Inexactness of the Hydro-Thermal Coordination Semidefinite Relaxation

Hydro-thermal coordination is the problem of determining the optimal economic dispatch of hydro and thermal power plants over time. The physics of hydroelectricity generation is commonly simplified in the literature to account for its fundamentally nonlinear nature. Advances in convex relaxation theory have allowed the advent of Shor's semidefinite programming (SDP) relaxations of quadratic models of the problem. This paper shows how a recently published SDP relaxation is only exact if a very strict condition regarding turbine efficiency is observed, failing otherwise. It further proposes the use of a set of convex envelopes as a strategy to successfully obtain a stricter lower bound of the optimal solution. This strategy is combined with a standard iterative convex-concave procedure to recover a stationary point of the original non-convex problem.Comment: Submitted to IEEE PES General Meeting 201

Noncommutative Field Theory and the Dynamics of Quantum Hall Fluids

We study the spectrum of density fluctuations of Fractional Hall Fluids in the context of the noncommutative hidrodynamical model of Susskind. We show that, within the weak-field expansion, the leading correction to the noncommutative Chern--Simons Lagrangian (a Maxwell term in the effective action,) destroys the incompressibility of the Hall fluid due to strong UV/IR effects at one loop. We speculate on possible relations of this instability with the transition to the Wigner crystal, and conclude that calculations within the weak-field expansion must be carried out with an explicit ultraviolet cutoff at the noncommutativity scale. We point out that the noncommutative dipoles exactly match the spatial structure of the Halperin--Kallin quasiexcitons. Therefore, we propose that the noncommutative formalism must describe accurately the spectrum at very large momenta, provided no weak-field approximations are made. We further conjecture that the noncommutative open Wilson lines are `vertex operators' for the quasiexcitons.Comment: 20 pages, harvma

Klebanov-Witten theory with massive dynamical flavors

We consider the addition of a large number of massive dynamical flavors to the Klebanov-Witten theory, the quiver gauge theory describing the low energy dynamics of Nc D3-branes at the conifold singularity. Massive flavors are introduced by means of Nf D7-branes which are holomorphically embedded and smeared along the transverse directions. After some general comments on the validity of the smearing procedure, we find the full backreacted supergravity solution corresponding to a particular class of massive embeddings. The solution depends on a running effective number of flavors, whose functional form follows from the smeared embedding. The running reflects the integrating in/out of massive degrees of freedom in the dual field theory as the energy scale is changed. We study how the dynamics of the theory depends on the flavor parameters, mainly focusing on the static quark-antiquark potential. As expected, we find that the dynamical flavors tend to screen the static color charges.Comment: 31 pages, 8 figures; v2: few comments and a reference added, minor change

Non chiral dynamical flavors and screening on the conifold

We present a new class of string theory solutions which are conjectured to be dual to the N=1 conifold theory by Klebanov and Witten coupled to non chiral massive dynamical flavors. These are introduced, in the Veneziano limit, by means of suitably embedded and smeared D7-branes whose full backreaction on the background is taken into account. The string solutions are used to study chromoelectric charge screening effects due to the dynamical flavors in the non perturbative regime of the dual gauge theories.Comment: 6 pages, 1 figure, previously unpublished results presented. Contribution to the proceedings of the RTN workshop "Constituents, Fundamental Forces and Symmetries of the Universe", Varna, Bulgaria, September 11-17, 200

Holographic Flavored Quark-Gluon Plasmas

Holography provides a novel method to study the physics of Quark Gluon Plasmas, complementary to the ordinary field theory and lattice approaches. In this context, we analyze the informations that can be obtained for strongly coupled Plasmas containing dynamical flavors, also in the presence of a finite baryon chemical potential. In particular, we discuss the jet quenching and the hydrodynamic transport coefficients.Comment: 10 pages. Contribution to the proceedings of the workshop "The many faces of QCD", Ghent (Belgium), November 1-5 201

Nonthermal processes and neutrino emission from the black hole GRO J0422+32 in a bursting state

GRO J0422+32 is a member of the class of low-mass X-ray binaries (LMXBs). It was discovered during an outburst in 1992. During the entire episode a persistent power-law spectral component extending up to $\sim 1$ MeV was observed, which suggests that nonthermal processes should have occurred in the system. We study relativistic particle interactions and the neutrino production in the corona of GRO J0422+32, and explain the behavior of GRO J0422+32 during its recorded flaring phase. We have developed a magnetized corona model to fit the spectrum of GRO J0422+32 during the low-hard state. We also estimate neutrino emission and study the detectability of neutrinos with 1 km$^3$ detectors, such as IceCube. The short duration of the flares ($\sim$ hours) and an energy cutoff around a few TeV in the neutrino spectrum make neutrino detection difficult. There are, however, many factors that can enhance neutrino emission. The northern-sky coverage and full duty cycle of IceCube make it possible to detect neutrino bursts from objects of this kind through time-dependent analysis.Comment: 12 pages, 11 figures, accepted for publication in A&