A Multiscale Model for Substorms

Most substorm researchers assume substorms to be caused by a unique large-scale process. However, a critical evaluation of substorm observations indicates that a new paradigm is needed to understand the substorm phenomenon and the magnetospheric dynamics in general. It is proposed here that substorms involve a number of physical processes covering over a wide range of spatial and temporal scales. Potential candidates include the kinetic or shear ballooning instability, the Kelvin-Helmholtz instability, the cross-field current instability, the tearing instability, and magnetic reconnection. An observational constraint on the qualified process for substorm onset is that it must be associated with magnetic field lines of auroral arcs since substorm onsets start with brightening of a pre-existing auroral arc. Which particular process dominates in a given substorm depends on the present and past states of the magnetosphere as well as the external solar wind. The magnetosphere is almost perpetually driven by the solar wind to be near a critical point and in a metastable state. Magnetospheric disturbances occur sporadically in multiple localized sites. A substorm is realized when the combined effect of these localized disturbances become global in extent, much like the system-wide activity in a sandpile or avalanche model.     

The influence of pressure on combustion intensity

The influence of pressure in the range of 3–15 kgf/cm² on combustion intensity is studied experimentally in a medium-sized rig. The apparatus is described and temperature measurements by different thermocouple techniques are discussed; gas composition was monitored by gas chromatography. The experiments were performed at different cross sections allowing to map temperatures and gas concentrations. The results show that temperature and carbon dioxide concentration increase more rapidly as the pressure is raised. Carbon monoxide appears as an intermediate and is concentrated near the combustion axis. The combustion zone becomes shorter with increasing pressure and the combustion intensity increases correspondingly.     

Kalman filtering for matrix estimation

A general discrete-time Kalman filter (KF) for state matrix estimation using matrix measurements is presented. The new algorithm evaluates the state matrix estimate and the estimation error covariance matrix in terms of the original system matrices. The proposed algorithm naturally fits systems which are most conveniently described by matrix process and measurement equations. Its formulation uses a compact notation for aiding both intuition and mathematical manipulation. It is a straightforward extension of the classical KF, and includes as special cases other matrix filters that were developed in the past. Beyond the analytical value of the matrix filter, it is shown through various examples arising in engineering problems that this filter can be computationally more efficient than its vectorized version.     

Spectroscopic observations of the early-type contact binary AW Lacertae

Spectroscopic observations were performed of the early-type contact binary AW Lac with an image-intensified coude spectrograph of 1.9-m telescope at the Okayama Astrophysical Observatory. A total of twenty-two spectra covering blue region with a dispersion of 16 Amm^-1 have been secured on Kodak IIa-O baked plates. In every spectra sharp interstellar CaII H,K lines are clearly seen. The spectral type of AW Lac has been estimated as early B, which substantially confirms the one adopted in the photometric analysis by Jiang et al. (1983) and is diffrent from A0 listed in General Catalogue of Variable Stars (Kholopov et al. 1985). Contrary to the suggestion by the photometric solution of Jiang et al., no definite secondary lines could be separated, though some indications of light contamination due to the secondary component are surely observed. This would imply that the light ratio of the components should be somewhat smaller than that derived by photometric analysis. No emission features appeared either. The measurement of radial velocities of the primary component for the orbital elements was made for twenty spectra by a conventional method. It was difficult to measure the radial velocities because the lines are quite broadened and deformed. Hence the measured values for the radial velocities should be regarded as rather preliminary. The derived spectroscopic elements, combined with the photometric data, give the absolute dimensions of the system for each assumed mass ratio q. For q = 1, being the adopted photometric solution by Jiang et al., we obtain too small value for the primary's mass, comparing with its spectral type. For the mass ratio as small as q = 0.6, we can obtain a reasonable value for the mass of the primary. However, in order to get more definite conclusion the cross-correlation method would be more appropriate for the spectroscopic analysis of this system.     

Tracking a maneuvering target using input estimation versus theinteracting multiple model algorithm

Two maneuvering-target tracking techniques are compared. The first, called input estimation, models the maneuver as constant unknown input, estimates its magnitude and onset time, and then corrects the state estimate accordingly. The second models the maneuver as a switching of the target state model, where the various state models can be of different dimension and driven by process noises of different intensities, and estimates the state according to the interacting multiple model (IMM) algorithm. While the first requires around twenty parallel filters, it is shown that the latter, implemented in the form of the IMM, performs equally well or better with two or three filters     

Geolocation of a known altitude object from TDOA and FDOA measurements

Most satellite systems for locating an object on Earth use only time difference of arrival (TDOA) measurements. When there are relative motions between an emitter and receivers, frequency difference of arrival (FDOA) measurements can be used as well. Often, the altitude of an object is known (it is zero, for example) or can be measured with an altimeter. Two sets of geolocation solutions are proposed which exploit the altitude constraint to improve the localization accuracy. One is for TDOAs alone and the other for the combination of TDOA and FDOA measurements. The additional complexity by imposing the constraint is a one-dimensional Newton's search and the rooting of a polynomial. The covariance matrices of the new estimators are derived under a small measurement noise assumption and shown to attain the constrained Cramer-Rao lower bound (CRLB). When there is a bias error in the assumed altitude, using the altitude constraint will introduce a bias to the solution. Since applying the constraint decreases the variance, there is a tradeoff between variance and bias in the mean square error (MSE). The maximum allowable altitude error such that the constraint solution will remain superior to the unconstraint is given. Simulation results are included to corroborate the theoretical development.