Stochastic Dynamic System Suboptimal Control with Uncertain Parameters

The control of a linear system with random coefficients is studied here. The cost function is of a quadratic form and the random coefficients are assumed to be partially observable by the controller. By means of the stochastic Bellman equation, the optimal control of stochastic dynamic models with partially observable coefficients is derived. The optimal control is shown to be a linear function of the observable states and a nonlinear function of random parameters. The theory is applied to an optimal control design of an aircraft landing in wind gust.     

Nonlinear Adaptive Control of a Synchronous Machine

A nonlinear adaptive controller for a load-commutated brushless dc machine that allows the machine to develop high torque over a wide range of operating conditions, while satisfying voltage and current constraints on both stator and field circuits, is presented. The approach taken is fundamentally different from past work in that a nonlinear control is formulated from the steady-state model of the synchronous machine. Adaptive algorithms are presented for both the unknown load and motor cases.     

UVCS Observations and Modeling of Streamers

We present results derived from the analysis of an equatorial streamer structure as observed by the UVCS instrument aboard SOHO. From observations of the H I Lyα and Lyβ lines we infer the density and temperature of the plasma. We develop a preliminary axisymmetric, magnetostatic model of the corona which includes the effects of gas pressure gradients on the magnetic structure. We infer a coronal plasma β > 1 in the closed field regions and near the cusp of the streamer. We add to the model a parallel velocity field assuming mass flux conservation along magnetic flux tubes. We then compute the Lyα emissivity and the line-of-sight integrals to obtain images of Lyα intensity, taking into account projection effects and Doppler dimming. The images we obtain from this preliminary model are in good general agreement with the UVCS observations, both qualitatively and quantitatively. This revised version was published online in June 2006 with corrections to the Cover Date.     

Composition Variations in the Solar Corona and Solar Wind

Order of magnitude variations in relative elemental abundances are observed in the solar corona and solar wind. The instruments aboard SOHO make it possible to explore these variations in detail to determine whether they arise near the solar surface or higher in the corona. A substantial enhancement of low First Ionization Potential (FIP) elements relative to high FIP elements is often seen in both the corona and the solar wind, and that must arise in the chromosphere. Several theoretical models have been put forward to account for the FIP effect, but as yet even the basic physical mechanism responsible remains an open question. Evidence for gravitational settling is also found at larger heights in quiescent streamers. The question is why the heavier elements don't settle out completely. This revised version was published online in June 2006 with corrections to the Cover Date.     

Streamer Evaporation

Streamer evaporation is the consequence of heating in ideal MHD models because plasma is weakly contained by the magnetic field. Heating causes inflation, opening of field lines, and release of solar wind. It was discovered in simulations and, due to the absence of loss mechanisms, the ultimate end point is the complete evaporation of the streamer. Of course streamers do not behave in this way because of losses by thermal conduction and radiation. Heating is also expected to depend on ambient conditions. We use a global MHD model with thermal conduction to examine the effect of changing the heating scale height. We also extend an analytic model of streamers developed by Pneuman (1968) to show that steady streamers are unable to contain plasma for temperatures near the cusp greater than ∼ 2 × 10⁶ K. This revised version was published online in June 2006 with corrections to the Cover Date.     

UVCS/SOHO Observations of Spectral Line Profiles in Polar Coronal Holes

Ultraviolet emission line profiles have been measured on 15-29 September 1997 for H I 1216 Å, O VI 1032, 1037 Å and Mg X 625 Å in a polar coronal hole, at heliographic heights ? (in solar radii) between 1.34 and 2.0. Observations of H I 1216 Å and the O VI doublet from January 1997 for ? = 1.5 to 3.0 are provided for comparison. Mg X 625 Å is observed to have a narrow component at ? = 1.34 which accounts for only a small fraction of the observed spectral radiance, and a broad component that exists at all observed heights. The widths of O VI broad components are only slightly larger than those for H I at ? = 1.34, but are significantly larger at ? = 1.5 and much larger for ? > 1.75. In contrast, the Mg X values are less than those of H I up to 1.75 and then increase rapidly up to at least ? = 2.0, but never reach the values of O VI.     

Soho Observations of Density Fluctuations in Coronal Holes

In recent UVCS/SOHO White Light Channel (WLC) observations we found quasi-periodic variations in the polarized brightness (pB) in the polar coronal holes at heliocentric distances of 1.9 to 2.45 solar radii. The motivation for the observation is the 2.5D MHD model of solar wind acceleration by nonlinear waves, that predicts compressive fluctuations in coronal holes. In February 1998 we performed new observations using the UVCS/WLC in the coronal hole and obtained additional data. The new data corroborate our earlier findings with higher statistical significance. The new longer observations show that the power spectrum peaks in the 10–12 minute range. These timescales agree with EIT observations of brightness fluctuations in polar plumes. We performed preliminary LASCO/C2 observations in an effort to further establish the coronal origin of the fluctuations. This revised version was published online in June 2006 with corrections to the Cover Date.     

3D nonlinear wave heating of coronal loops

The heating of solar coronal loops by the resonant absorption or phase-mixing of incident wave energy is investigated in the framework of 3D nonlinear magnetohydrodynamics (MHD) by means of numerical simulations.     

Stellar flares

Radio and X-ray observations of stellar flares provide the most direct probes of energy relaase particle acceleration, and energy transport on stars other than the Sun. In this review, the observational basis for our understanding of the flare phenomenon on other stars is briefly described and outstanding interpretive and theoretical issues are discussed. I shall confine my attention to objects which are solar-like, to the extent that they possess deep convective envelopes and display activity which is presumed to be magnetic in origin. These include pre-main sequence objects, classical flare stars, and close binaries. Future directions are briefly discussed.