Polarization and light curve variability: the "patchy shell" model

Recent advances in early detection and detailed monitoring of GRB afterglows have revealed variability in some afterglow light curves. One of the leading models for this behavior is the patchy shell model. This model attributes the variability to random angular fluctuations in the relativistic jet energy. These an-axisymmetric fluctuations should also impose variations in the degree and angle of polarization that are correlated to the light curve variability. In this letter we present a solution of the light curve and polarization resulting from a given spectrum of energy fluctuations. We compare light curves produced using this solution to the variable light curve of GRB 021004 and we show that the main features in both the light curve and the polarization fluctuations are very well reproduced by this model. We use our results to draw constraints on the characteristics of the energy fluctuations that might have been present in GRB 021004.Comment: 10 pages, 2 figures, Final version to appear in ApJ

The Pricing War Continues: On Competitive Multi-Item Pricing

We study a game with \emph{strategic} vendors who own multiple items and a single buyer with a submodular valuation function. The goal of the vendors is to maximize their revenue via pricing of the items, given that the buyer will buy the set of items that maximizes his net payoff. We show this game may not always have a pure Nash equilibrium, in contrast to previous results for the special case where each vendor owns a single item. We do so by relating our game to an intermediate, discrete game in which the vendors only choose the available items, and their prices are set exogenously afterwards. We further make use of the intermediate game to provide tight bounds on the price of anarchy for the subset games that have pure Nash equilibria; we find that the optimal PoA reached in the previous special cases does not hold, but only a logarithmic one. Finally, we show that for a special case of submodular functions, efficient pure Nash equilibria always exist

Lack of static lattice distortion in Tb2Ti2O7Tb_2 Ti_2 O_7

We investigated the possibility of temperature dependent lattice distortions in the pyrochlore compound Tb$_{2}$Ti$_{2}$O$_{7}$ by measuring the internal magnetic field distribution, using muon spin resonance, and comparing it to the susceptibility. The measurements are done at temperatures as low as 70 mK and external fields up to 6 kG. We find that the evolution of the width of the field distribution can be explained by spin susceptibility only, thus ruling out a temperature dependent hyperfine coupling. We conclude that lattice deformations are absent in Tb$_{2}$Ti$_{2}$O$_{7}$.Comment: 8 pages, 5 figures, accepted for publication in J. Phys. Condens. Matter. (Proceedings of Highly Frustrated Magnetism 2006); Corrections of various typo