13,726 research outputs found
Stability Limits in Resonant Planetary Systems
The relationship between the boundaries for Hill and Lagrange stability in
orbital element space is modified in the case of resonantly interacting
planets. Hill stability requires the ordering of the planets to remain constant
while Lagrange stability also requires all planets to remain bound to the
central star. The Hill stability boundary is defined analytically, but no
equations exist to define the Lagrange boundary, so we perform numerical
experiments to estimate the location of this boundary. To explore the effect of
resonances, we consider orbital element space near the conditions in the HD
82943 and 55 Cnc systems. Previous studies have shown that, for non-resonant
systems, the two stability boundaries are nearly coincident. However the Hill
stability formula are not applicable to resonant systems, and our investigation
shows how the two boundaries diverge in the presence of a mean-motion
resonance, while confirming that the Hill and Lagrange boundaries are similar
otherwise. In resonance the region of stability is larger than the domain
defined by the analytic formula for Hill stability. We find that nearly all
known resonant interactions currently lie in this extra stable region, i.e.
where the orbits would be unstable according to the non-resonant Hill stability
formula. This result bears on the dynamical packing of planetary systems,
showing how quantifying planetary systems' dynamical interactions (such as
proximity to the Hill-stability boundary) provides new constraints on planet
formation models.Comment: 13 pages, 3 figures, 2 tables, accepted for publication in ApJ
Letters. A version with full resolution figures is available at
http://www.lpl.arizona.edu/~rory/research/xsp/resstab.pd
A Supersymmetric Composite Model of Quarks and Leptons
We present a class of supersymmetric models with complete generations of
composite quarks and leptons using recent non-perturbative results for the low
energy dynamics of supersymmetric QCD. In these models, the quarks arise as
composite "mesons" and the leptons emerge as composite "baryons." The quark and
lepton flavor symmetries are linked at the preon level. Baryon number violation
is automatically suppressed by accidental symmetries. We give some speculations
on how this model might be made realistic.Comment: 10 pages, LaTeX 2
Resonance at the Rabi frequency in a superconducting flux qubit
We analyze a system composed of a superconducting flux qubit coupled to a
transmission-line resonator driven by two signals with frequencies close to the
resonator's harmonics. The first strong signal is used for exciting the system
to a high energetic state while a second weak signal is applied for probing
effective eigenstates of the system. In the framework of doubly dressed states
we showed the possibility of amplification and attenuation of the probe signal
by direct transitions at the Rabi frequency. We present a brief review of
theoretical and experimental works where a direct resonance at Rabi frequency
have been investigated in superconducting flux qubits. The interaction of the
qubit with photons of two harmonics has prospects to be used as a quantum
amplifier (microwave laser) or an attenuator.Comment: This paper is the extended version of the talk given by one of the
authors at the Conference On Nuclei And Mesoscopic Physics, 5-9 May 2014,
Michigan State University, East Lansing, US
Tidal Effects on the Habitability of Exoplanets: The Case of GJ 581 d
Tides may be crucial to the habitability of exoplanets. If such planets form
around low-mass stars, then those in the circumstellar habitable zone will be
close enough to their host stars to experience strong tidal forces. Tides may
result in orbital decay and circularization, evolution toward zero obliquity, a
fixed rotation rate (not necessarily synchronous), and substantial internal
heating. Due to tidal effects, the range of habitable orbital locations may be
quite different from that defined by the traditional concept of a habitable
zone (HZ) based on stellar insolation, atmospheric effects, and liquid water on
a planet's surface. Tidal heating may make locations within the traditional HZ
too hot, while planets outside the traditional zone could be rendered quite
habitable due to tides. Here we consider these effects on the exoplanet GJ 581
d.Comment: 2 pages, 1 figure
Tidal Constraints on Planetary Habitability
We review how tides may impact the habitability of terrestrial-like planets.
If such planets form around low-mass stars, then planets in the circumstellar
habitable zone will be close enough to their host stars to experience strong
tidal forces. We discuss 1) decay of semi-major axis, 2) circularization of
eccentric orbits, 3) evolution toward zero obliquity, 4) fixed rotation rates
(not necessarily synchronous), and 5) internal heating. We briefly describe
these effects using the example of a 0.25 solar mass star with a 10 Earth-mass
companion. We suggest that the concept of a habitable zone should be modified
to include the effects of tides.Comment: 6 pages, 3 figures. Proceedings submitted to "Pathways Towards
Habitable Planets" Symposium (eds.: D. Gelino, V. Coude du Foresto, I. Ribas
Formation of laser plasma channels in a stationary gas
The formation of plasma channels with nonuniformity of about +- 3.5% has been
demonstrated. The channels had a density of 1.2x10^19 cm-3 with a radius of 15
um and with length >= 2.5 mm. The channels were formed by 0.3 J, 100 ps laser
pulses in a nonflowing gas, contained in a cylindrical chamber. The laser beam
passed through the chamber along its axis via pinholes in the chamber walls. A
plasma channel with an electron density on the order of 10^18 - 10^19 cm-3 was
formed in pure He, N2, Ar, and Xe. A uniform channel forms at proper time
delays and in optimal pressure ranges, which depend on the sort of gas. The
influence of the interaction of the laser beam with the gas leaking out of the
chamber through the pinholes was found insignificant. However, the formation of
an ablative plasma on the walls of the pinholes by the wings of the radial
profile of the laser beam plays an important role in the plasma channel
formation and its uniformity. A low current glow discharge initiated in the
chamber slightly improves the uniformity of the plasma channel, while a high
current arc discharge leads to the formation of overdense plasma near the front
pinhole and further refraction of the laser beam. The obtained results show the
feasibility of creating uniform plasma channels in non-flowing gas targets.Comment: 15 pages, 7 figures, submitted to Physics of Plasma
On a conjecture of Bennewitz, and the behaviour of the Titchmarsh-Weyl matrix near a pole
For any real limit- th-order selfadjoint linear differential
expression on , Titchmarsh- Weyl matrices
can be defined. Two matrices of particu lar interest are the
matrices and assoc iated respectively with
Dirichlet and Neumann boundary conditions at . These satisfy
. It is known that when these matrices
have poles (which can only lie on the real axis) the existence of valid HELP
inequalities depends on their behaviour in the neighbourhood of these poles. We
prove a conjecture of Bennewitz and use it, together with a new algorithm for
computing the Laurent expansion of a Titchmarsh-Weyl matrix in the
neighbourhood of a pole, to investigate the existence of HELP inequalities for
a number of differential equations which have so far proved awkward to analys
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