On the electrical current distributions for the generalized Ohm's Law

The paper studies a particular class of analytic solutions for the Generalized Ohm's Law, approached by means of the so called formal powers of the Pseudoanalytic Function Theory. The reader will find a description of the electrical current distributions inside bounded domains, within inhomogeneous media, and their corresponding electric potentials near the boundary. Finally, it is described a technique for approaching separable-variables conductivity functions, a requisite when applying the constructive methods posed in this work.Comment: 24 pages, 12 figure

A non-Abelian Black Ring

We construct a supersymmetric black ring solution of SU(2) N=1, d=5 Super-Einstein-Yang-Mills (SEYM) theory by adding a distorted BPST instanton to an Abelian black ring solution of the same theory. The change cannot be observed from spatial infinity: neither the mass, nor the angular momenta or the values of the scalars at infinity differ from those of the Abelian ring. The entropy is, however, sensitive to the presence of the non-Abelian instanton, and it is smaller than that of the Abelian ring, in analogy to what happens in the supersymmetric coloured black holes recently constructed in the same theory and in N=2, d=4 SEYM. By taking the limit in which the two angular momenta become equal we derive a non-Abelian generalization of the BMPV rotating black-hole solution.Comment: 19 pages, no figure

Stress-tensor OPE in N=2 Superconformal Theories

We carry out a detailed superspace analysis of the OPE of two N=2 stress-tensor multiplets. Knowledge of the multiplets appearing in the expansion, together with the two-dimensional chiral algebra description of N=2 SCFTs, imply an analytic bound on the central charge c. This bound is valid for any N=2 SCFT regardless of its matter content and flavor symmetries, and is saturated by the simplest Argyres-Douglas fixed point. We also present a partial conformal block analysis for the scalar superconformal primary of the multiplet.Comment: 29 page

One Thousand and One Bubbles

We propose a novel strategy that permits the construction of completely general five-dimensional microstate geometries on a Gibbons-Hawking space. Our scheme is based on two steps. First, we rewrite the bubble equations as a system of linear equations that can be easily solved. Second, we conjecture that the presence or absence of closed timelike curves in the solution can be detected through the evaluation of an algebraic relation. The construction we propose is systematic and covers the whole space of parameters, so it can be applied to find all five-dimensional BPS microstate geometries on a Gibbons-Hawking base. As a first result of this approach, we find that the spectrum of scaling solutions becomes much larger when non-Abelian fields are present. We use our method to describe several smooth horizonless multicenter solutions with the asymptotic charges of three-charge (Abelian and non-Abelian) black holes. In particular, we describe solutions with the centers lying on lines and circles that can be specified with exact precision. We show the power of our method by explicitly constructing a 50-center solution. Moreover, we use it to find the first smooth five-dimensional microstate geometries with arbitrarily small angular momentum.Comment: 33 pages. v2: typos correcte

Harvesting technology and catch-to-biomass dependence: The case of small pelagic fish

This note deals with a harvesting model for a single stock fishery. In the case of small pelagic fish it seems reasonable to consider harvest functions depending nonlinearly on fishing effort and on fish stock. Empirical evidence about these fish species suggests that marginal catch does not necessarily react in a linear way to changes in fishing effort and fish stock levels. This is in contradiction with traditional fishery models where catch-to-input marginal productivities are normally assumed to be constant. While allowing for non linearities in both catch-to-effort and catch-to-stock parameters, this note extends the traditional analysis by focusing on the dependence of the stationary solutions upon the nonlinear catch-to-biomass parameter. Given the emphasis on the case of small pelagic fish, the analysis considers positive but small values for the catch-to-stock parameter.small pelagic fisheries, harvesting functions, Cobb-Douglas production function, optimal control, maximum principle.

N=2 Einstein-Yang-Mills' static two-center solutions

We construct bona fide one- and two-center supersymmetric solutions to N=2, d=4 supergravity coupled to SU(2) non-Abelian vector multiplets. The solutions describe black holes and global monopoles alone or in equilibrium with each other and exhibit non-Abelian hairs of different kinds.Comment: 46 pages, 1 figure; v2 references adde