3,024 research outputs found
Equilibration and Approximate Conservation Laws: Dipole Oscillations and Perfect Drag of Ultracold Atoms in a Harmonic Trap
The presence of (approximate) conservation laws can prohibit the fast
relaxation of interacting many-particle quantum systems. We investigate this
physics by studying the center-of-mass oscillations of two species of fermionic
ultracold atoms in a harmonic trap. If their trap frequencies are equal, a
dynamical symmetry (spectrum generating algebra), closely related to Kohn's
theorem, prohibits the relaxation of center-of-mass oscillations. A small
detuning of the trap frequencies for the two species breaks the
dynamical symmetry and ultimately leads to a damping of dipole oscillations
driven by inter-species interactions. Using memory-matrix methods, we calculate
the relaxation as a function of frequency difference, particle number,
temperature, and strength of inter-species interactions. When interactions
dominate, there is almost perfect drag between the two species and the
dynamical symmetry is approximately restored. The drag can either arise from
Hartree potentials or from friction. In the latter case (hydrodynamic limit),
the center-of-mass oscillations decay with a tiny rate, , where is a single particle scattering rate.Comment: 9 pages + 5 pages of appendix, 9 figures; changes in v2: updated
citation
Spacecraft rendezvous by differential drag under uncertainties
At low Earth orbits, differentials in the drag forces between spacecraft can be used for controlling their relative motion in the orbital plane. Current methods for determining the drag force may result in errors due to inaccuracies in the density models and drag coefficients. In this work, a methodology for relative maneuvering of spacecraft based on differential drag, accounting for uncertainties in the drag model, is proposed. A dynamical model composed of the mean semimajor axis and the argument of latitude is used for describing long-range maneuvers. For this model, a linear quadratic regulator is implemented, accounting for the uncertainties in the drag force. The actuation is the pitch angle of the satellites, considering saturation. The control scheme guarantees asymptotic stability of the system up to a certain magnitude of the state vector, which is determined by the uncertainties. Numerical simulations show that the method exhibits consistent robustness to accomplish the maneuvers, even in the presence of realistic modeling of density fields, drag coefficients, the corotation of the atmosphere, and zonal harmonics up to J(8)
Photogrammetry and ballistic analysis of a high-flying projectile in the STS-124 space shuttle launch
A method combining photogrammetry with ballistic analysis is demonstrated to
identify flying debris in a rocket launch environment. Debris traveling near
the STS-124 Space Shuttle was captured on cameras viewing the launch pad within
the first few seconds after launch. One particular piece of debris caught the
attention of investigators studying the release of flame trench fire bricks
because its high trajectory could indicate a flight risk to the Space Shuttle.
Digitized images from two pad perimeter high-speed 16-mm film cameras were
processed using photogrammetry software based on a multi-parameter optimization
technique. Reference points in the image were found from 3D CAD models of the
launch pad and from surveyed points on the pad. The three-dimensional reference
points were matched to the equivalent two-dimensional camera projections by
optimizing the camera model parameters using a gradient search optimization
technique. Using this method of solving the triangulation problem, the xyz
position of the object's path relative to the reference point coordinate system
was found for every set of synchronized images. This trajectory was then
compared to a predicted trajectory while performing regression analysis on the
ballistic coefficient and other parameters. This identified, with a high degree
of confidence, the object's material density and thus its probable origin
within the launch pad environment. Future extensions of this methodology may
make it possible to diagnose the underlying causes of debris-releasing events
in near-real time, thus improving flight safety.Comment: 26 pages, 11 figures, 3 table
Hypersonic Flight Mechanics
The effects of aerodynamic forces on trajectories at orbital speeds are discussed in terms of atmospheric models. The assumptions for the model are spherical symmetry, nonrotating, and an exponential atmosphere. The equations of flight, and the performance in extra-atmospheric flight are discussed along with the return to the atmosphere, and the entry. Solutions of the exact equations using directly matched asymptotic expansions are presented
A distribution model for the aerial application of granular agricultural particles
A model is developed to predict the shape of the distribution of granular agricultural particles applied by aircraft. The particle is assumed to have a random size and shape and the model includes the effect of air resistance, distributor geometry and aircraft wake. General requirements for the maintenance of similarity of the distribution for scale model tests are derived and are addressed to the problem of a nongeneral drag law. It is shown that if the mean and variance of the particle diameter and density are scaled according to the scaling laws governing the system, the shape of the distribution will be preserved. Distributions are calculated numerically and show the effect of a random initial lateral position, particle size and drag coefficient. A listing of the computer code is included
Stokes imaging, Doppler mapping and Roche tomography of the AM Her system V834 Cen
We report on new simultaneous phase resolved spectroscopic and polarimetric
observations of the polar (AM Herculis star) V834 Cen during a high state of
accretion. Strong emission lines and high levels of variable circular and
linear polarization are observed over the orbital period. The polarization data
is modelled using the Stokes imaging technique of Potter et al. The
spectroscopic emission lines are investigated using the Doppler tomography
technique of Marsh and Horne and the Roche tomography technique of Dhillon and
Watson. Up to now all three techniques have been used separately to investigate
the geometry and accretion dynamics in Cataclysmic Variables. For the first
time, we apply all three techniques to simultaneous data for a single system.
This allows us to compare and test each of the techniques against each other
and hence derive a better understanding of the geometry, dynamics and system
parameters of V834 Cen.Comment: 10 pages, 8 figures; Accepted for publication in MNRA
Stochastic Models for the Kinematics of Moisture Transport and Condensation in Homogeneous Turbulent Flows
The transport of a condensing passive scalar is studied as a prototype model for the kinematics of moisture transport on isentropic surfaces. Condensation occurs whenever the scalar concentration exceeds a specified local saturation value. Since condensation rates are strongly nonlinear functions of moisture content, the mean moisture flux is generally not diffusive. To relate the mean moisture content, mean condensation rate, and mean moisture flux to statistics of the advecting velocity field, a one-dimensional stochastic model is developed in which the Lagrangian velocities of air parcels are independent Ornstein–Uhlenbeck (Gaussian colored noise) processes. The mean moisture evolution equation for the stochastic model is derived in the Brownian and ballistic limits of small and large Lagrangian velocity correlation time. The evolution equation involves expressions for the mean moisture flux and mean condensation rate that are nonlocal but remarkably simple. In a series of simulations of homogeneous two-dimensional turbulence, the dependence of mean moisture flux and mean condensation rate on mean saturation deficit is shown to be reproducible by the one-dimensional stochastic model, provided eddy length and time scales are taken as given. For nonzero Lagrangian velocity correlation times, condensation reduces the mean moisture flux for a given mean moisture gradient compared with the mean flux of a noncondensing scalar
Longitudinal control effectiveness and entry dynamics of a single-stage-to-orbit vehicle
The classical theory of flight dynamics for airplane longitudinal stability and control analysis was extended to the case of a hypervelocity reentry vehicle. This includes the elements inherent in supersonic and hypersonic flight such as the influence of the Mach number on aerodynamic characteristics, and the effect of the reaction control system and aerodynamic controls on the trim condition through a wide range of speed. Phugoid motion and angle of attack oscillation for typical cases of cruising flight, ballistic entry, and glide entry are investigated. In each case, closed form solutions for the variations in altitude, flight path angle, speed and angle of attack are obtained. The solutions explicitly display the influence of different regions design parameters and trajectory variables on the stability of the motion
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