759 research outputs found
The symplectic structure of rational Lax pair systems
We consider dynamical systems associated to Lax pairs depending rationnally
on a spectral parameter. We show that we can express the symplectic form in
terms of algebro--geometric data provided that the symplectic structure on L is
of Kirillov type. In particular, in this case the dynamical system is
integrable.Comment: 8 pages, no figure, Late
Kowalevski's analysis of the swinging Atwood's machine
We study the Kowalevski expansions near singularities of the swinging
Atwood's machine. We show that there is a infinite number of mass ratios
where such expansions exist with the maximal number of arbitrary constants.
These expansions are of the so--called weak Painlev\'e type. However, in view
of these expansions, it is not possible to distinguish between integrable and
non integrable cases.Comment: 30 page
A Cost-Benefit Analysis of Pilot Training Next
The United States Air Force (USAF) is currently facing a 2,400-pilot shortage in an increasingly constrained budgetary environment. Without pilots to engage the enemy, deliver weapons, and provide logistics support for operations, the USAF could lose the ability to fly, fight, and win global engagements and defend the homeland. This study focused on Undergraduate Pilot Training (UPT) as a means of producing the USAF’s pilots to offset the current shortage. Specifically, this study compared UPT to the recently initiated Pilot Training-Next (PTN) program through a cost-benefit analysis. Like any new technology integration, PTN’s virtual reality training will require further study for proofing and justification prior to full-scale implementation and further utilization of constrained USAF resources. This study’s use of extant financial and historical production data, coupled with interviews with PTN instructors, highlights the potential of PTN. Ultimately, this study’s cost-benefit analysis uniquely contributes to the growing body of virtual reality training research through a Formula for Change theoretical lens, while simultaneously providing USAF decision makers a comparison of program costs, projected production capacity, and quality of training
Spectrum of the quantum Neumann model
We study numerically the spectrum and eigenfunctions of the quantum Neumann
model, illustrating some general properties of a non trivial integrable model.Comment: 12 pages, 5 figures. Expanded introduction and references to put our
work in the proper historical contex
Stokes flow paths separation and recirculation cells in X-junctions of varying angle
Fluid and solute transfer in X-junctions between straight channels is shown
to depend critically on the junction angle in the Stokes flow regime.
Experimentally, water and a water-dye solution are injected at equal flow rates
in two facing channels of the junction: Planar Laser Induced fluorescence
(PLIF) measurements show that the largest part of each injected fluid "bounces
back" preferentially into the outlet channel at the lowest angle to the
injection; this is opposite to the inertial case and requires a high curvature
of the corresponding streamlines. The proportion of this fluid in the other
channel decreases from 50% at 90\degree to zero at a threshold angle. These
counterintuitive features reflect the minimization of energy dissipation for
Stokes flows. Finite elements numerical simulations of a 2D Stokes flow of
equivalent geometry con rm these results and show that, below the threshold
angle 33.8\degree recirculation cells are present in the center part of the
junction and separate the two injected flows of the two solutions. Reducing
further leads to the appearance of new recirculation cells with lower flow
velocities
3He-Driven Mixing in Low-Mass Red Giants: Convective Instability in Radiative and Adiabatic Limits
We examine the stability and observational consequences of mixing induced by
3He burning in the envelopes of first ascent red giants. We demonstrate that
there are two unstable modes: a rapid, nearly adiabatic mode that we cannot
identify with an underlying physical mechanism, and a slow, nearly radiative
mode that can be identified with thermohaline convection. We present
observational constraints that make the operation of the rapid mode unlikely to
occur in real stars. Thermohaline convection turns out to be fast enough only
if fluid elements have finger-like structures with a length to diameter ratio
l/d > 10. We identify some potentially serious obstacles for thermohaline
convection as the predominant mixing mechanism for giants. We show that
rotation-induced horizontal turbulent diffusion may suppress the 3He-driven
thermohaline convection. Another potentially serious problem for it is to
explain observational evidence of enhanced extra mixing. The 3He exhaustion in
stars approaching the red giant branch (RGB) tip should make the 3He mixing
inefficient on the asymptotic giant branch (AGB). In spite of this, there are
observational data indicating the presence of extra mixing in low-mass AGB
stars similar to that operating on the RGB. Overmixing may also occur in
carbon-enhanced metal-poor stars.Comment: 25 pages, 6 figures, modified version, accepted by Ap
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