14,519 research outputs found
Symmetry Reduction of Optimal Control Systems and Principal Connections
This paper explores the role of symmetries and reduction in nonlinear control
and optimal control systems. The focus of the paper is to give a geometric
framework of symmetry reduction of optimal control systems as well as to show
how to obtain explicit expressions of the reduced system by exploiting the
geometry. In particular, we show how to obtain a principal connection to be
used in the reduction for various choices of symmetry groups, as opposed to
assuming such a principal connection is given or choosing a particular symmetry
group to simplify the setting. Our result synthesizes some previous works on
symmetry reduction of nonlinear control and optimal control systems. Affine and
kinematic optimal control systems are of particular interest: We explicitly
work out the details for such systems and also show a few examples of symmetry
reduction of kinematic optimal control problems.Comment: 23 pages, 2 figure
Apparent suppression of turbulent magnetic dynamo action by a dc magnetic field
Numerical studies of the effect of a dc magnetic field on dynamo action
(development of magnetic fields with large spatial scales), due to
helically-driven magnetohydrodynamic turbulence, are reported. The apparent
effect of the dc magnetic field is to suppress the dynamo action, above a
relatively low threshold. However, the possibility that the suppression results
from an improper combination of rectangular triply spatially-periodic boundary
conditions and a uniform dc magnetic field is addressed: heretofore a common
and convenient computational convention in turbulence investigations. Physical
reasons for the observed suppression are suggested. Other geometries and
boundary conditions are offered for which the dynamo action is expected not to
be suppressed by the presence of a dc magnetic field component.Comment: To appear in Physics of Plasma
The jumping champion conjecture
An integer is called a jumping champion for a given if is the
most common gap between consecutive primes up to . Occasionally several gaps
are equally common. Hence, there can be more than one jumping champion for the
same . For the th prime , the th primorial is
defined as the product of the first primes. In 1999, Odlyzko, Rubinstein
and Wolf provided convincing heuristics and empirical evidence for the truth of
the hypothesis that the jumping champions greater than 1 are 4 and the
primorials , that is, In this paper, we
prove that an appropriate form of the Hardy-Littlewood prime -tuple
conjecture for prime pairs and prime triples implies that all sufficiently
large jumping champions are primorials and that all sufficiently large
primorials are jumping champions over a long range of .Comment: 19 pages, 1 tabl
Driving in ZZ Ceti stars - Problem solved?
There is a fairly tight correlation between the pulsation periods and
effective temperatures of ZZ Ceti stars (cooler stars have longer periods).
This seems to fit the theoretical picture, where driving occurs in the partial
ionization zone, which lies deeper and deeper within the star as it cools. It
is reasonable to assume that the pulsation periods should be related to the
thermal timescale in the region where driving occurs. As that region sinks
further down below the surface, that thermal timescale increases. Assuming this
connection, the pulsation periods could provide an additional way to determine
effective temperatures, independent of spectroscopy. We explore this idea and
find that in practice, things are not so simple.Comment: 4 pages, 3 figure
A Self-Consistent Marginally Stable State for Parallel Ion Cyclotron Waves
We derive an equation whose solutions describe self-consistent states of
marginal stability for a proton-electron plasma interacting with
parallel-propagating ion cyclotron waves. Ion cyclotron waves propagating
through this marginally stable plasma will neither grow nor damp. The
dispersion relation of these waves, {\omega} (k), smoothly rises from the usual
MHD behavior at small |k| to reach {\omega} = {\Omega}p as k \rightarrow
\pm\infty. The proton distribution function has constant phase-space density
along the characteristic resonant surfaces defined by this dispersion relation.
Our equation contains a free function describing the variation of the proton
phase-space density across these surfaces. Taking this free function to be a
simple "box function", we obtain specific solutions of the marginally stable
state for a range of proton parallel betas. The phase speeds of these waves are
larger than those given by the cold plasma dispersion relation, and the
characteristic surfaces are more sharply peaked in the v\bot direction. The
threshold anisotropy for generation of ion cyclotron waves is also larger than
that given by estimates which assume bi-Maxwellian proton distributions.Comment: in press in Physics of Plasma
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
A New Timescale for Period Change in the Pulsating DA White Dwarf WD 0111+0018
We report the most rapid rate of period change measured to date for a
pulsating DA (hydrogen atmosphere) white dwarf (WD), observed in the 292.9 s
mode of WD 0111+0018. The observed period change, faster than 10^{-12} s/s,
exceeds by more than two orders of magnitude the expected rate from cooling
alone for this class of slow and simply evolving pulsating WDs. This result
indicates the presence of an additional timescale for period evolution in these
pulsating objects. We also measure the rates of period change of nonlinear
combination frequencies and show that they share the evolutionary
characteristics of their parent modes, confirming that these combination
frequencies are not independent modes but rather artifacts of some nonlinear
distortion in the outer layers of the star.Comment: 10 pages, 6 figures, accepted for publication in The Astrophysical
Journa
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