Thermalization through Hagedorn states - the importance of multiparticle collisions

Quick chemical equilibration times of hadrons within a hadron gas are explained dynamically using Hagedorn states, which drive particles into equilibrium close to the critical temperature. Within this scheme master equations are employed for the chemical equilibration of various hadronic particles like (strange) baryon and antibaryons. A comparison of the Hagedorn model to recent lattice results is made and it is found that for both Tc =176 MeV and Tc=196 MeV, the hadrons can reach chemical equilibrium almost immediately, well before the chemical freeze-out temperatures found in thermal fits for a hadron gas without Hagedorn states.Comment: 8 pages, 3 figures, talk presented at the International Conference on Strangeness in Quark Matter, Buzios, Rio de Janeiro, Brazil, Sept. 27 - Oct. 2, 200

A linear programming based heuristic framework for min-max regret combinatorial optimization problems with interval costs

This work deals with a class of problems under interval data uncertainty, namely interval robust-hard problems, composed of interval data min-max regret generalizations of classical NP-hard combinatorial problems modeled as 0-1 integer linear programming problems. These problems are more challenging than other interval data min-max regret problems, as solely computing the cost of any feasible solution requires solving an instance of an NP-hard problem. The state-of-the-art exact algorithms in the literature are based on the generation of a possibly exponential number of cuts. As each cut separation involves the resolution of an NP-hard classical optimization problem, the size of the instances that can be solved efficiently is relatively small. To smooth this issue, we present a modeling technique for interval robust-hard problems in the context of a heuristic framework. The heuristic obtains feasible solutions by exploring dual information of a linearly relaxed model associated with the classical optimization problem counterpart. Computational experiments for interval data min-max regret versions of the restricted shortest path problem and the set covering problem show that our heuristic is able to find optimal or near-optimal solutions and also improves the primal bounds obtained by a state-of-the-art exact algorithm and a 2-approximation procedure for interval data min-max regret problems

Particle Ratios and the QCD Critical Temperature

We show how the measured particle ratios at RHIC can be used to provide non-trivial information about the critical temperature of the QCD phase transition. This is obtained by including the effects of highly massive Hagedorn resonances on statistical models, which are used to describe hadronic yields. Hagedorn states are relevant close to $T_c$ and have been shown to decrease $\eta/s$ to the KSS limit and allow for quick chemical equilibrium times in dynamical calculations of hadrons. The inclusion of Hagedorn states creates a dependence of the thermal fits on the Hagedorn temperature, $T_H$, which is assumed to be equal to $T_c$, and leads to an overall improvement of thermal fits. We find that for Au+Au collisions at RHIC at $\sqrt{s_{NN}}=200$ GeV the best square fit measure, $\chi^2$, occurs at $T_c \sim 176$ MeV and produces a chemical freeze-out temperature of 170.4 MeV and a baryon chemical potential of 27.8 MeV.Comment: 6 pages, 2 figures, talk presented at the International Conference on Strangeness in Quark Matter, Buzios, Rio de Janeiro, Brazil, Sept. 27 - oct. 2, 200

Contribution of Sm-Nd and Rb-Sr isotope systems to the petrogenetic study of the peraluminous two-mica granite pluton in Oporto town (NW Portugal)

O Granito do Porto corresponde a um granito hercínico, leucocrata, de duas micas, fortemente peraluminoso. No presente trabalho foram realizadas análises para os sistemas isotópicos Rb-Sr e Sm-Nd, em cinco amostras frescas do granito em estudo. Obteve -se uma isócrona Rb-Sr de 306±7 Ma (MSWD=0,71; 87Sr/86Sr inicial=0,7128), que dentro da margem de erro, deverá refletir a instalação magmática. Em termos de geoquímica isotópica, as razões isotópicas iniciais de Sr e Nd, calculadas de acordo com aquela isócrona, testemunham um claro enriquecimento em Sr radiogénico e um ligeiro empobrecimento em Nd radiogénico, típico de granitos de tipo S. Os valores ligeiramente negativos de εNd inicial (entre -1,9 e -3,6) apontam para que a fonte do magma granítico sejam litologias metapelíticas.The Oporto Granite is a Variscan, highly peraluminous, leucocratic, two-mica granite. In this work, information resulting from isotopic Rb-Sr and Sm-Nd analyses on five fresh samples of the Oporto granite is presented. Rb-Sr data give a 306±7 Ma isochron(MSWD=0.72,87Sr/86Sr=0.7128), which, within error, should reflect the emplacement age. Geochemically, initial isotopic Sr and Nd ratios, calculated according to that isochron, show a strong enrichment in radiogenic Sr and a slight depletion in radiogenic Nd,typical of S-type granites. In addition, the range of initial εNd values (from -1.9 to -3.6) suggests that metapelites could have been the source of the granitic melt

Discussão sobre a determinação da idade do granito do Porto pelo sistema Rb-Sr: implicações do valor da constante de decaimento do 87Rb

A determinação da idade absoluta por métodos isotópicos constitui um dado indispensável no constrangimento das condições petrogenéticas e evolutivas de uma rocha, contribuindo para uma melhor caraterização do seu enquadramento geológico e tectónico. As rochas graníticas da região do Porto têm sido alvo de diversos estudos isotópicos e geocronológicos que permitiram estabelecer comparações recorrendo a diferentes métodos, nomeadamente U-Pb, Rb-Sr e Sm-Nd. No presente trabalho discute-se a determinação da idade do granito peraluminoso de duas micas do Porto pelo sistema Rb-Sr com base em propostas mais recentes de um valor da constante de decaimento do 87Rb, assumida como mais rigorosa da habitualmente recomendada, tendo-se obtido a idade de 312±7 Ma para a instalação do granito do Porto, confirmando a sua afiliação com o grupo dos granitos sintectónicos. Estes resultados passam também a ser mais concordantes com as idades sugeridas em trabalhos anteriores pelo método U-Pb em zircão e monazite para o mesmo granito.The determination of absolute ages by isotopic systematics is an indispensable datum to constrain the petrogenesis and evolution conditions of a rock, being a contribution to a better characterization of the geological and tectonic settings. The granitic rocks of Porto region have been the object of several isotopic and geochronological studies that have allowed a comparative approach by different methods, namely U-Pb, Rb-Sr and Sm-Nd. In the present paper the age determination of the Porto peraluminous two-mica granite by the Rb-Sr systematics is discussed on the basis of recent estimates of the Rb decay constant, assumed as more accurate than the constant usually recommended, suggesting the age of 312±7 Ma for the emplacement of the Porto granite, in agreement with its affiliation to the group of syntectonic granites related with the third Hercynian deformation phase. These results are also more concordant with the U-Pb ages reported in previous works for zircon and monazite of the same granite