Symplectic map description of Halley's comet dynamics

The main features of 1P/Halley chaotic dynamics can be described by a two dimensional symplectic map. Using Mel'nikov integral we semi-analytically determine such a map for 1P/Halley taking into account gravitational interactions from the Sun and the eight planets. We determine the Solar system kick function ie the energy transfer to 1P/Halley along one passage through the Solar system. Our procedure allows to compute for each planet its contribution to the Solar system kick function which appears to be the sum of the Keplerian potential of the planet and of a rotating circular gravitational dipole potential due to the Sun movement around Solar system barycenter. We test the robustness of the symplectic Halley map by directly integrating Newton's equations over $\sim 2.4\cdot 10^4$ yr around Y2K and by reconstructing the Solar system kick function. Our results show that the Halley map with fixed parameters gives a reliable description of comet dynamics on time scales of $10^4$ yr while on a larger scales the parameters of the map are slowly changing due to slow oscillations of orbital momentum.Comment: To be published in Physics Letter A, 8 pages, 5 figures, supplementary material at http://perso.utinam.cnrs.fr/~lages/publications/sm/sm21.htm

Shortening of the Short Refractory Periods in Short QT Syndrome.

BACKGROUND: Diagnosis of short QT syndrome (SQTS) remains difficult in case of borderline QT values as often found in normal populations. Whether some shortening of refractory periods (RP) may help in differentiating SQTS from normal subjects is unknown. METHODS AND RESULTS: Atrial and right ventricular RP at the apex and right ventricular outflow tract as determined during standard electrophysiological study were compared between 16 SQTS patients (QTc 324±24 ms) and 15 controls with similar clinical characteristics (QTc 417±32 ms). Atrial RP were significantly shorter in SQTS compared with controls at 600- and 500-ms basic cycle lengths. Baseline ventricular RP were significantly shorter in SQTS patients than in controls, both at the apex and right ventricular outflow tract and for any cycle length. Differences remained significant for RP of any subsequent extrastimulus at any cycle length and any pacing site. A cut-off value of baseline RP <200 ms at the right ventricular outflow tract either at 600- or 500-ms cycle length had a sensitivity of 86% and a specificity of 100% for the diagnosis of SQTS. CONCLUSIONS: Patients with SQTS have shorter ventricular RP than controls, both at baseline during various cycle lengths and after premature extrastimuli. A cut-off value of 200 ms at the right ventricular outflow tract during 600- and 500-ms basic cycle length may help in detecting true SQTS from normal subjects with borderline QT values

Drag Reduction by Polymers in Wall Bounded Turbulence

We address the mechanism of drag reduction by polymers in turbulent wall bounded flows. On the basis of the equations of fluid mechanics we present a quantitative derivation of the "maximum drag reduction (MDR) asymptote" which is the maximum drag reduction attained by polymers. Based on Newtonian information only we prove the existence of drag reduction, and with one experimental parameter we reach a quantitative agreement with the experimental measurements.Comment: 4 pages, 1 fig., included, PRL, submitte

High-temperature, high-pressure oxygen metering valve

A control valve includes a body defining a central cavity arranged between a fluid inlet and outwardly-diverging first and second fluid outlets respectively disposed in a common transverse plane. A valve member is arranged in the cavity for rotation between first and second operating positions where a transverse fluid passage through the valve member alternatively communicates the fluid inlet with one or the other of the fluid outlets. To minimize fluid turbulence when the valve member is rotated to an alternate operating position, the fluid passage has a convergent entrance for maintaining the passage in permanent communication with the fluid inlet as well as an oblong exit opening with spaced side walls for enabling the exit opening to temporarily span the first and second fluid outlets as the valve member is turned between its respective operating positions

Group 62 Section Leaders Meeting-- AN/FSQ-7 Equipment Design Program

Two situations urgently need attention at the present time. The vacuum tube count for a central has become rather large, and every effort should be made to see what can be done to reduce the count. The space required for XD-1 exceeds the space available in the basement of building A, and several alternate arrangements are being investigated. Progress in other fields is fairly satisfactory

EPSCOM Biweekly Report for 20 April 1956

EPSCOM, now Group 66, with 37 people including a new secretary at Murphy Hospital, is being reorganized into 3 subsections

WWII Block Diagrams Meeting of April 22, 1952

This report summarizes the discussion of the meeting for the benefit of those who may want to trace the development of thought on this subject

The Mirror: A Proposed Simplified Symbol for Magnetic Circuits

A coil can be wound on a magnetic core in one of only two directions. There are several dot-conventions which can bo used to indicate which direction is desired. A simpler symbol, which is quicker to draw and easier to follow, is proposed: The "mirror symbol", which "reflects" current to find resultant flux

EPSCOM Biweekly Report for 4 May 1956

EPSCOM now includes 38 people. A chart showing most of the EPSCOM programs includes scheduling information

Risk-Neutral Pricing and Hedging of In-Play Football Bets

A risk-neutral valuation framework is developed for pricing and hedging in-play football bets based on modelling scores by independent Poisson processes with constant intensities. The Fundamental Theorems of Asset Pricing are applied to this set-up which enables us to derive novel arbitrage-free valuation formulæ for contracts currently traded in the market. We also describe how to calibrate the model to the market and how trades can be replicated and hedged