12,952 research outputs found
Ill-posedness in the Einstein equations
It is shown that the formulation of the Einstein equations widely in use in
numerical relativity, namely, the standard ADM form, as well as some of its
variations (including the most recent conformally-decomposed version), suffers
from a certain but standard type of ill-posedness. Specifically, the norm of
the solution is not bounded by the norm of the initial data irrespective of the
data. A long-running numerical experiment is performed as well, showing that
the type of ill-posedness observed may not be serious in specific practical
applications, as is known from many numerical simulations.Comment: 13 pages, 3 figures, accepted for publication in Journal of
Mathematical Physics (to appear August 2000
A Rich Example of Geometrically Induced Nonlinearity: From Rotobreathers and Kinks to Moving Localized Modes and Resonant Energy Transfer
We present an experimentally realizable, simple mechanical system with linear
interactions whose geometric nature leads to nontrivial, nonlinear dynamical
equations. The equations of motion are derived and their ground state
structures are analyzed. Selective ``static'' features of the model are
examined in the context of nonlinear waves including rotobreathers and
kink-like solitary waves. We also explore ``dynamic'' features of the model
concerning the resonant transfer of energy and the role of moving intrinsic
localized modes in the process
An SMLLC Conundrum: Disregarded for Federal Tax Purposes but Not in Federal Court
In Federal Court, the only member of a SMLLC may not represent the SMLLC unless that owner is also a lawyer. To do so exposes the SMLLC to dismissal as well as the owner to the unauthorized practice of law. The article explores the implications of these rules to small closely held LLCs
Cosmic Electromagnetic Fields due to Perturbations in the Gravitational Field
We use non-linear gauge-invariant perturbation theory to study the
interaction of an inflation produced seed magnetic field with density and
gravitational wave perturbations in an almost
Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetime. We compare the effects
of this coupling under the assumptions of poor conductivity, infinite
conductivity and the case where the electric field is sourced via the coupling
of velocity perturbations to the seed field in the ideal magnetohydrodynamic
(MHD) regime, thus generalizing, improving on and correcting previous results.
We solve our equations for long wavelength limits and numerically integrate the
resulting equations to generate power spectra for the electromagnetic field
variables, showing where the modes cross the horizon. We find that the rotation
of the electric field dominates the power spectrum on small scales, in
agreement with previous arguments.Comment: 16 pages, 3 figures, published in PR
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