13,247 research outputs found
Velocity field distributions due to ideal line vortices
We evaluate numerically the velocity field distributions produced by a
bounded, two-dimensional fluid model consisting of a collection of parallel
ideal line vortices. We sample at many spatial points inside a rigid circular
boundary. We focus on ``nearest neighbor'' contributions that result from
vortices that fall (randomly) very close to the spatial points where the
velocity is being sampled. We confirm that these events lead to a non-Gaussian
high-velocity ``tail'' on an otherwise Gaussian distribution function for the
Eulerian velocity field. We also investigate the behavior of distributions that
do not have equilibrium mean-field probability distributions that are uniform
inside the circle, but instead correspond to both higher and lower mean-field
energies than those associated with the uniform vorticity distribution. We find
substantial differences between these and the uniform case.Comment: 21 pages, 9 figures. To be published in Physical Review E
(http://pre.aps.org/) in May 200
Hyperk\"ahler Arnold Conjecture and its Generalizations
We generalize and refine the hyperk\"ahler Arnold conjecture, which was
originally established, in the non-degenerate case, for three-dimensional time
by Hohloch, Noetzel and Salamon by means of hyperk\"ahler Floer theory. In
particular, we prove the conjecture in the case where the time manifold is a
multidimensional torus and also establish the degenerate version of the
conjecture. Our method relies on Morse theory for generating functions and a
finite-dimensional reduction along the lines of the Conley-Zehnder proof of the
Arnold conjecture for the torus.Comment: 13 page
A Bayesian approach to the estimation of maps between riemannian manifolds
Let \Theta be a smooth compact oriented manifold without boundary, embedded
in a euclidean space and let \gamma be a smooth map \Theta into a riemannian
manifold \Lambda. An unknown state \theta \in \Theta is observed via
X=\theta+\epsilon \xi where \epsilon>0 is a small parameter and \xi is a white
Gaussian noise. For a given smooth prior on \Theta and smooth estimator g of
the map \gamma we derive a second-order asymptotic expansion for the related
Bayesian risk. The calculation involves the geometry of the underlying spaces
\Theta and \Lambda, in particular, the integration-by-parts formula. Using this
result, a second-order minimax estimator of \gamma is found based on the modern
theory of harmonic maps and hypo-elliptic differential operators.Comment: 20 pages, no figures published version includes correction to eq.s
31, 41, 4
Post-Election Litigation in Pennsylvania
The Article focuses on the causes and consequences of post-election litigation in Pennsylvania. The Authors conclude that the Pennsylvania Election Code has been strictly construed by Pennsylvania courts out of a reluctance to interfere with, and to promote, the finality of election returns
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