135,059 research outputs found
Dynamical Instability of Shear-free Collapsing Star in Extended Teleparallel Gravity
We study the spherically symmetric collapsing star in terms of dynamical
instability. We take the framework of extended teleparallel gravity with
non-diagonal tetrad, power-law form of model presenting torsion and matter
distribution as non-dissipative anisotropic fluid. The vanishing shear scalar
condition is adopted to search the insights of collapsing star. We apply first
order linear perturbation scheme to metric, matter and functions. The
dynamical equations are formulated under this perturbation scheme to develop
collapsing equation for finding dynamical instability limits in two regimes
such as Newtonian and post-Newtonian. We obtain constraint free solution of
perturbed time dependent part with the help of vanishing shear scalar. The
adiabatic index exhibits the instability ranges through second dynamical
equation which depend on physical quantities such as density, pressure
components, perturbed parts of symmetry of star, etc. We also develop some
constraints on positivity of these quantities and obtain instability ranges to
satisfy the dynamical instability condition.Comment: 21 pages; Accepted in EPJC for publicatio
Subexponential instability implies infinite invariant measure
We study subexponential instability to characterize a dynamical instability
of weak chaos. We show that a dynamical system with subexponential instability
has an infinite invariant measure, and then we present the generalized Lyapunov
exponent to characterize subexponential instability.Comment: 7 pages, 5 figure
Unstable regimes for a Bose-Einstein condensate in an optical lattice
We report on the experimental characterization of energetic and dynamical
instability, two mechanisms responsible for the breakdown of Bloch waves in a
Bose-Einstein condensate interacting with a 1D optical lattice. A clear
separation of these two regimes is obtained performing measurements at
different temperatures of the atomic sample. The timescales of the two
processes have been determined by measuring the losses induced in the
condensate. A simple phenomenological model is introduced for energetic
instability while a full comparison is made between the experiment and the 3D
Gross-Pitaevskii theory that accounts for dynamical instability
Nonlinear parametric instability in double-well lattices
A possibility of a nonlinear resonant instability of uniform oscillations in
dynamical lattices with harmonic intersite coupling and onsite nonlinearity is
predicted. Numerical simulations of a lattice with a double-well onsite
anharmonic potential confirm the existence of the nonlinear instability with an
anomalous value of the corresponding power index, 1.57, which is intermediate
between the values 1 and 2 characterizing the linear and nonlinear (quadratic)
instabilities. The anomalous power index may be a result of competition between
the resonant quadratic instability and nonresonant linear instabilities. The
observed instability triggers transition of the lattice into a chaotic
dynamical state.Comment: A latex text file and three pdf files with figures. Physical Review
E, in pres
Rotational Instabilities and Centrifugal Hangup
One interesting class of gravitational radiation sources includes rapidly
rotating astrophysical objects that encounter dynamical instabilities. We have
carried out a set of simulations of rotationally induced instabilities in
differentially rotating polytropes. An =1.5 polytrope with the Maclaurin
rotation law will encounter the =2 bar instability at .
Our results indicate that the remnant of this instability is a persistent
bar-like structure that emits a long-lived gravitational radiation signal.
Furthermore, dynamical instability is shown to occur in =3.33 polytropes
with the -constant rotation law at . In this case, the
dominant mode of instability is =1. Such instability may allow a
centrifugally-hung core to begin collapsing to neutron star densities on a
dynamical timescale. If it occurs in a supermassive star, it may produce
gravitational radiation detectable by LISA.Comment: 13 pages (includes 11 figures) and 1 separate jpeg figure; to appear
in Astrophysical Sources of Gravitational Radiation, AIP conference
proceedings, edited by Joan M. Centrell
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