1,723 research outputs found
Gravitational Waves from The Newtonian plus H\'enon-Heiles System
In this work we analyze the emission of gravitational waves from a
gravitational system described by a Newtonian term plus a H\'enon-Heiles term.
The main concern is to analyze how the inclusion of the Newtonian term changes
the emission of gravitational waves, considering its emission in the chaotic
and regular regime.Comment: 10 pages, RevTex, three PS figures, to be published in Phys.Lett.
Probing an nonequilibrium Einstein relation in an aging colloidal glass
We present a direct experimental measurement of an effective temperature in a
colloidal glass of Laponite, using a micrometric bead as a thermometer. The
nonequilibrium fluctuation-dissipation relation, in the particular form of a
modified Einstein relation, is investigated with diffusion and mobility
measurements of the bead embedded in the glass. We observe an unusual
non-monotonic behavior of the effective temperature : starting from the bath
temperature, it is found to increase up to a maximum value, and then decreases
back, as the system ages. We show that the observed deviation from the Einstein
relation is related to the relaxation times previously measured in dynamic
light scattering experiments.Comment: 4 pages, 4 figures, corrected references, published in Phys. Rev.
Lette
PT-Scotch: A tool for efficient parallel graph ordering
The parallel ordering of large graphs is a difficult problem, because on the
one hand minimum degree algorithms do not parallelize well, and on the other
hand the obtainment of high quality orderings with the nested dissection
algorithm requires efficient graph bipartitioning heuristics, the best
sequential implementations of which are also hard to parallelize. This paper
presents a set of algorithms, implemented in the PT-Scotch software package,
which allows one to order large graphs in parallel, yielding orderings the
quality of which is only slightly worse than the one of state-of-the-art
sequential algorithms. Our implementation uses the classical nested dissection
approach but relies on several novel features to solve the parallel graph
bipartitioning problem. Thanks to these improvements, PT-Scotch produces
consistently better orderings than ParMeTiS on large numbers of processors
Quadratic Volume-Preserving Maps: Invariant Circles and Bifurcations
We study the dynamics of the five-parameter quadratic family of
volume-preserving diffeomorphisms of R^3. This family is the unfolded normal
form for a bifurcation of a fixed point with a triple-one multiplier and also
is the general form of a quadratic three-dimensional map with a quadratic
inverse. Much of the nontrivial dynamics of this map occurs when its two fixed
points are saddle-foci with intersecting two-dimensional stable and unstable
manifolds that bound a spherical ``vortex-bubble''. We show that this occurs
near a saddle-center-Neimark-Sacker (SCNS) bifurcation that also creates, at
least in its normal form, an elliptic invariant circle. We develop a simple
algorithm to accurately compute these elliptic invariant circles and their
longitudinal and transverse rotation numbers and use it to study their
bifurcations, classifying them by the resonances between the rotation numbers.
In particular, rational values of the longitudinal rotation number are shown to
give rise to a string of pearls that creates multiple copies of the original
spherical structure for an iterate of the map.Comment: 53 pages, 29 figure
Escape of stars from gravitational clusters in the Chandrasekhar model
We study the evaporation of stars from globular clusters using the simplified
Chandrasekhar model. This is an analytically tractable model giving reasonable
agreement with more sophisticated models that require complicated numerical
integrations. In the Chandrasekhar model: (i) the stellar system is assumed to
be infinite and homogeneous (ii) the evolution of the velocity distribution of
stars f(v,t) is governed by a Fokker-Planck equation, the so-called
Kramers-Chandrasekhar equation (iii) the velocities |v| that are above a
threshold value R>0 (escape velocity) are not counted in the statistical
distribution of the system. In fact, high velocity stars leave the system, due
to free evaporation or to the attraction of a neighboring galaxy (tidal
effects). Accordingly, the total mass and energy of the system decrease in
time. If the star dynamics is described by the Kramers-Chandrasekhar equation,
the mass decreases to zero exponentially rapidly. Our goal is to obtain
non-perturbative analytical results that complement the seminal studies of
Chandrasekhar, Michie and King valid for large times and large
escape velocities . In particular, we obtain an exact
semi-explicit solution of the Kramers-Chandrasekhar equation with the absorbing
boundary condition f(R,t)=0. We use it to obtain an explicit expression of the
mass loss at any time t when . We also derive an exact integral
equation giving the exponential evaporation rate , and the
corresponding eigenfunction , when for any
sufficiently large value of the escape velocity R. For , we
obtain an explicit expression of the evaporation rate that refines the
Chandrasekhar results
Stability of Distant Satellites of Giant Planets in the Solar System
We conduct a systematic survey of the regions in which distant satellites can
orbit stably around the four giant planets in the solar system, using orbital
integrations of up to yr. In contrast to previous investigations, we use
a grid of initial conditions on a surface of section to explore phase space
uniformly inside and outside the planet's Hill sphere (radius ;
satellites outside the Hill sphere sometimes are also known as
quasi-satellites). Our confirmations and extensions of old results and new
findings include the following: (i) many prograde and retrograde satellites can
survive out to radii and , respectively,
while some coplanar retrograde satellites of Jupiter and Neptune can survive
out to ; (ii) stable orbits do not exist within the Hill sphere
at high ecliptic inclinations when the semi-major axis is large enough that the
solar tide is the dominant non-Keplerian perturbation; (iii) there is a gap
between and in which no stable orbits exist; (iv)
at distances stable satellite orbits exist around Jupiter,
Uranus and Neptune (but not Saturn). For Uranus and Neptune, in particular,
stable orbits are found at distances as large as ; (v) the
differences in the stable zones beyond the Hill sphere arise mainly from
differences in the planet/Sun mass ratio and perturbations from other planets;
in particular, the absence of stable satellites around Saturn is mainly due to
perturbations from Jupiter. It is therefore likely that satellites at distances
could survive for the lifetime of the solar system around
Uranus, Neptune, and perhaps Jupiter.Comment: AJ in press; updated discussion and reference
Orbits in the H2O molecule
We study the forms of the orbits in a symmetric configuration of a realistic
model of the H2O molecule with particular emphasis on the periodic orbits. We
use an appropriate Poincar\'e surface of section (PSS) and study the
distribution of the orbits on this PSS for various energies. We find both
ordered and chaotic orbits. The proportion of ordered orbits is almost 100% for
small energies, but decreases abruptly beyond a critical energy. When the
energy exceeds the escape energy there are still non-escaping orbits around
stable periodic orbits. We study in detail the forms of the various periodic
orbits, and their connections, by providing appropriate stability and
bifurcation diagrams.Comment: 21 pages, 14 figures, accepted for publication in CHAO
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