2,928 research outputs found
Aubry transition studied by direct evaluation of the modulation functions of infinite incommensurate systems
Incommensurate structures can be described by the Frenkel Kontorova model.
Aubry has shown that, at a critical value K_c of the coupling of the harmonic
chain to an incommensurate periodic potential, the system displays the
analyticity breaking transition between a sliding and pinned state. The ground
state equations coincide with the standard map in non-linear dynamics, with
smooth or chaotic orbits below and above K_c respectively. For the standard
map, Greene and MacKay have calculated the value K_c=.971635. Conversely,
evaluations based on the analyticity breaking of the modulation function have
been performed for high commensurate approximants. Here we show how the
modulation function of the infinite system can be calculated without using
approximants but by Taylor expansions of increasing order. This approach leads
to a value K_c'=.97978, implying the existence of a golden invariant circle up
to K_c' > K_c.Comment: 7 pages, 5 figures, file 'epl.cls' necessary for compilation
provided; Revised version, accepted for publication in Europhysics Letter
Observable Properties of Orbits in Exact Bumpy Spacetimes
We explore the properties of test-particle orbits in "bumpy" spacetimes -
stationary, reflection-symmetric, asymptotically flat solutions of Einstein
equations that have a non-Kerr (anomalous) higher-order multipole-moment
structure but can be tuned arbitrarily close to the Kerr metric. Future
detectors should observe gravitational waves generated during inspirals of
compact objects into supermassive central bodies. If the central body deviates
from the Kerr metric, this will manifest itself in the emitted waves. Here, we
explore some of the features of orbits in non-Kerr spacetimes that might lead
to observable signatures. As a basis for this analysis, we use a family of
exact solutions proposed by Manko & Novikov which deviate from the Kerr metric
in the quadrupole and higher moments, but we also compare our results to other
work in the literature. We examine isolating integrals of the orbits and find
that the majority of geodesic orbits have an approximate fourth constant of the
motion (in addition to the energy, angular momentum and rest mass) and the
resulting orbits are tri-periodic to high precision. We also find that this
fourth integral can be lost for certain orbits in some oblately deformed
Manko-Novikov spacetimes. However, compact objects will probably not end up on
these chaotic orbits in nature. We compute the location of the innermost stable
circular orbit (ISCO) and find that the behavior of orbtis near the ISCO can be
qualitatively different depending on whether the ISCO is determined by the
onset of an instability in the radial or vertical direction. Finally, we
compute periapsis and orbital-plane precessions for nearly circular and nearly
equatorial orbits in both the strong and weak field, and discuss weak-field
precessions for eccentric equatorial orbits.Comment: 42 pages, 20 figures, accepted by Phys. Rev. D, v2 has minor changes
to make it consistent with published versio
The role of quantum fluctuations in the optomechanical properties of a Bose-Einstein condensate in a ring cavity
We analyze a detailed model of a Bose-Einstein condensate trapped in a ring
optical resonator and contrast its classical and quantum properties to those of
a Fabry-P{\'e}rot geometry. The inclusion of two counter-propagating light
fields and three matter field modes leads to important differences between the
two situations. Specifically, we identify an experimentally realizable region
where the system's behavior differs strongly from that of a BEC in a
Fabry-P\'{e}rot cavity, and also where quantum corrections become significant.
The classical dynamics are rich, and near bifurcation points in the mean-field
classical system, the quantum fluctuations have a major impact on the system's
dynamics.Comment: 11 pages, 11 figures, submitted to PR
Spacetime Encodings II - Pictures of Integrability
I visually explore the features of geodesic orbits in arbitrary stationary
axisymmetric vacuum (SAV) spacetimes that are constructed from a complex Ernst
potential. Some of the geometric features of integrable and chaotic orbits are
highlighted. The geodesic problem for these SAV spacetimes is rewritten as a
two degree of freedom problem and the connection between current ideas in
dynamical systems and the study of two manifolds sought. The relationship
between the Hamilton-Jacobi equations, canonical transformations, constants of
motion and Killing tensors are commented on. Wherever possible I illustrate the
concepts by means of examples from general relativity. This investigation is
designed to build the readers' intuition about how integrability arises, and to
summarize some of the known facts about two degree of freedom systems. Evidence
is given, in the form of orbit-crossing structure, that geodesics in SAV
spacetimes might admit, a fourth constant of motion that is quartic in momentum
(by contrast with Kerr spacetime, where Carter's fourth constant is quadratic).Comment: 11 pages, 10 figure
A new integrable generalization of the Korteweg - de Vries equation
A new integrable sixth-order nonlinear wave equation is discovered by means
of the Painleve analysis, which is equivalent to the Korteweg - de Vries
equation with a source. A Lax representation and a Backlund self-transformation
are found of the new equation, and its travelling wave solutions and
generalized symmetries are studied.Comment: 13 pages, 2 figure
The RANLUX generator: resonances in a random walk test
Using a recently proposed directed random walk test, we systematically
investigate the popular random number generator RANLUX developed by Luescher
and implemented by James. We confirm the good quality of this generator with
the recommended luxury level. At a smaller luxury level (for instance equal to
1) resonances are observed in the random walk test. We also find that the
lagged Fibonacci and Subtract-with-Carry recipes exhibit similar failures in
the random walk test. A revised analysis of the corresponding dynamical systems
leads to the observation of resonances in the eigenvalues of Jacobi matrix.Comment: 18 pages with 14 figures, Essential addings in the Abstract onl
Convection and AGN Feedback in Clusters of Galaxies
A number of studies have shown that the convective stability criterion for
the intracluster medium (ICM) is very different from the Schwarzchild criterion
due to the effects of anisotropic thermal conduction and cosmic rays. Building
on these studies, we develop a model of the ICM in which a central active
galactic nucleus (AGN) accretes hot intracluster plasma at the Bondi rate and
produces cosmic rays that cause the ICM to become convectively unstable. The
resulting convection heats the intracluster plasma and regulates its
temperature and density profiles. By adjusting a single parameter in the model
(the size of the cosmic-ray acceleration region), we are able to achieve a good
match to the observed density and temperature profiles in a sample of eight
clusters. Our results suggest that convection is an important process in
cluster cores. An interesting feature of our solutions is that the cooling rate
is more sharply peaked about the cluster center than is the convective heating
rate. As a result, in several of the clusters in our sample, a compact cooling
flow arises in the central region with a size R that is typically a few kpc.
The cooling flow matches onto a Bondi flow at smaller radii. The mass accretion
rate in the Bondi flow is equal to, and controlled by, the rate at which mass
flows in through the cooling flow. Our solutions suggest that the AGN regulates
the mass accretion rate in these clusters by controlling R: if the AGN power
rises above the equilibrium level, R decreases, the mass accretion rate drops,
and the AGN power drops back down to the equilibrium level.Comment: 41 pages, 7 figures, accepted for publication in ApJ. Changes in this
version: extended discussion of Bondi accretion in clusters, better mass
model, new numerical solution
Gravitational waves from intermediate-mass-ratio inspirals for ground-based detectors
We explore the prospects for Advanced LIGO to detect gravitational waves from
neutron stars and stellar mass black holes spiraling into intermediate-mass
( to ) black holes. We estimate an event rate
for such \emph{intermediate-mass-ratio inspirals} (IMRIs) of up to --. Our numerical simulations show that if the central
body is not a black hole but its metric is stationary, axisymmetric, reflection
symmetric and asymptotically flat then the waves will likely be tri-periodic,
as for a black hole. We report generalizations of a theorem due to Ryan (1995)
which suggest that the evolutions of the waves' three fundamental frequencies
and of the complex amplitudes of their spectral components encode (in
principle) a full map of the central body's metric, full details of the energy
and angular momentum exchange between the central body and the orbit, and the
time-evolving orbital elements. We estimate that Advanced LIGO can measure or
constrain deviations of the central body from a Kerr black hole with modest but
interesting accuracy.Comment: Accepted for publication in Physical Review Letter
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