16,476 research outputs found
Embeddings of rearrangement invariant spaces that are not strictly singular
We give partial answers to the following conjecture: the natural embedding of
a rearrangement invariant space E into L_1([0,1]) is strictly singular if and
only if G does not embed into E continuously, where G is the closure of the
simple functions in the Orlicz space L_Phi with Phi(x) = exp(x^2)-1.Comment: Also available at http://www.math.missouri.edu/~stephen/preprint
Power dissipation in nanoscale conductors: classical, semi-classical and quantum dynamics
Modelling Joule heating is a difficult problem because of the need to introduce correct correlations between the motions of the ions and the electrons. In this paper we analyse three different models of current induced heating (a purely classical model, a fully quantum model and a hybrid model in which the electrons are treated quantum mechanically and the atoms are treated classically). We find that all three models allow for both heating and cooling processes in the presence of a current, and furthermore the purely classical and purely quantum models show remarkable agreement in the limit of high biases. However, the hybrid model in the Ehrenfest approximation tends to suppress heating. Analysis of the equations of motion reveals that this is a consequence of two things: the electrons are being treated as a continuous fluid and the atoms cannot undergo quantum fluctuations. A means for correcting this is suggested
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
Chow's theorem and universal holonomic quantum computation
A theorem from control theory relating the Lie algebra generated by vector
fields on a manifold to the controllability of the dynamical system is shown to
apply to Holonomic Quantum Computation. Conditions for deriving the holonomy
algebra are presented by taking covariant derivatives of the curvature
associated to a non-Abelian gauge connection. When applied to the Optical
Holonomic Computer, these conditions determine that the holonomy group of the
two-qubit interaction model contains . In particular, a
universal two-qubit logic gate is attainable for this model.Comment: 13 page
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A Status Report On A Planet Search Around White Dwarf Stars
We have continued monitoring a pilot sample of 15 isolated, pulsating DA white dwarfs for center-of-mass motion caused by a planetary companion. Roughly 7 years into our survey, we have preliminary evidence for periodic variations in pulse arrival times for at least two white dwarfs in our sample. The variations in these systems are unlikely to be caused by secular evolution and are possibly the result of motion of the white dwarf around a center of mass. We have yet to claim confirmation of a planet. GD66 is a previously published candidate system, with a modulation in pulse arrival times that could be caused by a 2.0 M-J sin i planetary companion with an 8.3 year orbital period. Another candidate system, WD1354+0108, has a phase modulation consistent with a 0.7 M-J sin i planet at 2.3 AU (a 4.5 year orbit). We see similar behavior in two independent frequencies within this star, and while a sinusoid is currently a marginally better fit to the data than a straight line (as we might expect from cooling alone in a DAV), we are hesitant to over-interpret our results. Finally, we have a third system, WD0018+0031, that shows a change in pulse arrival times inconsistent with cooling alone; a 2.7 M-J planet at an orbit of about 5 AU could cause the observed trend. Observations of these candidate systems are ongoing in order to constrain any planetary companions that may be present.Astronom
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
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