σ-stability analysis of hydromagnetic instabilities in stars with toroidal magnetic fields

-stability analysis is used to investigate the adiabatic stability of a star containing an axisymmetric toroidal magnetic field. Necessary and sufficient conditions for -stability are derived. Special attention is devoted to the typical hydromagnetic instabilities that can be introduced by a weak toroidal magnetic field in a star that is stably stratified in the absence of any magnetic field. An expression for the maximum growth rate of instability is derived and the basic properties of the displacement fields associated with the instabilities are indicated.     

X-ray burst sources — A simple two zone model

With the help of a very simple two zone model, we demonstrate the possibility of periodic thermal relaxation (limit cycle) oscillations in the helium burning envelope of accreting neutron stars. Physically reasonable model parameters can be chosen which yield agreement with the observed features of x-ray bursts and we suggest that this limit cycle is operative in neutron stars which have an accretion rate in a specific range. For hydrogen burning a similar cycle is possible, but it operates at such high temperatures that an unrealistically large accretion rate would be required.     

The effect of a magnetic field on stellar pulsations as a singular perturbation problem

The perturbation problem that describes the effect of a weak magnetic field on stellar adiabatic oscillation is considered. This perturbation problem is singular when the magnetic field does not vanish at the stellar surface, and a regular perturbation scheme fails where the magnetic pressure is comparable to the thermodynamic pressure. The application of the Method of Matched Asymptotic Expansion is used to obtain expressions for the eigenfunctions and the eigenfrequencies.     

The morphology of the Martian surface

Most of the southern hemisphere of Mars is densely cratered and stands 1–3 km above the topographic datum. The northern hemisphere is more sparsely cratered and elevations are generally below the datum. A broad rise, the Tharsis bulge, centered at 14° S, 101° W, is 8000 km across and 10 km above the datum at its summit. The densely cratered terrain has two main components; very ancient crust, nearly saturated with large craters, and younger intercrater plains. In many areas the older unit is fractured and extensively dissected by small channels. The younger intercrater plains are distinctly layered in places and less dissected, less fractured, and less cratered. Both units probably date from very early in the planet's history. Cratered plains cover much of the northern hemisphere and are highly variegated. Those around the large volcanoes are covered with numerous volcanic flows whereas in other areas the plains are featureless except for craters and lunar mare-like ridges. Between 40° N and 60° N the plains are complex with various kinds of striped and patterned ground, low escarpments, and isolated irregularly shaped mesas. Their peculiar morphology has been attributed, in part, to the repeated deposition and removal of volatile-rich debris layers. Along the boundary between the northern plains and the densely cratered terrain to the south, the plains and cratered terrain complexly inter-finger. The old terrain forms the high ground and appears to have undergone mass wasting on a large scale. In several areas, particularly south of Chryse Planitia, the old, cratered surface has collapsed to form chaotic terrain. Large channels, tens of kilometers wide and hundreds of kilometers long, with numerous characteristics suggestive of catastrophic flooding, commonly emerge from the chaotic areas. Much of the area between 50° W and 180° W and 50° N and 50° S is cut by fractures radial to the center of the Tharsis bulge. The equatorial canyon system, Valles Marineris, is radial to the bulge and appears to have formed largely by faulting along the radial fractures, although it has also been extensively modified by various mass wasting and fluvial processes. Most but not all volcanoes are in the Tharsis and Elysium regions. The largest resemble terrestrial shield volcanoes except for scale; the edifices, flow features and calderas are all far larger than their terrestrial counterparts. Most impact craters on Mars are surrounded by layers of ejecta, each with a distil ridge. This unique morphology coupled with other surface characteristics suggests large amounts of ground ice. Layered deposits at both poles appear to be relatively young, volatile-rich, aeolian deposits. The north pole is also surrounded by a continuous belt of dunes several tens of kilometers across. In most other places, aeolian modification of the surface at a scale of several tens of meters appears slight despite annual global dust storms.     

Improved Feedback Loop for Adaptive Arrays

This paper is concerned with the problem of time constants in adaptive arrays. The paper presents a improved form of an adaptive array feedback loop, which has the property that its time constants are fixed. This property is an advantage over the well-known least mean square (LMS) loop, for which time constants depend on received signal power. Fixed time constants are of interest because they simplify dynamic range problems for adaptive arrays in communication and radar systems.     

Crossarray Beamforming with a Parametric Receiving Array and a Line Array

A beamforming technique involving cross correlation of the outputs of two directional arrays is investigated. The performance characteristics of the crossarray system are determined and related to the characteristics of the two individual arrays. It is found that the crossarray beam pattern is the average (in decibels) of the beam patterns of the individual arrays, and that the crossarray gain (rejection of spatially distributed noise) is 1.5 dB greater than the average (in decibels) of the individual array gains. The most interesting applications for this system may be those where the two arrays are quite different, as in the case of a parametric acoustic receiving array (PARRAY) and a broadside line array.     

Testing the Independence of Nonhomogeneous Rayleigh Clutter

Two attractive real-time implementation tests are presented that discriminate between correlated and uncorrelated clutter. A clutter model is assumed in which the envelope distribution within a cell is Rayleigh, but the mean clutter level fluctuates from cell to cell. Both the tests utilize observations made in pairs on two clutter envelopes corresponding to two consecutive azimuth sweeps. The results are applicable to real-time testing of the effectiveness of various decorrelation techniques employed by radar systems.     

M-ary CPSK Detection with Noisy Reference and Interferences

A general expression of the error probability on an M-ary coherent phase-shift-keyed (MCPSK) signal purturbed by a noisy reference carrier, multiple interferences, and additive Gaussian noise is presented taking into account the frequencey divider in the carrier recovery circuit. First, a new expression for the probability density function (pdf) of the phase of a composite wave of signal, multiple interferences, and additive Gaussian noise is derived. Then this result and a pdf of the phase error modified from the Tikhonov distribution are used to obtain the erro probability of an MCPSK detector. In addition, the comparison between the error probabilities with and without the frequency divider is given, and it is found that the estimation is more pessimistic when the frequency divider is included.     

A Gaussian Mixture PHD Filter for Jump Markov System Models

The probability hypothesis density (PHD) filter is an attractive approach to tracking an unknown and time-varying number of targets in the presence of data association uncertainty, clutter, noise, and detection uncertainty. The PHD filter admits a closed-form solution for a linear Gaussian multi-target model. However, this model is not general enough to accommodate maneuvering targets that switch between several models. In this paper, we generalize the notion of linear jump Markov systems to the multiple target case to accommodate births, deaths, and switching dynamics. We then derive a closed-form solution to the PHD recursion for the proposed linear Gaussian jump Markov multi-target model. Based on this an efficient method for tracking multiple maneuvering targets that switch between a set of linear Gaussian models is developed. An analytic implementation of the PHD filter using statistical linear regression technique is also proposed for targets that switch between a set of nonlinear models. We demonstrate through simulations that the proposed PHD filters are effective in tracking multiple maneuvering targets.