10,290 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
Atmospheric Dynamics of Short-period Extra Solar Gas Giant Planets I: Dependence of Night-Side Temperature on Opacity
More than two dozen short-period Jupiter-mass gas giant planets have been
discovered around nearby solar-type stars in recent years, several of which
undergo transits, making them ideal for the detection and characterization of
their atmospheres. Here we adopt a three-dimensional radiative hydrodynamical
numerical scheme to simulate atmospheric circulation on close-in gas giant
planets. In contrast to the conventional GCM and shallow water algorithms, this
method does not assume quasi hydrostatic equilibrium and it approximates
radiation transfer from optically thin to thick regions with flux-limited
diffusion. In the first paper of this series, we consider
synchronously-spinning gas giants. We show that a full three-dimensional
treatment, coupled with rotationally modified flows and an accurate treatment
of radiation, yields a clear temperature transition at the terminator. Based on
a series of numerical simulations with varying opacities, we show that the
night-side temperature is a strong indicator of the opacity of the planetary
atmosphere. Planetary atmospheres that maintain large, interstellar opacities
will exhibit large day-night temperature differences, while planets with
reduced atmospheric opacities due to extensive grain growth and sedimentation
will exhibit much more uniform temperatures throughout their photosphere's. In
addition to numerical results, we present a four-zone analytic approximation to
explain this dependence.Comment: 35 Pages, 13 Figure
Social cost considerations and legal constraints in implementing modular integrated utility systems
Social costs associated with the design, demonstration, and implementation of the Modular Integrated Utility System are considered including the social climate of communities, leadership patterns, conflicts and cleavages, specific developmental values, MIUS utility goal assessment, and the suitability of certian alternative options for use in a program of implementation. General considerations are discussed in the field of socio-technological planning. These include guidelines for understanding the conflict and diversity; some relevant goal choices and ideas useful to planners of the MIUS facility
Tidal Barrier and the Asymptotic Mass of Proto Gas-Giant Planets
Extrasolar planets found with radial velocity surveys have masses ranging
from several Earth to several Jupiter masses. While mass accretion onto
protoplanetary cores in weak-line T-Tauri disks may eventually be quenched by a
global depletion of gas, such a mechanism is unlikely to have stalled the
growth of some known planetary systems which contain relatively low-mass and
close-in planets along with more massive and longer period companions. Here, we
suggest a potential solution for this conundrum. In general, supersonic infall
of surrounding gas onto a protoplanet is only possible interior to both of its
Bondi and Roche radii. At a critical mass, a protoplanet's Bondi and Roche
radii are equal to the disk thickness. Above this mass, the protoplanets' tidal
perturbation induces the formation of a gap. Although the disk gas may continue
to diffuse into the gap, the azimuthal flux across the protoplanets' Roche lobe
is quenched. Using two different schemes, we present the results of numerical
simulations and analysis to show that the accretion rate increases rapidly with
the ratio of the protoplanet's Roche to Bondi radii or equivalently to the disk
thickness. In regions with low geometric aspect ratios, gas accretion is
quenched with relatively low protoplanetary masses. This effect is important
for determining the gas-giant planets' mass function, the distribution of their
masses within multiple planet systems around solar type stars, and for
suppressing the emergence of gas-giants around low mass stars
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
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
Interferometric weak value deflections: quantum and classical treatments
We derive the weak value deflection given in a paper by Dixon et al. (Phys.
Rev. Lett. 102, 173601 (2009)) both quantum mechanically and classically. This
paper is meant to cover some of the mathematical details omitted in that paper
owing to space constraints
On the motion of spinning test particles in plane gravitational waves
The Mathisson-Papapetrou-Dixon equations for a massive spinning test particle
in plane gravitational waves are analysed and explicit solutions constructed in
terms of solutions of certain linear ordinary differential equations. For
harmonic waves this system reduces to a single equation of Mathieu-Hill type.
In this case spinning particles may exhibit parametric excitation by
gravitational fields. For a spinning test particle scattered by a gravitational
wave pulse, the final energy-momentum of the particle may be related to the
width, height, polarisation of the wave and spin orientation of the particle.Comment: 11 page
A Preliminary Investigation of Relational Network Influence on Horse-Track Betting
Adult gamblers completed a task that assessed !preference among eight horses during a computerized pari-mutuel horse racing game. During Experiment 1, assessments of bet allocation were conducted before and after temporal and visual discrimination !training procedures where 3 three-member stimulus classes were established. Experiment 2 controlled for participant reinforcement histories by blocking the results of each horse race. Results indicated that some participants tended increase responding toward specific horses that shared similar formal properties to those stimuli used in visual discrimination training even !though such features !had no !bearing !on !race !!outcomes
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