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

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

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 $M/m$ 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

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