20,608 research outputs found
The field inside a random distribution of parallel dipoles
We determine the probability distribution for the field inside a random
uniform distribution of electric or magnetic dipoles.
For parallel dipoles, simulations and an analytical derivation show that
although the average contribution from any spherical shell around the probe
position vanishes, the Levy stable distribution of the field is symmetric
around a non-vanishing field amplitude.
In addition we show how omission of contributions from a small volume around
the probe leads to a field distribution with a vanishing mean, which, in the
limit of vanishing excluded volume, converges to the shifted distribution.Comment: RevTeX, 4 pages, 3 figures. Submitted to Phys. Rev. Let
Timelike self-similar spherically symmetric perfect-fluid models
Einstein's field equations for timelike self-similar spherically symmetric
perfect-fluid models are investigated. The field equations are rewritten as a
first-order system of autonomous differential equations. Dimensionless
variables are chosen in such a way that the number of equations in the coupled
system is reduced as far as possible and so that the reduced phase space
becomes compact and regular. The system is subsequently analysed qualitatively
using the theory of dynamical systems.Comment: 23 pages, 6 eps-figure
The state space and physical interpretation of self-similar spherically symmetric perfect-fluid models
The purpose of this paper is to further investigate the solution space of
self-similar spherically symmetric perfect-fluid models and gain deeper
understanding of the physical aspects of these solutions. We achieve this by
combining the state space description of the homothetic approach with the use
of the physically interesting quantities arising in the comoving approach. We
focus on three types of models. First, we consider models that are natural
inhomogeneous generalizations of the Friedmann Universe; such models are
asymptotically Friedmann in their past and evolve fluctuations in the energy
density at later times. Second, we consider so-called quasi-static models. This
class includes models that undergo self-similar gravitational collapse and is
important for studying the formation of naked singularities. If naked
singularities do form, they have profound implications for the predictability
of general relativity as a theory. Third, we consider a new class of
asymptotically Minkowski self-similar spacetimes, emphasizing that some of them
are associated with the self-similar solutions associated with the critical
behaviour observed in recent gravitational collapse calculations.Comment: 24 pages, 12 figure
Spatially self-similar spherically symmetric perfect-fluid models
Einstein's field equations for spatially self-similar spherically symmetric
perfect-fluid models are investigated. The field equations are rewritten as a
first-order system of autonomous differential equations. Dimensionless
variables are chosen in such a way that the number of equations in the coupled
system is reduced as far as possible and so that the reduced phase space
becomes compact and regular. The system is subsequently analysed qualitatively
with the theory of dynamical systems.Comment: 21 pages, 6 eps-figure
U-duality covariant membranes
We outline a formulation of membrane dynamics in D=8 which is fully covariant
under the U-duality group SL(2,Z) x SL(3,Z), and encodes all interactions to
fields in the eight-dimensional supergravity, which is constructed through
Kaluza-Klein reduction on T^3. Among the membrane degrees of freedom is an
SL(2,R) doublet of world-volume 2-form potentials, whose quantised electric
fluxes determine the membrane charges, and are conjectured to provide an
interpretation of the variables occurring in the minimal representation of
E_{6(6)} which appears in the context of automorphic membranes. We solve the
relevant equations for the action for a restricted class of supergravity
backgrounds. Some comments are made on supersymmetry and lower dimensions.Comment: LaTeX, 21 pages. v2: Minor changes in text, correction of a sign. v3:
some changes in text, a sign convention changed; version to appear in JHE
Role of low- component in deformed wave functions near the continuum threshold
The structure of deformed single-particle wave functions in the vicinity of
zero energy limit is studied using a schematic model with a quadrupole deformed
finite square-well potential. For this purpose, we expand the single-particle
wave functions in multipoles and seek for the bound state and the Gamow
resonance solutions. We find that, for the states, where is
the -component of the orbital angular momentum, the probability of each
multipole components in the deformed wave function is connected between the
negative energy and the positive energy regions asymptotically, although it has
a discontinuity around the threshold. This implies that the
resonant level exists physically unless the component is inherently large
when extrapolated to the well bound region. The dependence of the multipole
components on deformation is also discussed
Light-cone analysis of ungauged and topologically gauged BLG theories
We consider three-dimensional maximally superconformal
Bagger-Lambert-Gustavsson (BLG) theory and its topologically gauged version
(constructed recently in arXiv:0809.4478 [hep-th]) in the light-cone gauge.
After eliminating the entire Chern-Simons gauge field, the ungauged BLG theory
looks more conventional and, apart from the order of the interaction terms,
resembles N=4 super-Yang-Mills theory in four dimensions. The light-cone
superspace version of the BLG theory is given to quadratic and quartic order
and some problems with constructing the sixth order interaction terms are
discussed. In the topologically gauged case, we analyze the field equations
related to the three Chern-Simons type terms of N=8 conformal supergravity and
discuss some of the special features of this theory and its couplings to BLG.Comment: 22 pages; v2 some typos correcte
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