The Existence of Transverse Homoclinic Points in the Sitnikov Problem

AbstractUsing Melnikov′s method we are able to prove the existence of transverse homoclinic orbits and therefore the existence of a horseshoe in a special restricted three-body problem. This analysis is an alternative to the one described by Moser ("Stable and Random Motions in Dynamical Systems," Princeton Univ. Press, Princeton, NJ, 1973), based on Sitnikov′s original work (Dokl. Akad. Nauk. USSR 133, No. 2 (1960), 303-306), where the task is accomplished using a more direct construction of the horseshoe

Gravitational wave recoil in Robinson-Trautman spacetimes

We consider the gravitational recoil due to non-reflection-symmetric gravitational wave emission in the context of axisymmetric Robinson-Trautman spacetimes. We show that regular initial data evolve generically into a final configuration corresponding to a Schwarzschild black-hole moving with constant speed. For the case of (reflection-)symmetric initial configurations, the mass of the remnant black-hole and the total energy radiated away are completely determined by the initial data, allowing us to obtain analytical expressions for some recent numerical results that have been appeared in the literature. Moreover, by using the Galerkin spectral method to analyze the non-linear regime of the Robinson-Trautman equations, we show that the recoil velocity can be estimated with good accuracy from some asymmetry measures (namely the first odd moments) of the initial data. The extension for the non-axisymmetric case and the implications of our results for realistic situations involving head-on collision of two black holes are also discussed.Comment: 9 pages, 6 figures, final version to appear in PR

A flight evaluation of a trailing anemometer for low-speed calibrations of airspeed systems on research aircraft

Research airspeed systems on three low-speed general aviation airplanes were calibrated by the trailing anemometer method. Each airplane was fitted with an NASA pitot-static pressure tube mounted on either a nose or wing boom. The uncalibrated airspeed systems contained residual static-pressure position errors which were too large for high-accuracy flight research applications. The trailing anemometer calibration was in agreement with the tower flyby calibration for the one aircraft for which the comparison was made. The continuous deceleration technique for the trailing anemometer method offers reduced test time with no appreciable loss of accuracy for airspeed systems with pitot-static system lag characteristics similar to those described

Quantifying Spatiotemporal Chaos in Rayleigh-B\'enard Convection

Using large-scale parallel numerical simulations we explore spatiotemporal chaos in Rayleigh-B\'enard convection in a cylindrical domain with experimentally relevant boundary conditions. We use the variation of the spectrum of Lyapunov exponents and the leading order Lyapunov vector with system parameters to quantify states of high-dimensional chaos in fluid convection. We explore the relationship between the time dynamics of the spectrum of Lyapunov exponents and the pattern dynamics. For chaotic dynamics we find that all of the Lyapunov exponents are positively correlated with the leading order Lyapunov exponent and we quantify the details of their response to the dynamics of defects. The leading order Lyapunov vector is used to identify topological features of the fluid patterns that contribute significantly to the chaotic dynamics. Our results show a transition from boundary dominated dynamics to bulk dominated dynamics as the system size is increased. The spectrum of Lyapunov exponents is used to compute the variation of the fractal dimension with system parameters to quantify how the underlying high-dimensional strange attractor accommodates a range of different chaotic dynamics

Ultra-wide detuning planar Bragg grating fabrication technique based on direct UV grating writing with electro-optic phase modulation

A direct UV grating writing technique based on phase-controlled interferometry is proposed and demonstrated in a silica-on-silicon platform, with a wider wavelength detuning range than any previously reported UV writing technology. Electro-optic phase modulation of one beam in the interferometer is used to manipulate the fringe pattern and thus control the parameters of the Bragg gratings and waveguides. Various grating structures with refractive index apodization, phase shifts and index contrasts of up to 0.8×10-3 have been demonstrated. The method offers significant time/energy efficiency as well as simplified optical layout and fabrication process. We have shown Bragg gratings can be made from 1200 nm to 1900 nm exclusively under software control and the maximum peak grating reflectivity only decreases by 3dB over a 250 nm (~32THz) bandwidth

Cardiorespiratory Fitness Is Inversely Associated With Clustering of Metabolic Syndrome Risk Factors: The Ball State Adult Fitness Program Longitudinal Lifestyle Study

Objective: The focus of this study was the association between the metabolic syndrome (MetSyn) and cardiorespiratory fitness (CRF) defined as maximal oxygen uptake (VO2max). Although previous research has shown a relationship between MetSyn and CRF, most studies are based on less objective measures of CRF and different cardiometabolic risk factor thresholds from earlier guidelines

The low dimensional dynamical system approach in General Relativity: an example

In this paper we explore one of the most important features of the Galerkin method, which is to achieve high accuracy with a relatively modest computational effort, in the dynamics of Robinson-Trautman spacetimes.Comment: 7 pages, 5 figure

The Association Between the Long-Term Change in Directly Measured Cardiorespiratory Fitness and Mortality Risk

Introduction: There is a strong inverse association between cardiorespiratory fitness (CRF) and mortality outcomes. This relationship has predominantly been assessed cross-sectionally, however low CRF is a modifiable risk factor, thus assessing this association using a single baseline measure may be sub-optimal. Purpose: To examine the association of the long-term change in CRF, measured using cardiopulmonary exercise testing (CPX) with all-cause and disease-specific mortality. Methods: Participants included 833 apparently healthy men and women (42.9±10.8 years) who underwent two maximal CPXs, the second CPX being ≥ 1 year following the baseline assessment. Participants were followed for 17.7 ± 11.8 years for allcause, cardiovascular disease (CVD), and cancer mortality. Cox-proportional hazard models were performed to determine the association between the change in CRF, computed as visit 1 (V1) peak oxygen consumption (VO2peak (ml·kg-1·min-1)) – visit 2 (V2) VO2peak, and mortality outcomes. Results: During follow-up, 172 participants died. Overall, the change in CPX-derived CRF was inversely related to all-cause, CVD, and cancer mortality (p\u3c0.05). Each 1 ml·kg-1·min-1 increase was associated with a 10.8, 14.7, and 15.9% reductions in allcause, CVD, and cancer mortality, respectively. The inverse relationship between CRF and all-cause mortality remained significant (p\u3c0.05) when men and women were examined independently, after adjusting for years since first CPX, baseline VO2peak, and age. Conclusion: Long-term changes in CRF were inversely related to mortality outcomes, and mortality was better predicted by CRF measured at subsequent examination than baseline CRF. These findings support the recent American Heart Association scientific statement advocating CRF as a clinical vital sign that should be assessed routinely in clinical practice, as well as support regular participation in physical activity to maintain adequate CRF levels across the lifespan