A Comparison of Numerical Methods for Solving Optimal Control Problems

Linear systems with quadratic performance criteria typically lead to two-point boundary value problems. The numerical solution of such problems is often difficult because of roundoff and truncation errors. In this paper numerical methods for digital computer solutions are considered for a system described by a given second-order linear differential equation and the results are compared. The results show that where accurate analytic solutions cannot be obtained, the invariant imbedding technique yields more accurate results, for a given integration grid interval, than the other methods considered.     

MHD ANALYSIS OF PETSCHEK-TYPE RECONNECTION IN NON-UNIFORM FIELD AND FLOW GEOMETRIES

Analytical studies of reconnection have, for the most part, been confined to steady and uniform current sheet geometries. In contrast to these implifications, natural phenomena associated with the presence of current sheets indicate highly non-uniform structure and time-varying behaviour. Examples include the violent outbursts of energy on the Sun known as solar flares, and magnetospheric phenomena such as flux transfer events, plasmoids, and auroral activity. Unlike the theoretical models, reconnection therefore occurs in a highly dynamic and structured plasma environment. In this article we review the mathematical tools and techniques which are available to formulate models capable of describing the effects of reconnection in such situations. We confine attention to variants of the reconnection model first discussed by Petschek in the 1960s, in view of its successful application in predicting and interpreting phenomena in the terrestrial magnetosphere. The analysis of Petschek-type reconnection is based on the equations of ideal magnetohydrodynamics (MHD), which describe the large-scale behaviour of the magnetic field and plasma flow outside the diffusion region, which we determine as a localised part of the current sheet in which reconnection is initiated. The approach we adopt here is to transform the MHD equations into a Lagrangian or so-called 'frozen-in' coordinate system. In this coordinate system, the equation of motion transforms into a set of coupled nonlinear equations, in which the presence of inhomogeneous magnetic fields and/or plasma flows gives rise to a term similar to that which appears in the study of the ordinary string equation in a non-homogeneous medium. As demonstrated here, this approach not only clarifies and highlights the effects of such non-uniformities, it also simplifies the solution of the original set of MHD equations. In particular, this is true for those types of problem in which the total pressure can be considered as a known quantity from the outset. To illustrate the method, we solve several 2D problems involving magnetic field and flow non-uniformities: reconnection in a stagnation-point flow geometry with antiparallel magnetic fields; reconnection in a Y-type magnetic field geometry with and without velocity shear across the current sheet; and reconnection in a force-free magnetic field geometry with field lines of the form xy = const. These case examples, chosen for their tractability, each incorporate some aspects of the field and flow geomtries encountered in solar-terrestrial applications, and they provide a starting point for further analytical as well as numerical studies of reconnection.     

Resonant inverters for photovoltaic array to utility interface

A number of high-frequency link power converter schemes suitable for interconnecting a photovoltaic (PV) array to the utility line using resonant inverters are presented. Use of high-frequency resonant inverters (HFRI) results in reduced size, weight and cost. Scheme 1 uses the HFRI-cycloconverter, scheme 2 uses the HFRI-rectifier pulsewidth-modulated voltage source inverter, scheme 3 uses the HFRI-rectifier line commutated inverter working with a fixed maximum possible inverting fringe angle, and scheme 4 uses the HFRI-rectifier line-connected inverter (with line current modulation). These schemes are compared. Based on the comparison, scheme 3 was selected for an initial study. To overcome various problems associated with scheme 3, the line current is modulated sinusoidally in scheme 4. In this scheme, the HFRI is controlled appropriately to obtain a rectified sine wave of 120 Hz in the DC link and the function of the line-connected inverter is to unfold this waveform on alternate half cycles to obtain a sinusoidal line current with the line voltage. Methods of commutation of the line connected inverter are explained. Experimental results obtained with scheme 4 are presented     

Spatio-temporal pattern recognition using hidden Markov models

A spatio-temporal method for identifying objects contained in an image sequence is presented. The Hidden Markov Model (HMM) technique is used as the classification algorithm, making classification decisions based on a spatio-temporal sequence of observed object features. A five class problem is considered. Classification accuracies of 100% and 99.7%, are obtained for sequences of images generated over two separate regions of viewing positions. HMMs trained on image sequences of the objects moving in opposite directions showed a 98.1% successful classification rate by class and direction of movement. The HMM technique proved robust to image corruption with additive correlated noise and had a higher accuracy than a single-look nearest neighbor method. A real image sequence of one of the objects used was successfully recognized with the HMMs trained on synthetic data. This study shows the temporal changes that observed feature vectors undergo due to object motion hold information that can yield superior classification accuracy when compared with single-frame techniques     

Remote Sensing of H from Ulysses and Galileo

We model interplanetary H Lyman-α (Lα) observations from Galileo UVS (Ultraviolet Spectrometer) and EUVS (Extreme Ultraviolet Spectrometer) (Hord et al., 1992) and the Ulysses interstellar neutral gas (GAS) instrument (Witte et al., 1992). EUVS measurements near solar maximum (max) in 1990–1992 have a peaked brightness maximum upwind due to a rather isotropic solar wind charge-exchange ionization pattern (A=0–0.25). GAS measurements from solar minimum (min) in 1997 have a plateau in the upwind direction that we model using Ulysses SWOOPS (solar wind plasma experiment) solar min data on solar wind density and velocity at different heliographic latitudes. The isotropic ionization pattern deduced from EUVS at solar max may be consistent with recent SWOOPS results (McComas et al., 2000b, c) that high speed solar wind is absent at high latitudes during solar max. Galileo and Ulysses Lα data favor higher H temperatures (15 000–18 000 K) than previous models. This revised version was published online in August 2006 with corrections to the Cover Date.     

Proton phase space densities (0.5eV<Ep<5MeV) at midlatitudes from Ulysses SWICS/HI-SCALE measurements

Proton phase space densities in the solar wind frame from suprathermal velocities 10 km s^–1 to 30,000 km s^–1 (0.5 eV–5 MeV) were derived from combined SWICS and HISCALE measurements when Ulysses was at 5 AU and –24° heliolatitude. The period (19–23 January 1993) encompasses a forward/reverse shock pair (20 January, 0500 UT and 22 January, 0300 UT). Strong evidence is found for shock acceleration of pickup protons from interstellar hydrogen at all energies measured.     

THE CLUSTER ION SPECTROMETRY (CIS) EXPERIMENT

The Cluster Ion Spectrometry (CIS) experiment is a comprehensive ionic plasma spectrometry package on-board the four Cluster spacecraft capable of obtaining full three-dimensional ion distributions with good time resolution (one spacecraft spin) with mass per charge composition determination. The requirements to cover the scientific objectives cannot be met with a single instrument. The CIS package therefore consists of two different instruments, a Hot Ion Analyser (HIA) and a time-of-flight ion COmposition and DIstribution Function analyser (CODIF), plus a sophisticated dual-processor-based instrument-control and Data-Processing System (DPS), which permits extensive on-board data-processing. Both analysers use symmetric optics resulting in continuous, uniform, and well-characterised phase space coverage. CODIF measures the distributions of the major ions (H⁺, He⁺, He⁺⁺, and O⁺) with energies from ~0 to 40 keV/e with medium (22.5°) angular resolution and two different sensitivities. HIA does not offer mass resolution but, also having two different sensitivities, increases the dynamic range, and has an angular resolution capability (5.6° × 5.6°) adequate for ion-beam and solar-wind measurements.     

Digital Communication Systems in Impulsive Atmospheric Radio Noise

Analyses are presented of the performance of binary and M-ary coherent and noncoherent communication systems operating in the impulsive atmospheric radio noise environment. The receiver is usually a maximum likelihood detector for white Gaussian interference and therefore has the form of a parallel bank of matched filters followed by decision circuitry. By employing a Poisson or generalized Shot noise model for the impulsive noise with a suitable probability density function (pdf), closed-form expressions and bounds of error probabilities for M-ary noncoherent and coherent amplitude-shift keying (ASK), phase-shift keying (PSK), and frequency-shift keying (FSK) systems are obtained and the results discussed.     

ETS-II Experiments Part III: Weather Radar System

The weather radar system used in conjunction with Earth-satellite propagation experiments for quantifying rainfall rate in a unit volume, determined by the beamwidth and the pulselength, is described. Firstly, methods for deriving rainfall rate per unit volume are stated in detail with special emphasis on calibration to determine unknown parameters associated with propagation losses in waveguides and the atmosphere. The calibration method is somewhat different from a conventional one but is useful for routine observation. Secondly, in addition to a simple explanation of the hardware of this radar system, the data modes, developed for measuring rainfall rate along the propagation path and radar reflectivity factor in the horizontal and vertical cross sections around the station are described. These data modes are effectively combined by the operational scanning modes for routine observation of propagation experiments, while each data mode can also be operated independently. Examples obtained by each data mode are also given.