6,708 research outputs found
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
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