativistic heavy-ion collisions to the transition between quark and hadronic matter (physics of the softest point of the Equation of State). A kink in the centrality dependence of elliptic flow has been suggested as a signature for the phase transition in hot QCD matter. Indeed, preliminary data of NA49 presented at this conference show first indications for the predicted kink. In the second part I have a look at the present theories of heavy-ion reactions. These remarks may also be seen as a critical comment to B. Mueller's summary talk (nucl-th/9906029) presented at this conference.Comment: Write-up of QM '99 talk. Typo's correcte

Strangeness in ultrarelativistic nucleus-nucleus collisions

I discuss strangeness production in nucleus-nucleus reactions at ultrarelativistic energies (up to 200 AGeV). In these reactions matter may be created with densities and temperatures in the transition region between quark-gluon plasma (QGP) and hadron gas. Strange anti-baryon enhancement at 200 AGeV and probably even more so at 10 AGeV signals importance of interactions beyond hadron gas dynamics. The systematics of strangeness production indicates that energy and baryon density are key variables while the size of the production volume plays no visible role. Analysis of strangeness appears useful to explore thermalization, flow and the post-equilibrium stage in ultrarelativistic nucleus-nucleus collisions.Comment: 13 pages LaTeX including 6 postscript figures; needs style files espcrc1,floatfig,epsfig. Invited talk presented at 6th International Conference on Nucleus-Nucleus Collisions at Gatlinburg, June 2-6, 1997. To be published in Proceedings in Nuclear Physics

A More Complicated Hardness Proof for Finding Densest Subgraphs in Bounded Degree Graphs

We consider the Densest-Subgraph problem, where a graph and an integer k is given and we search for a subgraph on exactly k vertices that induces the maximum number of edges. We prove that this problem is NP-hard even when the input graph has maximum degree three

Masking Femininity: Women and Power in Shakespeare\u27s Macbeth, As You Like It, and Titus Andronicus

This paper analyzes the power that Lady Macbeth from Macbeth, Rosalind from As You Like It, and Tamora from Titus Andronicus assert and answers the questions of how women assert power in Shakespeare and the role gender plays in power

Temperatures and Non-ideal Expansion in Ultrarelativistic Nucleus-Nucleus Collisions

The hadronic phase space distributions calculated with the transport model RQMD for central S(200 AGeV) on S and Pb(160AGeV) on Pb collisions are analyzed to study the deviations from ideal hydrodynamical evolution. After the preequilibrium stage, which lasts for approximately 4 (2) fm/c in Pb+Pb (S+S) the source stays in approximate kinetic equilibrium for about 2 fm/c at a temperature close to 140 MeV. The interactions of mesons last until around 14 (5) fm/c during which time strong transverse flow is generated. The interactions in the hadronic resonance gas are not sufficiently strong to maintain ideal fluid expansion. While pions acquire average transverse fluid velocities around 0.47-0.58 c, heavier particles like protons and kaons cannot keep up with the pionic fluid, since their average velocities are smaller by about 20 to 30 \%. Although kinetic equilibrium breaks down in the final dilute stage of $AA$ collisions, the system resembles a thermal system at a temperature of 130 MeV, if the free streaming of hadrons after freeze-out is suppressed. This freeze-out temperature is consistent with estimates based on mean free paths and expansion rates in a thermal fireball but lower than values derived from fits to measured particle ratios and transverse momentum spectra. The processes in RQMD to which the differences can be attributed to are the non-ideal expansion of the hadronic matter and the absence of chemical equilibrium at freeze-out.Comment: 12 pages + 3 postscript figures (uuencoded and included

New Scaling Law for Deuteron Production in Ultra-Relativistic Nucleus Nucleus Collisions

Deuteron production in S and Pb induced collisions at beam energies of 200 and 160 AGeV is studied in the framework of the transport theoretical approach RQMD. Strong transverse flow invalidates the differential coalescence formula in momentum space. The transverse momentum integrated $d$ yields scale in a broad rapidity interval with the squared proton densities and inversely with the produced particle rapidity densities. This kind of scaling can be linked to constant relative sizes of nucleon and pion sources at freeze-out. With increasing projectile mass the nucleon source blows up stronger than the pion source. As a result, the scaled deuteron densities drop in central Pb+Pb collisions by 15 percent as compared to S induced reactions.Comment: 12 pages + 4 postscript figures (uuencoded and included

Collective effects in microscopic transport models

We give a reminder on the major inputs of microscopic hadronic transport models and on the physics aims when describing various aspects of relativistic heavy ion collisions at SPS energies. We then first stress that the situation of particle ratios being reproduced by a statistical description does not necessarily mean a clear hint for the existence of a fully isotropic momentum distribution at hadrochemical freeze-out. Second, a short discussion on the status of strangeness production is given. Third we demonstrate the importance of a new collective mechanism for producing (strange) antibaryons within a hadronic description, which guarantees sufficiently fast chemical equilibration.Comment: 10 pages, 8 figures; invited talk at the 16th Int. Conf. on Ultra-Relativistic Nucleus-Nucleus Collisions, QM2002, Nantes, France, 18-24 Jul

Organizing societal space within globalization: Bringing society back in

The notion of 'society' is increasingly debated, recently, under the impact of 'globalization'. This debate is carried out in both sociology and business studies, and it also has implications in political theory. A theoretical grounding of society is provided following G.H. Mead, which bears sufficient regard to actors and avoids determinism. Society is conceptualized as 'societal space', open to layering in different forms. Incongruent layering is then put forward as a feature of societal evolution which has hitherto been neglected as an engine of modernization. This form of layering is also suggested to be important for current debates. Following this concept, the business and organizational literature can be linked with social theory in a way which shows how 'provincialization' of identity, institutions and culture is pervasively linked with the extension of horizons of action under globalization. Various comparative findings are adduced to show how the dialectics of globalization and provincialization work, and how socio-institutional patterns interact with the evolution of enterprise strategies in order to fuel this dialectic. In such an evolution, society has an important part to play. But this is not because society re-asserts itself as a co-extensive entity on a higher plane. Instead, it is precisely the layering of societal space which makes societal effects a necessary concept. --

Soft transverse expansion in Pb(158 AGeV) on Pb collisions: preequilibrium motion or 1st order phase transition?

Transverse expansion of centrally produced matter in Pb on Pb collisions at beam energies around 158 AGeV appears to be rather `soft'. Two possible reasons -- an extended preequilibrium stage and a first order phase transition from a quark-gluon-plasma into hadronic matter -- are discussed. The softening of transverse expansion caused by preequilibrium dynamics is estimated with the aid of the transport model RQMD which does not contain a first order phase transition. It is found that the anisotropy of transverse flow in non-central reactions is very different in the preequilibrium and hydrodynamic scenarios even if the latter are based on a strong 1st order transition.Comment: 14 pages LaTeX including 3 postscript figure