On the radial expansion of tubular structures in a quark gluon plasma

We study the radial expansion of cylindrical tubes in a hot QGP. These tubes are treated as perturbations in the energy density of the system which is formed in heavy ion collisions at RHIC and LHC. We start from the equations of relativistic hydrodynamics in two spatial dimensions and cylindrical symmetry and perform an expansion of these equations in a small parameter, conserving the nonlinearity of the hydrodynamical formalism. We consider both ideal and viscous fluids and the latter are studied with a relativistic Navier-Stokes equation. We use the equation of state of the MIT bag model. In the case of ideal fluids we obtain a breaking wave equation for the energy density fluctuation, which is then solved numerically. We also show that, under certain assumptions, perturbations in a relativistic viscous fluid are governed by the Burgers equation. We estimate the typical expansion time of the tubes

Sound waves and solitons in hot and dense nuclear matter

Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density. The equation of state is derived from a relativistic mean field model, which is a variant of the non-linear Walecka model. The expansion of the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations leads to differential equations for the density fluctuations. We solve them numerically for linear and spherical perturbations and follow the time evolution of the initial pulses. For linear perturbations we find single soliton solutions and solutions with one or more solitons followed by radiation. Depending on the equation of state a strong damping may occur. Spherical perturbations are strongly damped and almost do not propagate. We study these equations also for matter at finite temperature. Finally we consider the limiting case of shock wave formation.Comment: 28 pages, 8 figure

Solitons in relativistic mean field models

Assuming that the nucleus can be treated as a perfect fluid we study the conditions for the formation and propagation of Korteweg-de Vries (KdV) solitons in nuclear matter. The KdV equation is obtained from the Euler and continuity equations in nonrelativistic hydrodynamics. The existence of these solitons depends on the nuclear equation of state, which, in our approach, comes from well known relativistic mean field models. We reexamine early works on nuclear solitons, replacing the old equations of state by new ones, based on QHD and on its variants. Our analysis suggests that KdV solitons may indeed be formed in the nucleus with a width which, in some cases, can be smaller than one fermi.Comment: 15 pages, 1 figur

Enraizamento de corticeira-da-serra em função do tipo de estaca e variações sazonais

Erythrina falcata Benth. may be used as an ornamental plant, in rehabilitation of degraded land and as a component in agroforestry systems. However seedling production from seeds is difficult. The aim of this work was to evaluate vegetative propagation of E. falcata by using stem cuttings obtained from adult trees (softwood cuttings, hardwood cuttings and regrowth cuttings) and cuttings from seedlings collected in the four seasons of the year as well as the effect of indolebutyric acid on rooting of stem cuttings. After cutting preparation, the material was treated with an indolebutyric acid solution (IBA, 0, 1.5 and 3 g L-1). Cuttings were grown in 55-mL tapered plastic containers in a greenhouse at 25 to 30°C and relative humidity above 80%. The substrate for growing of cuttings was middle texture vermiculite. The highest percentage of rooted cuttings (73%) and root length of four longest roots (46 mm) and root number (6.2) were obtained in seedling cuttings collected in the summer. No rooting was observed in cuttings collected from softwood cuttings raised from adult trees. Cutting immersion in IBA solutions had no effect on rooting. Cuttings from seedlings collected in the summer are recommended because of their high percentage of rooting and survival