166 research outputs found

### Shaped superconductor cylinder retains intense magnetic field

The curve of the inner walls of a superconducting cylinder is plotted from the flux lines of the magnetic field to be contained. This shaping reduces maximum flux densities and permits a stronger and more uniform magnetic field

### Rigid motions in Einstein spaces

Rigid motion in Einstein space-time using dyadic formulation of general relativit

### On Waylen's regular axisymmetric similarity solutions

We review the similarity solutions proposed by Waylen for a regular
time-dependent axisymmetric vacuum space-time, and show that the key equation
introduced to solve the invariant surface conditions is related by a Baecklund
transform to a restriction on the similarity variables. We further show that
the vacuum space-times produced via this path automatically possess a (possibly
homothetic) Killing vector, which may be time-like.Comment: 8 pages, LaTeX2

### Bosonic Super Liouville System: Lax Pair and Solution

We study the bosonic super Liouville system which is a statistical
transmutation of super Liouville system. Lax pair for the bosonic super
Liouville system is constructed using prolongation method, ensuring the Lax
integrability, and the solution to the equations of motion is also considered
via Leznov-Saveliev analysis.Comment: LaTeX, no figures, 11 page

### Properties of equations of the continuous Toda type

We study a modified version of an equation of the continuous Toda type in 1+1
dimensions. This equation contains a friction-like term which can be switched
off by annihilating a free parameter \ep. We apply the prolongation method,
the symmetry and the approximate symmetry approach. This strategy allows us to
get insight into both the equations for \ep =0 and \ep \ne 0, whose
properties arising in the above frameworks are mutually compared. For \ep =0,
the related prolongation equations are solved by means of certain series
expansions which lead to an infinite- dimensional Lie algebra. Furthermore,
using a realization of the Lie algebra of the Euclidean group $E_{2}$, a
connection is shown between the continuous Toda equation and a linear wave
equation which resembles a special case of a three-dimensional wave equation
that occurs in a generalized Gibbons-Hawking ansatz \cite{lebrun}. Nontrivial
solutions to the wave equation expressed in terms of Bessel functions are
determined.
For \ep\,\ne\,0, we obtain a finite-dimensional Lie algebra with four
elements. A matrix representation of this algebra yields solutions of the
modified continuous Toda equation associated with a reduced form of a
perturbative Liouville equation. This result coincides with that achieved in
the context of the approximate symmetry approach. Example of exact solutions
are also provided. In particular, the inverse of the exponential-integral
function turns out to be defined by the reduced differential equation coming
from a linear combination of the time and space translations. Finally, a Lie
algebra characterizing the approximate symmetries is discussed.Comment: LaTex file, 27 page

### Axistationary perfect fluids -- a tetrad approach

Stationary axisymmetric perfect fluid space-times are investigated using the
curvature description of geometries. Attention is focused on space-times with a
vanishing electric part of the Weyl tensor. It is shown that the only
incompressible axistationary magnetic perfect fluid is the interior
Schwarzschild solution. The existence of a rigidly rotating perfect fluid,
generalizing the interior Schwarzschild metric is proven. Theorems are stated
on Petrov types and electric/magnetic Weyl tensors.Comment: 12 page

### Phasing of gravitational waves from inspiralling eccentric binaries

We provide a method for analytically constructing high-accuracy templates for
the gravitational wave signals emitted by compact binaries moving in
inspiralling eccentric orbits. By contrast to the simpler problem of modeling
the gravitational wave signals emitted by inspiralling {\it circular} orbits,
which contain only two different time scales, namely those associated with the
orbital motion and the radiation reaction, the case of {\it inspiralling
eccentric} orbits involves {\it three different time scales}: orbital period,
periastron precession and radiation-reaction time scales. By using an improved
`method of variation of constants', we show how to combine these three time
scales, without making the usual approximation of treating the radiative time
scale as an adiabatic process. We explicitly implement our method at the 2.5PN
post-Newtonian accuracy. Our final results can be viewed as computing new
`post-adiabatic' short period contributions to the orbital phasing, or
equivalently, new short-period contributions to the gravitational wave
polarizations, $h_{+,\times}$, that should be explicitly added to the
`post-Newtonian' expansion for $h_{+,\times}$, if one treats radiative effects
on the orbital phasing of the latter in the usual adiabatic approximation. Our
results should be of importance both for the LIGO/VIRGO/GEO network of ground
based interferometric gravitational wave detectors (especially if Kozai
oscillations turn out to be significant in globular cluster triplets), and for
the future space-based interferometer LISA.Comment: 49 pages, 6 figures, high quality figures upon reques

### Slowly, rotating non-stationary, fluid solutions of Einstein's equations and their match to Kerr empty space-time

A general class of solutions of Einstein's equation for a slowly rotating
fluid source, with supporting internal pressure, is matched using Lichnerowicz
junction conditions, to the Kerr metric up to and including first order terms
in angular speed parameter. It is shown that the match applies to any
previously known non-rotating fluid source made to rotate slowly for which a
zero pressure boundary surface exists. The method is applied to the dust source
of Robertson-Walker and in outline to an interior solution due to McVittie
describing gravitational collapse. The applicability of the method to
additional examples is transparent. The differential angular velocity of the
rotating systems is determined and the induced rotation of local inertial frame
is exhibited

### Zero curvature representation for a new fifth-order integrable system

In this brief note we present a zero-curvature representation for one of the
new integrable system found by Mikhailov, Novikov and Wang in nlin.SI/0601046.Comment: 2 pages, LaTeX 2e, no figure

### Solution generating with perfect fluids

We apply a technique, due to Stephani, for generating solutions of the
Einstein-perfect fluid equations. This technique is similar to the vacuum
solution generating techniques of Ehlers, Harrison, Geroch and others. We start
with a ``seed'' solution of the Einstein-perfect fluid equations with a Killing
vector. The seed solution must either have (i) a spacelike Killing vector and
equation of state P=rho or (ii) a timelike Killing vector and equation of state
rho+3P=0. The new solution generated by this technique then has the same
Killing vector and the same equation of state. We choose several simple seed
solutions with these equations of state and where the Killing vector has no
twist. The new solutions are twisting versions of the seed solutions

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