Drag reduction by polymer additives from turbulent spectra

We extend the analysis of the friction factor for turbulent pipe flow reported by G. Gioia, P. Chakraborty and N. Goldenfeld (GCG) (G. Gioia and P. Chakraborty, Phys. Rev. Lett. 96, 044502 (2006), N. Goldenfeld, Phys. Rev. Lett. 96, 044503 (2006)) to the case where drag is reduced by polymer additives.Comment: 19 pages, major changes, accepted for publication in Phys. Rev.

A hydrodynamic approach to boost invariant free streaming

We consider a family of exact boost invariant solutions of the transport equation for free streaming massless particles, where the one particle distribution function is defined in terms of a function of a single variable. The evolution of second and third moments of the one particle distribution function (the second moment being the energy momentum tensor (EMT) and the third moment the non equilibrium current (NEC)) depends only on two moments of that function. Given those two moments we show how to build a non linear hydrodynamic theory which reproduces the early time evolution of the EMT and the NEC. The structure of these theories may give insight on nonlinear hydrodynamic phenomena on short time scales.Comment: 20 pages, 8 figures. Accepted for publication in Phys. Rev.

Analog cosmology with spinor BECs

We show that the properties of spinor Bose-Einstein condensates allow us to build an analog Taub (axisymmetric Bianchi IX) Universe. We shall develop this proposal on the example of a rubidium condensate, where the relevant experiments are well within present day capabilities. A better Taub analog however would be built out of a collective Rydberg excitation.Comment: Talk given at the "II Amazonian Symposium on Physics - Analogue Models of Gravity 30 Years Celebration

Primordial Magnetic Helicity from Stochastic Electric Currents

We study the possibility that primordial magnetic fields generated in the transition between inflation and reheating posses magnetic helicity, $H_M$. The fields are induced by stochastic currents of scalar charged particles created during the mentioned transition. We estimate the rms value of the induced magnetic helicity by computing different four-point SQED Feynman diagrams. For any considered volume, the magnetic flux across its boundaries is in principle non null, which means that the magnetic helicity in those regions is gauge dependent. We use the prescription given by Berger and Field and interpret our result as the difference between two magnetic configurations that coincide in the exterior volume. In this case the magnetic helicity gives only the number of magnetic links inside the considered volume. We calculate a concrete value of $H_M$ for large scales and analyze the distribution of magnetic defects as a function of the scale. Those defects correspond to regular as well as random fields in the considered volume. We find that the fractal dimension of the distribution of topological defects is $D = 1/2$. We also study if the regular fields induced on large scales are helical, finding that they are and that the associated number of magnetic defects is independent of the scale. In this case the fractal dimension is $D=0$. We finally estimate the intensity of fields induced at the horizon scale of reheating, and evolve them until the decoupling of matter and radiation under the hypothesis of inverse cascade of magnetic helicity. The resulting intensity is high enough and the coherence length long enough to have an impact on the subsequent process of structure formation.Comment: 32 pages, 4 figure

Non abelian hydrodynamics and heavy ion collisions

The goal of the relativistic heavy ion collisions (RHIC) program is to create a state of matter where color degrees of freedom are deconfined. The dynamics of matter in this state, in spite of the complexities of quantum chromodynamics, is largely determined by the conservation laws of energy momentum and color currents. Therefore it is possible to describe its main features in hydrodynamic terms, the very short color neutralization time notwithstanding. In this lecture we shall give a simple derivation of the hydrodynamics of a color charged fluid, by generalizing the usual derivation of hydrodynamics from kinetic theory to the non abelian case.Comment: Talk given at the 5th Leopoldo Garc\'ia-Col\'in Mexican Meeting on Mathematical and Experimental Physics, Mexico City, September 9 - 13, 201