Jackknife Estimation of Stationary Autoregressive Models

This paper reports the results of an extensive investigation into the use of the jackknife as a method of estimation in stationary autoregressive models. In addition to providing some general theoretical results concerning jackknife methods it is shown that a method based on the use of non-overlapping sub-intervals is found to work particularly well and is capable of reducing bias and root mean squared error (RMSE) compared to ordinary least squares (OLS), subject to a suitable choice of the number of sub-samples, rules-of-thumb for which are provided. The jackknife estimators also outperform OLS when the distribution of the disturbances departs from normality and when it is subject to autoregressive conditional heteroskedasticity. Furthermore the jackknife estimators are much closer to being median-unbiased than their OLS counterparts.

Pseudo-High-Order Symplectic Integrators

Symplectic N-body integrators are widely used to study problems in celestial mechanics. The most popular algorithms are of 2nd and 4th order, requiring 2 and 6 substeps per timestep, respectively. The number of substeps increases rapidly with order in timestep, rendering higher-order methods impractical. However, symplectic integrators are often applied to systems in which perturbations between bodies are a small factor of the force due to a dominant central mass. In this case, it is possible to create optimized symplectic algorithms that require fewer substeps per timestep. This is achieved by only considering error terms of order epsilon, and neglecting those of order epsilon^2, epsilon^3 etc. Here we devise symplectic algorithms with 4 and 6 substeps per step which effectively behave as 4th and 6th-order integrators when epsilon is small. These algorithms are more efficient than the usual 2nd and 4th-order methods when applied to planetary systems.Comment: 14 pages, 5 figures. Accepted for publication in the Astronomical Journa

Temperature controller for a fluid cooled garment

An automatic controller for controlling the inlet temperature of the coolant to a fluid cooled garment without requiring skin sensors is described. Temperature is controlled by the wearer's evaporative water loss rate

Jackknife Bias Reduction in the Presence of a Unit Root

This paper analyses the properties of jackknife estimators of the first-order autoregressive coefficient when the time series of interest contains a unit root. It is shown that, when the sub-samples do not overlap, the sub-sample estimators have different limiting distributions from the full-sample estimator and, hence, the jackknife estimator in its usual form does not eliminate fully the first-order bias as intended. The joint moment generating function of the numerator and denominator of these limiting distributions is derived and used to calculate the expectations that determine the optimal jackknife weights. Two methods of avoiding this procedure are proposed and investigated, one based on inclusion of an intercept in the regressions, the other based on adjusting the observations in the sub-samples. Extensions to more general augmented Dickey-Fuller (ADF) regressions are also considered. In addition to the theoretical results extensive simulations reveal the impressive bias reductions that can be obtained with these computationally simple jackknife estimators and they also highlight the importance of correct lag-length selection in ADF regressions.

A liquid cooled garment temperature controller based on sweat rate

An automatic controller for liquid cooled space suits is reported that utilizes human sweat rate as the primary input signal. The controller is so designed that the coolant inlet temperature is inversely proportional to the subject's latent heat loss as evidenced by evaporative water loss

Hamiltonian model of capture into mean motion resonance

Mean motion resonances are a common feature of both our own Solar System and of extrasolar planetary systems. Bodies can be trapped in resonance when their orbital semi-major axes change, for instance when they migrate through a protoplanetary disc. We use a Hamiltonian model to thoroughly investigate the capture behaviour for first and second order resonances. Using this method, all resonances of the same order can be described by one equation, with applications to specific resonances by appropriate scaling. We focus on the limit where one body is a massless test particle and the other a massive planet. We quantify how the the probability of capture into a resonance depends on the relative migration rate of the planet and particle, and the particle's eccentricity. Resonant capture fails for high migration rates, and has decreasing probability for higher eccentricities, although for certain migration rates, capture probability peaks at a finite eccentricity. We also calculate libration amplitudes and the offset of the libration centres for captured particles, and the change in eccentricity if capture does not occur. Libration amplitudes are higher for larger initial eccentricity. The model allows for a complete description of a particle's behaviour as it successively encounters several resonances. The model is applicable to many scenarios, including (i) Planet migration through gas discs trapping other planets or planetesimals in resonances; (ii) Planet migration through a debris disc; (iii) Dust migration through PR drag. Full details can be found in \cite{2010submitted}. (Abridged)Comment: 4 pages, Proceedings of IAUS276 "The Astrophysics of Planetary Systems: Formation, Structure, and Dynamical Evolution

Aerodynamic characteristics of airplanes at high angles of attack

An introduction to, and a broad overiew of, the aerodynamic characteristics of airplanes at high angles of attack are provided. Items include: (1) some important fundamental phenomena which determine the aerodynamic characteristics of airplanes at high angles of attack; (2) static and dynamic aerodynamic characteristics near the stall; (3) aerodynamics of the spin; (4) test techniques used in stall/spin studies; (5) applications of aerodynamic data to problems in flight dynamics in the stall/spin area; and (6) the outlook for future research in the area. Although stalling and spinning are flight dynamic problems of importance to all aircraft, including general aviation aircraft, commercial transports, and military airplanes, emphasis is placed on military configurations and the principle aerodynamic factors which influence the stability and control of such vehicles at high angles of attack

Survival of Terrestrial Planets in the Presence of Giant Planet Migration

The presence of ``Hot Jupiters'', Jovian mass planets with very short orbital periods orbiting nearby main sequence stars, has been proposed to be primarily due to the orbital migration of planets formed in orbits initially much further from the parent star. The migration of giant planets would have profound effects on the evolution of inner terrestrial planets in these systems, and previous analyses have assumed that no terrestrial planets survive after migration has occurred. We present numerical simulations showing that a significant fraction of terrestrial planets could survive the migration process, eventually returning to circular orbits relatively close to their original positions. A fraction of the final orbits are in the Habitable Zone, suggesting that planetary systems with close-in giant planets are viable targets for searches for Earth-like habitable planets around other stars.Comment: 5 pages, 3 figures, emulateapj. ApJL in press, referee comments changes and edited for lengt

Results of recent NASA studies on automatic spin prevention for fighter aircraft

A broad based research program was developed to eliminate or minimize inadvertent spins for advanced military aircraft. Recent piloted simulator studies and airplane flight tests have demonstrated that the automatic control systems in use on current fighters can be tailored to provide a high degree of spin resistance for some configurations without restrictions to maneuverability. Such systems result in greatly increased tactical effectiveness, safety, and pilot confidence