367 research outputs found
Regular order reductions of ordinary and delay-differential equations
We present a C program to compute by successive approximations the regular
order reduction of a large class of ordinary differential equations, which
includes evolution equations in electrodynamics and gravitation. The code may
also find the regular order reduction of delay-differential equations.Comment: 4 figure
Order reductions of Lorentz-Dirac-like equations
We discuss the phenomenon of preacceleration in the light of a method of
successive approximations used to construct the physical order reduction of a
large class of singular equations. A simple but illustrative physical example
is analyzed to get more insight into the convergence properties of the method.Comment: 6 pages, LaTeX, IOP macros, no figure
General behaviour of Bianchi VI_0 solutions with an exponential-potential scalar field
The solutions to the Einstein-Klein-Gordon equations without a cosmological
constant are investigated for an exponential potential in a Bianchi VI_0
metric. There exists a two-parameter family of solutions which have a power-law
inflationary behaviour when the exponent of the potential, k, satisfies k^2<2.
In addition, there exists a two-parameter family of singular solutions for all
k^2 values. A simple anisotropic exact solution is found to be stable when
2<k^2.Comment: 10 pages, no figures. To be published in General Relativity and
Gravitatio
Exponential-Potential Scalar Field Universes I: The Bianchi I Models
We obtain a general exact solution of the Einstein field equations for the
anisotropic Bianchi type I universes filled with an exponential-potential
scalar field and study their dynamics. It is shown, in agreement with previous
studies, that for a wide range of initial conditions the late-time behaviour of
the models is that of a power-law inflating FRW universe. This property, does
not hold, in contrast, when some degree of inhomogeneity is introduced, as
discussed in our following paper II.Comment: 16 pages, Plain LaTeX, 1 Figure to be sent on request, to appear in
Phys. Rev.
On the Solutions of the Lorentz-Dirac Equation
We discuss the unstable character of the solutions of the Lorentz-Dirac
equation and stress the need of methods like order reduction to derive a
physically acceptable equation of motion. The discussion is illustrated with
the paradigmatic example of the non-relativistic harmonic oscillator with
radiation reaction. We also illustrate removal of the noncasual
pre-acceleration with the introduction of a small correction in the
Lorentz-Dirac equation.Comment: 4 eps figs. to be published in GR
Rigidity of cosmic acceleration in a class of k-essence cosmologies
We study the structural stability of a cosmic acceleration (inflation) in a
class of k-essence cosmologies against changes in the shape of the potential.
Those models may be viewed as generalized tachyon cosmologies and this analysis
extends previous results on the structural stability of cosmic acceleration in
tachyon cosmologies. The study considers both phantom and non-phantom cases.
The concepts of rigidity and fragility are defined through a condition on the
functional form of the Hubble factor. Given the known result of the existence
of inflationary (non-phantom) and super-inflationary (phantom) attractors we
formulate the question of their structural stability. We find that those
attractors are rigid in the sense that they never change as long as the
conditions for inflation or super-inflation are met.Comment: 10 page
Linear Momentum Density in Quasistatic Electromagnetic Systems
We discuss a couple of simple quasistatic electromagnetic systems in which
the density of electromagnetic linear momentum can be easily computed. The
examples are also used to illustrate how the total electromagnetic linear
momentum, which may also be calculated by using the vector potential, can be
understood as a consequence of the violation of the action-reaction principle,
because a non-null external force is required to maintain constant the
mechanical linear momentum. We show how one can avoid the divergence in the
interaction linear electromagnetic momentum of a system composed by an
idealization often used in textbooks (an infinite straight current) and a point
charge.Comment: 22 pages, 5 figures, to appear in Eur. J. Phy
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