192 research outputs found
Recursion Operators of Some Equations of Hydrodynamic Type
We give a general method for constructing recursion operators for some
equations of hydrodynamic type, admitting a nonstandard Lax representation. We
give several examples for N=2 and N=3 containing the equations of shallow water
waves and its generalizations with their first two higher symmetries and their
recursion operators. We also discuss a reduction of systems to
systems of some new equations of hydrodynamic type.Comment: Latex File (amssymb), 22 page
Exact static solutions in four dimensional Einstein-Maxwell-Dilaton gravity
Classes of exact static solutions in four-dimensional
Einstein-Maxwell-Dilaton gravity are found. Besides of the well-known solutions
previously found in the literature, new solutions are presented.It's shown that
spherically symmetric solutions, except the case of charged dilaton black hole,
represent globally naked strong curvature singularities.Comment: 8 pages, late
On the naming of innovation districts
Name plays a fundamental role in defining and differentiating a company within a category. In this paper we identify how the leaders of 7 innovation districts (22@Barcelona, Ann Arbor Spark, EECi, Porto Digital, Ruta N – Medellín, SK-Skolkovo and TusPark) understand the construction of the names of their innovation districts. We take an inductive approach utilizing two types of data: exploring the innovation district directors' understanding through direct semi-structured interviews and analyzing secondary data consisting of website and brochures. We show how innovation district leaders use more than one classification name for their organization and that these names either tend towards a more strategic or institutional posture. We contribute by extending existing naming theory to include innovation districts, a complex organization composed by actors of the Triple Helix. We also contribute by providing managerial guidance to assist in understanding the importance of the role of their organization's name in long-term positioning
Relativistic Compact Objects in Isotropic Coordinates
We present a matrix method for obtaining new classes of exact solutions for
Einstein's equations representing static perfect fluid spheres. By means of a
matrix transformation, we reduce Einstein's equations to two independent
Riccati type differential equations for which three classes of solutions are
obtained. One class of the solutions corresponding to the linear barotropic
type fluid with an equation of state is discussed in detail.Comment: 9 pages, no figures, accepted for publication in Pramana-Journal of
Physic
All stationary axi-symmetric local solutions of topologically massive gravity
We classify all stationary axi-symmetric solutions of topologically massive
gravity into Einstein, Schr\"odinger, warped and generic solutions. We
construct explicitly all local solutions in the first three sectors and present
an algorithm for the numerical construction of all local solutions in the
generic sector. The only input for this algorithm is the value of one constant
of motion if the solution has an analytic centre, and three constants of motion
otherwise. We present several examples, including soliton solutions that
asymptote to warped AdS.Comment: 42 pages, 9 figures. v2: Changed potentially confusing labelling of
one sector, added references. v3: Minor changes, matches published versio
Chiral models in dilaton-Maxwell gravity
We study symmetry properties of the Einstein-Maxwell theory nonminimaly
coupled to the dilaton field. We consider a static case with pure electric
(magnetic) Maxwell field and show that the resulting system becomes a nonlinear
sigma-model wich possesses a chiral representation. We construct the
corresponding chiral matrix and establish a representation which is related to
the pair of Ernst-like potentials. These potentials are used for separation of
the symmetry group into the gauge and nongauge (charging) sectors. New
variables, which linearize the action of charging symmetries, are also
established; a solution generation technique based on the use of charging
symmetries is formulated. This technique is used for generation of the
elecricaly (magneticaly) charged dilatonic fields from the static General
Relativity ones.Comment: 9 pages in LaTex; published in Gen. Rel. Grav. 32 (2000) pp 1389-139
Behaviour of Magnetic Tubes in Neutron Star's Interior
It is found from Maxwell's equations that the magnetic field lines are good
analogues of relativistic strings. It is shown that the super-conducting
current in the neutron star's interior causes local rotation of magnetic flux
tubes carrying quantized flux.Comment: 6 pages, no figure
Topologically Massive Gravity and Ricci-Cotton Flow
We consider Topologically Massive Gravity (TMG), which is three dimensional
general relativity with a cosmological constant and a gravitational
Chern-Simons term. When the cosmological constant is negative the theory has
two potential vacuum solutions: Anti-de Sitter space and Warped Anti-de Sitter
space. The theory also contains a massive graviton state which renders these
solutions unstable for certain values of the parameters and boundary
conditions. We study the decay of these solutions due to the condensation of
the massive graviton mode using Ricci-Cotton flow, which is the appropriate
generalization of Ricci flow to TMG. When the Chern-Simons coupling is small
the AdS solution flows to warped AdS by the condensation of the massive
graviton mode. When the coupling is large the situation is reversed, and warped
AdS flows to AdS. Minisuperspace models are constructed where these flows are
studied explicitly
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