Relativistic hydrodynamics for heavy-ion collisions

Relativistic hydrodynamics is essential to our current understanding of nucleus-nucleus collisions at ultrarelativistic energies (current experiments at the Relativistic Heavy Ion Collider, forthcoming experiments at the CERN Large Hadron Collider). This is an introduction to relativistic hydrodynamics for graduate students. It includes a detailed derivation of the equations, and a description of the hydrodynamical evolution of a heavy-ion collisions. Some knowledge of thermodynamics and special relativity is assumed.Comment: Lectures given at the Advanced School on Quark-Gluon Plasma, Indian Institute of Technology, Bombay, 3-13 July, 200

Remarks on the notion of quantum integrability

We discuss the notion of integrability in quantum mechanics. Starting from a review of some definitions commonly used in the literature, we propose a different set of criteria, leading to a classification of models in terms of different integrability classes. We end by highlighting some of the expected physical properties associated to models fulfilling the proposed criteria.Comment: 22 pages, no figures, Proceedings of Statphys 2

Distribution of roots of random real generalized polynomials

The average density of zeros for monic generalized polynomials, $P_n(z)=\phi(z)+\sum_{k=1}^nc_kf_k(z)$, with real holomorphic $\phi ,f_k$ and real Gaussian coefficients is expressed in terms of correlation functions of the values of the polynomial and its derivative. We obtain compact expressions for both the regular component (generated by the complex roots) and the singular one (real roots) of the average density of roots. The density of the regular component goes to zero in the vicinity of the real axis like $|\hbox{\rm Im}\,z|$. We present the low and high disorder asymptotic behaviors. Then we particularize to the large $n$ limit of the average density of complex roots of monic algebraic polynomials of the form $P_n(z) = z^n +\sum_{k=1}^{n}c_kz^{n-k}$ with real independent, identically distributed Gaussian coefficients having zero mean and dispersion $\delta = \frac 1{\sqrt{n\lambda}}$. The average density tends to a simple, {\em universal} function of $\xi={2n}{\log |z|}$ and $\lambda$ in the domain $\xi\coth \frac{\xi}{2}\ll n|\sin \arg (z)|$ where nearly all the roots are located for large $n$.Comment: 17 pages, Revtex. To appear in J. Stat. Phys. Uuencoded gz-compresed tarfile (.66MB) containing 8 Postscript figures is available by e-mail from [email protected]

On the screening of static electromagnetic fields in hot QED plasmas

We study the screening of static magnetic and electric fields in massless quantum electrodynamics (QED) and massless scalar electrodynamics (SQED) at temperature $T$. Various exact relations for the static polarisation tensor are first reviewed and then verified perturbatively to fifth order (in the coupling) in QED and fourth order in SQED, using different resummation techniques. The magnetic and electric screening masses squared, as defined through the pole of the static propagators, are also calculated to fifth order in QED and fourth order in SQED, and their gauge-independence and renormalisation-group invariance is checked. Finally, we provide arguments for the vanishing of the magnetic mass to all orders in perturbation theory.Comment: 37 pages, 8 figure

The Effect of Spirulina platensis versus Soybean on Insulin Resistance in HIV-Infected Patients: A Randomized Pilot Study

HIV-infected patients develop abnormalities of glucose metabolism due to the virus and antiretroviral drugs. Spirulina and soybean are nutritional supplements that are cheap, accessible in our community and affect glucose metabolism. We carried out a randomized study to assess the effect of Spirulina platensis versus soybean as a food supplement on HIV/HAART-associated insulin resistance (IR) in 33 insulin-resistant HIV-infected patients. The study lasted for two months at the National Obesity Centre of Cameroon. Insulin resistance was measured using the short insulin tolerance test. Physical activity and diet did not change over the study duration. On-treatment analysis was used to analyze data. The Mann-Whitney U test, the Students T test and the Chi square test were used as appropriate. Curve gradients were analyzed using ANCOVA. Seventeen subjects were randomized to spirulina and 16 to soybean. Each received 19 g of supplement daily. The follow up rate was 65% vs. 100% for spirulina and soybean groups, respectively, and both groups were comparable at baseline. After eight weeks, insulin sensitivity (IS) increased by 224.7% vs. 60% in the spirulina and soybean groups respectively (p < 0.001). One hundred per cent vs. 69% of subjects on spirulina versus soybean, respectively, improved their IS (p = 0.049) with a 1.45 (1.05–2.02) chance of improving insulin sensitivity on spirulina. This pilot study suggests that insulin sensitivity in HIV patients improves more when spirulina rather than soybean is used as a nutritional supplement. Trial registration: ClinicalTrials.gov identifier NCT01141777

Warm and Dense Molecular Gas in the N159 Region: 12CO J=4-3 and 13CO J=3-2 Observations with NANTEN2 and ASTE

New 12CO J=4-3 and 13CO J=3-2 observations of the N159 region in the Large Magellanic Cloud have been made. The 12CO J=4-3 distribution is separated into three clumps. These new measurements toward the three clumps are used in coupled calculations of molecular rotational excitation and line radiation transfer, along with other transitions of the 12CO as well as the isotope transitions of 13CO. The temperatures and densities are determined to be ~70-80K and ~3x10^3 cm-3 in N159W and N159E and ~30K and ~1.6x10^3 cm-3 in N159S. These results are compared with the star formation activity. The N159E clump is associated with embedded cluster(s) as observed at 24 micron and the derived high temperature is explained as due to the heating by these sources. The N159E clump is likely responsible for a dark lane in a large HII region by the dust extinction. The N159W clump is associated with embedded clusters mainly toward the eastern edge of the clump only. These clusters show offsets of 20"-40" from the 12CO J=4-3 peak and are probably responsible for heating indicated by the derived high temperature. The N159W clump exhibits no sign of star formation toward the 12CO J=4-3 peak position and its western region. We suggest that the N159W peak represents a pre-star-cluster core of ~105M_sol which deserves further detailed studies. Note that recent star formation took place between N159W and N159E as indicated by several star clusters and HII regions, while the natal molecular gas toward the stars have already been dissipated by the ionization and stellar winds of the OB stars. The N159S clump shows little sign of star formation as is consistent with the lower temperature and somewhat lower density. The N159S clump is also a candidate for future star formation

Topology of Chaotic Mixing Patterns

A stirring device consisting of a periodic motion of rods induces a mapping of the fluid domain to itself, which can be regarded as a homeomorphism of a punctured surface. Having the rods undergo a topologically-complex motion guarantees at least a minimum amount of stretching of material lines, which is important for chaotic mixing. We use topological considerations to describe the nature of the injection of unmixed material into a central mixing region, which takes place at injection cusps. A topological index formula allow us to predict the possible types of unstable foliations that can arise for a fixed number of rods.Comment: 15 pages, 13 figures, RevTeX4 macros. Final versio

TAB Bonded SSD Module for the STAR and ALICE Trackers

Presentation made at LEB99, 20-24 September 1999A novel compact detector module has been produced by the "IReS"-"Subatech"-"Thomson-CSF-Detexis" collaboration. It includes a Double-Sided (DS) Silicon Strip Detector (SSD) and the related Front End Electronics (FEE) located on two hybrids, one for the N side and one for the P side. Bumpless Tape Automated Bonding (TAB) is used to connect the detector to the hybrids by means of microcables with neither wirebonding nor pitch adapter. Each of the six dedicated ALICE128C FE chip [1], located on the hybrid, is TABed on identical single layer microcables, which connect its inputs to the DS SSD and its outputs to the hybrid [2]. These microcables are bent in order to fold over the two hybrids on the DS SSD. This module meets the specifications of two experiments, ALICE (A Large Ion Collider Experiment) on the LHC accelerator at CERN [3] and STAR (Solenoid Tracker At Rhic) on the RHIC accelerator at BNL (Brookhaven National Laboratory)[4]. It can be used with air cooling (STAR) as well as with water cooling (ALICE)[5]. This mechanically self-consistent FE module has been tested on the SPS beam at CERN. Preliminary results are presented