4,623 research outputs found
Dynamic stability of space vehicles. Volume 8 - Atmospheric disturbances that affect flight control analysis
Space vehicle and control system dynamic response to atmospheric disturbance
Minkowski Tensors in Two Dimensions - Probing the Morphology and Isotropy of the Matter and Galaxy Density Fields
We apply the Minkowski Tensor statistics to two dimensional slices of the
three dimensional density field. The Minkowski Tensors are a set of functions
that are sensitive to directionally dependent signals in the data, and
furthermore can be used to quantify the mean shape of density peaks. We begin
by introducing our algorithm for constructing bounding perimeters around
subsets of a two dimensional field, and reviewing the definition of Minkowski
Tensors. Focusing on the translational invariant statistic - a matrix - we calculate its eigenvalues for both the entire excursion
set () and for individual connected regions and holes
within the set (). The ratio of eigenvalues
informs us of the presence of global anisotropies in
the data, and is a measure of the
mean shape of peaks and troughs in the density field. We study these quantities
for a Gaussian field, then consider how they are modified by the effect of
gravitational collapse using the latest Horizon Run 4 cosmological simulation.
We find are essentially independent of gravitational collapse,
as the process maintains statistical isotropy. However, the mean shape of peaks
is modified significantly - overdensities become relatively more circular
compared to underdensities of the same area. When applying the statistic to a
redshift space distorted density field, we find a significant signal in the
eigenvalues , suggesting that they can be used to probe the
large-scale velocity field.Comment: 17 pages, accepted for publication in AP
Collective Oscillations of Vortex Lattices in Rotating Bose-Einstein Condensates
The complete low-energy collective-excitation spectrum of vortex lattices is
discussed for rotating Bose-Einstein condensates (BEC) by solving the
Bogoliubov-de Gennes (BdG) equation, yielding, e.g., the Tkachenko mode
recently observed at JILA. The totally symmetric subset of these modes includes
the transverse shear, common longitudinal, and differential longitudinal modes.
We also solve the time-dependent Gross-Pitaevskii (TDGP) equation to simulate
the actual JILA experiment, obtaining the Tkachenko mode and identifying a pair
of breathing modes. Combining both the BdG and TDGP approaches allows one to
unambiguously identify every observed mode.Comment: 5 pages, 4 figure
Husimi Transform of an Operator Product
It is shown that the series derived by Mizrahi, giving the Husimi transform
(or covariant symbol) of an operator product, is absolutely convergent for a
large class of operators. In particular, the generalized Liouville equation,
describing the time evolution of the Husimi function, is absolutely convergent
for a large class of Hamiltonians. By contrast, the series derived by
Groenewold, giving the Weyl transform of an operator product, is often only
asymptotic, or even undefined. The result is used to derive an alternative way
of expressing expectation values in terms of the Husimi function. The advantage
of this formula is that it applies in many of the cases where the anti-Husimi
transform (or contravariant symbol) is so highly singular that it fails to
exist as a tempered distribution.Comment: AMS-Latex, 13 page
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