13,680 research outputs found
A Corollary for Nonsmooth Systems
In this note, two generalized corollaries to the LaSalle-Yoshizawa Theorem
are presented for nonautonomous systems described by nonlinear differential
equations with discontinuous right-hand sides. Lyapunov-based analysis methods
are developed using differential inclusions to achieve asymptotic convergence
when the candidate Lyapunov derivative is upper bounded by a negative
semi-definite function
Swimming in curved space or The Baron and the cat
We study the swimming of non-relativistic deformable bodies in (empty) static
curved spaces. We focus on the case where the ambient geometry allows for rigid
body motions. In this case the swimming equations turn out to be geometric. For
a small swimmer, the swimming distance in one stroke is determined by the
Riemann curvature times certain moments of the swimmer.Comment: 19 pages 6 figure
Effect of cryogenic irradiation on NERVA structural alloys
Several alloys (Hastelloy X, AISI 347, A-286 bolts, Inconel 718, Al 7039-T63 and Ti-5Al-2.5Sn ELI) were irradiated in liquid nitrogen (140 R) to neutron fluences between 10 to the 17th power and 10 to the 19th power nvt (E greater than 1.0 Mev). After irradiation, tensile properties were obtained in liquid nitrogen without permitting any warmup except for some specimens which were annealed at 540 R. The usual trend of radiation damage typical for materials irradiated at and above room temperature was observed, such as an increase in strength and decrease in ductility. However, the damage at 140 R was greater because this temperature prevented the annealing of radiation-induced defects which occurs above 140 R
The Dynamics of a Classical Spinning Particle in Vaidya Space-Time
Based on the Mathisson-Papapetrou-Dixon (MPD) equations and the Vaidya
metric, the motion of a spinning point particle orbiting a non-rotating star
while undergoing radiation-induced gravitational collapse is studied in detail.
A comprehensive analysis of the orbital dynamics is performed assuming distinct
central mass functions which satisfy the weak energy condition, in order to
determine a correspondence between the choice of mass function and the spinning
particle's orbital response, as reflected in the gravitational waves emitted by
the particle. The analysis presented here is likely most beneficial for the
observation of rotating solar mass black holes or neutron stars in orbit around
intermediate-sized Schwarzschild black holes undergoing radiation collapse. The
possibility of detecting the effects of realistic mass accretion based on this
approach is considered. While it seems unlikely to observe such effects based
on present technology, they may perhaps become observable with the advent of
future detectors.Comment: REVTeX file, 20 pages, 26 figure
Spinning test particles and clock effect in Schwarzschild spacetime
We study the behaviour of spinning test particles in the Schwarzschild
spacetime. Using Mathisson-Papapetrou equations of motion we confine our
attention to spatially circular orbits and search for observable effects which
could eventually discriminate among the standard supplementary conditions
namely the Corinaldesi-Papapetrou, Pirani and Tulczyjew. We find that if the
world line chosen for the multipole reduction and whose unit tangent we denote
as is a circular orbit then also the generalized momentum of the
spinning test particle is tangent to a circular orbit even though and
are not parallel four-vectors. These orbits are shown to exist because the spin
induced tidal forces provide the required acceleration no matter what
supplementary condition we select. Of course, in the limit of a small spin the
particle's orbit is close of being a circular geodesic and the (small)
deviation of the angular velocities from the geodesic values can be of an
arbitrary sign, corresponding to the possible spin-up and spin-down alignment
to the z-axis. When two spinning particles orbit around a gravitating source in
opposite directions, they make one loop with respect to a given static observer
with different arrival times. This difference is termed clock effect. We find
that a nonzero gravitomagnetic clock effect appears for oppositely orbiting
both spin-up or spin-down particles even in the Schwarzschild spacetime. This
allows us to establish a formal analogy with the case of (spin-less) geodesics
on the equatorial plane of the Kerr spacetime. This result can be verified
experimentally.Comment: IOP macros, eps figures n. 2, to appear on Classical and Quantum
gravity, 200
Innermost Stable Circular Orbit of a Spinning Particle in Kerr Spacetime
We study stability of a circular orbit of a spinning test particle in a Kerr
spacetime. We find that some of the circular orbits become unstable in the
direction perpendicular to the equatorial plane, although the orbits are still
stable in the radial direction. Then for the large spin case ($S < \sim O(1)),
the innermost stable circular orbit (ISCO) appears before the minimum of the
effective potential in the equatorial plane disappears. This changes the radius
of ISCO and then the frequency of the last circular orbit.Comment: 25 pages including 8 figure
Tail-induced spin-orbit effect in the gravitational radiation of compact binaries
Gravitational waves contain tail effects which are due to the back-scattering
of linear waves in the curved space-time geometry around the source. In this
paper we improve the knowledge and accuracy of the two-body inspiraling
post-Newtonian (PN) dynamics and gravitational-wave signal by computing the
spin-orbit terms induced by tail effects. Notably, we derive those terms at 3PN
order in the gravitational-wave energy flux, and 2.5PN and 3PN orders in the
wave polarizations. This is then used to derive the spin-orbit tail effects in
the phasing through 3PN order. Our results can be employed to carry out more
accurate comparisons with numerical-relativity simulations and to improve the
accuracy of analytical templates aimed at describing the whole process of
inspiral, merger and ringdown.Comment: Minor corrections. To be published in Physical Review
Self-forces on extended bodies in electrodynamics
In this paper, we study the bulk motion of a classical extended charge in
flat spacetime. A formalism developed by W. G. Dixon is used to determine how
the details of such a particle's internal structure influence its equations of
motion. We place essentially no restrictions (other than boundedness) on the
shape of the charge, and allow for inhomogeneity, internal currents,
elasticity, and spin. Even if the angular momentum remains small, many such
systems are found to be affected by large self-interaction effects beyond the
standard Lorentz-Dirac force. These are particularly significant if the
particle's charge density fails to be much greater than its 3-current density
(or vice versa) in the center-of-mass frame. Additional terms also arise in the
equations of motion if the dipole moment is too large, and when the
`center-of-electromagnetic mass' is far from the `center-of-bare mass' (roughly
speaking). These conditions are often quite restrictive. General equations of
motion were also derived under the assumption that the particle can only
interact with the radiative component of its self-field. These are much simpler
than the equations derived using the full retarded self-field; as are the
conditions required to recover the Lorentz-Dirac equation.Comment: 30 pages; significantly improved presentation; accepted for
publication in Phys. Rev.
Dynamics of test bodies with spin in de Sitter spacetime
We study the motion of spinning test bodies in the de Sitter spacetime of
constant positive curvature. With the help of the 10 Killing vectors, we derive
the 4-momentum and the tensor of spin explicitly in terms of the spacetime
coordinates. However, in order to find the actual trajectories, one needs to
impose the so-called supplementary condition. We discuss the dynamics of
spinning test bodies for the cases of the Frenkel and Tulczyjew conditions.Comment: 11 pages, RevTex forma
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