A family of pseudo-Anosov braids with large conjugacy invariant sets

We show that there is a family of pseudo-Anosov braids independently parameterized by the braid index and the (canonical) length whose smallest conjugacy invariant sets grow exponentially in the braid index and linearly in the length and conclude that the conjugacy problem remains exponential in the braid index under the current knowledge.Comment: 16 pages, 6 figure

Kaon dispersion relation and flow in relativistic heavy-ion collisions

Within the framework of a relativistic transport model (ART) for heavy-ion collisions at AGS energies, we examine the effects of kaon dispersion relation on the transverse flow of kaons and their transverse momentum and azimuthal angle distributions. We find that the transverse flow is the most sensitive observable for studying the kaon dispersion relation in dense medium.Comment: 7 pages, latex, 3 figures available upon request from the authors, Phys. Rev. C (1996) in pres

Pion flow and antiflow in relativistic heavy-ion collisions

Within the framework of a relativistic transport model (ART) for heavy-ion collisions at AGS energies, we study the transverse flow of pions with respect to that of nucleons using two complementary approaches. It is found that in central collisions pions develop a weak flow as a result of the flow of baryon resonances from which they are produced. On the other hand, they have a weak antiflow in peripheral collisions due to the shadowing of spectators. Furthermore, it is shown that both pion flow and antiflow are dominated by those with large transverse momenta.Comment: Phys. Rev. C, Rapid communication, in press. Figures are available from the authors upon reques

Medium effects on charged pion ratio in heavy ion collisions

We have recently studied in the delta-resonance--nucleon-hole model the dependence of the pion spectral function in hot dense asymmetric nuclear matter on the charge of the pion due to the pion p-wave interaction in nuclear medium. In a thermal model, this isospin-dependent effect enhances the ratio of negatively charged to positively charged pions in neutron-rich nuclear matter, and the effect is comparable to that due to the uncertainties in the theoretically predicted stiffness of nuclear symmetry energy at high densities. This effect is, however, reversed if we also take into account the s-wave interaction of the pion in nuclear medium as given by chiral perturbation theory, resulting instead in a slightly reduced ratio of negatively charged to positively charged pions. Relevance of our results to the determination of the nuclear symmetry energy from the ratio of negatively to positively charged pions produced in heavy ion collisions is discussed.Comment: 11 pages, 4 figures, contribution to The International Workshop on Nuclear Dynamics in Heavy-Ion Reactions and the Symmetry Energy (IWND2009), Shanghai, China, 22-25 August, 200

Density slope of the nuclear symmetry energy from the neutron skin thickness of heavy nuclei

Expressing explicitly the parameters of the standard Skyrme interaction in terms of the macroscopic properties of asymmetric nuclear matter, we show in the Skyrme-Hartree-Fock approach that unambiguous correlations exist between observables of finite nuclei and nuclear matter properties. We find that existing data on neutron skin thickness $\Delta r_{np}$ of Sn isotopes give an important constraint on the symmetry energy $E_{sym}({\rho _{0}})$ and its density slope $L$ at saturation density ${\rho _{0}}$. Combining these constraints with those from recent analyses of isospin diffusion and double neutron/proton ratio in heavy-ion collisions at intermediate energies leads to a more stringent limit on $L$ approximately independent of $E_{sym}({\rho _{0}})$. The implication of these new constraints on the $\Delta r_{np}$ of $^{208}$Pb as well as the core-crust transition density and pressure in neutron stars is discussed.Comment: 18 pages, 9 figures, 1 table. Significantly expanded to include a number of details and discussions. Title shortened. Accepted version to appear in PR

Transition density and pressure in hot neutron stars

Using the momentum-dependent MDI effective interaction for nucleons, we have studied the transition density and pressure at the boundary between the inner crust and liquid core of hot neutron stars. We find that their values are larger in neutrino-trapped neutron stars than in neutrino-free neutron stars. Furthermore, both are found to decrease with increasing temperature of a neutron star as well as increasing slope parameter of the nuclear symmetry energy, except that the transition pressure in neutrino-trapped neutron stars for the case of small symmetry energy slope parameter first increases and then decreases with increasing temperature. We have also studied the effect of the nuclear symmetry energy on the critical temperature above which the inner crust in a hot neutron star disappears and found that with increasing value of the symmetry energy slope parameter, the critical temperature decreases slightly in neutrino-trapped neutron stars but first decreases and then increases in neutrino-free neutron stars.Comment: 7 pages, 6 figures, version to appear in Phys. Rev.

Isospin- and momentum-dependent effective interactions for the baryon octet and the properties of hybrid stars

The isospin- and momentum-dependent MDI interaction, which has been extensively used in intermediate-energy heavy-ion reactions to study the properties of asymmetric nuclear matter, is extended to include the nucleon-hyperon and hyperon-hyperon interactions by assuming same density, momentum and isospin dependence as for the nucleon-nucleon interaction. The parameters in these interactions are determined from the empirical hyperon single-particle potentials in symmetric nuclear matter at saturation density. The extended MDI interaction is then used to study in the mean-field approximation the equation of state of hypernuclear matter and also the properties of hybrid stars by including the phase transition from the hypernuclear matter to the quark matter at high densities. In particular, the effects of attractive and repulsive $\Sigma$N interactions and different values of symmetry energies on the hybrid star properties are investigated.Comment: 13 pages, 12 figures, version to appear in Phys. Rev.