Differential equations for generalized Jacobi polynomials

We look for spectral type differential equations satisfied by the generalized Jacobi polynomials, which are orthogonal on the interval [-1,1] with respect to a weight function consisting of the classical Jacobi weight function together with two point masses at the endpoints of the interval of orthogonality. We show that such a differential equation is uniquely determined and we give explicit representations for the coefficients. In case of nonzero mass points the order of this differential equation is infinite, except for nonnegative integer values of (one of) the parameters. Otherwise, the finite order is explictly given in terms of the parameters.Comment: 33 pages, submitted for publicatio

Laser scattering by density fluctuations of ultra-cold atoms in a magneto-optical trap

We study the spectrum of density fluctuations in the ultra-cold gas of neutral atoms, confined in a magneto-optical trap. We determine the corresponding amplitude and spectra of laser light scattered by this medium. We derive an expression for the dynamical structure function, by using a test particle method. We propose to use the collective laser scattering as a diagnostic method for the microscopic properties of the ultra-cold matter. This will also allow us to check on the atomic correlations which are mediated by the collective mean field inside the gas.Comment: J. Phys. B (in press

Three Dimensional Structure and Energy Balance of a Coronal Mass Ejection

The Ultraviolet Coronagraph Spectrometer (UVCS) observed Doppler shifted material of a partial Halo Coronal Mass Ejection (CME) on December 13 2001. The observed ratio of [O V]/O V] is a reliable density diagnostic important for assessing the state of the plasma. Earlier UVCS observations of CMEs found evidence that the ejected plasma is heated long after the eruption. We have investigated the heating rates, which represent a significant fraction of the CME energy budget. The parameterized heating and radiative and adiabatic cooling have been used to evaluate the temperature evolution of the CME material with a time dependent ionization state model. The functional form of a flux rope model for interplanetary magnetic clouds was also used to parameterize the heating. We find that continuous heating is required to match the UVCS observations. To match the O VI-bright knots, a higher heating rate is required such that the heating energy is greater than the kinetic energy. The temperatures for the knots bright in Ly$\alpha$ and C III emission indicate that smaller heating rates are required for those regions. In the context of the flux rope model, about 75% of the magnetic energy must go into heat in order to match the O VI observations. We derive tighter constraints on the heating than earlier analyses, and we show that thermal conduction with the Spitzer conductivity is not sufficient to account for the heating at large heights.Comment: 40 pages, 16 figures, accepted for publication in ApJ For associated mpeg file, please see https://www.cora.nwra.com/~jylee/mpg/f5.mp

A Self-Consistent Marginally Stable State for Parallel Ion Cyclotron Waves

We derive an equation whose solutions describe self-consistent states of marginal stability for a proton-electron plasma interacting with parallel-propagating ion cyclotron waves. Ion cyclotron waves propagating through this marginally stable plasma will neither grow nor damp. The dispersion relation of these waves, {\omega} (k), smoothly rises from the usual MHD behavior at small |k| to reach {\omega} = {\Omega}p as k \rightarrow \pm\infty. The proton distribution function has constant phase-space density along the characteristic resonant surfaces defined by this dispersion relation. Our equation contains a free function describing the variation of the proton phase-space density across these surfaces. Taking this free function to be a simple "box function", we obtain specific solutions of the marginally stable state for a range of proton parallel betas. The phase speeds of these waves are larger than those given by the cold plasma dispersion relation, and the characteristic surfaces are more sharply peaked in the v\bot direction. The threshold anisotropy for generation of ion cyclotron waves is also larger than that given by estimates which assume bi-Maxwellian proton distributions.Comment: in press in Physics of Plasma

Gamma-Ray Burst Afterglow: Polarization and Analytic Light Curves

GRB afterglow polarization is discussed. We find an observable, up to 10%, polarization, if the magnetic field coherence length grows at about the speed of light after the field is generated at the shock front. Detection of a polarized afterglow would show that collisionless ultrarelativistic shocks can generate strong large scale magnetic fields and confirm the synchrotron afterglow model. Non-detection, at a 1% level, would imply that either the synchrotron emission model is incorrect, or that strong magnetic fields, after they are generated in the shock, somehow manage to stay un-dissipated at ``microscopic'', skin depth, scales. Analytic lightcurves of synchrotron emission from an ultrarelativistic self-similar blast wave are obtained for an arbitrary electron distribution function, taking into account the effects of synchrotron cooling. The peak synchrotron flux and the flux at frequencies much smaller than the peak frequency are insensitive to the details of the electron distribution function; hence their observational determination would provide strong constraints on blast wave parameters.Comment: 19 pages, submitted to Ap

The Anatomy of Last Glacial Maximum (LGM) Climate Change in the Southern Hemisphere Mid-Latitudes: Paleoecological Temperature Reconstructions from Terrestrial Archives

The objective of this research is to test if leading hypotheses about drivers of global ice ages explain climate change in the Southern Hemisphere mid-latitudes. The research establishes the timing, magnitude, and structure of southern mid-latitude Last Glacial Maximum climate from two sites bordering the Southern Alps, New Zealand, by reconstructing temperature changes from continuous, isotopically dated, paleo-chironomid and pollen re-cords. Hypotheses about what drives ice age climate change remain clouded with ambiguities because the timing and magnitude of maximum ice age cooling (Last Glacial Maximum, LGM) does not appear to match between the Northern and Southern Hemispheres. Northern solar insolation is held responsible for driving Southern Hemisphere climate changes even though the intensity and duration of southern insolation is out of phase with that of the north. Apparent mismatches in the timing of LGM climate changes between the hemispheres cannot be adequately explained by northern insolation forcing alone. High resolution records of the precise timing and magnitude of climate change in the mid-latitudes of the Southern Hemisphere are strategic for understanding the forces driving global glacial cycles and identifying interhemispheric leads and lags in the climate system. Terrestrial archives (lake sediment) from southern New Zealand are ideal for such research because the region is sensitive to subtle changes in the circumpolar westerlies and supports distinct vegetation and chironomid (non-biting midge fly) ecological zones. Pollen and chironomids from this region have known relationships to temperature and can provide continuous, datable, quantitative estimates of terrestrial temperature change. This research has two primary goals: 1) to develop paleotemperature reconstructions for the western and eastern margins of the Southern Alps from two lakes located outside LGM moraine belts using pollen and chironomid temperature inference models, and 2) to determine the precise timing and duration of LGM climate changes for this location using detailed AMS radiocarbon dating. The project will provide a comprehensive paleoclimate data set that will be directly applicable to testing hypotheses about forcing mechanisms responsible for major climate changes. The proposed research will provide training opportunities for four undergraduate students per semester. It will develop and enhance collaborative ties between the University of Maine and several New Zealand institutions. Benefits to society include documenting the temporal and spatial extent and magnitude of climatological phenomena to better understand the LGM climate of the southern mid-latitudes and testing the viability of several hypotheses about mechanisms that drive ice age change

Determining Patterns of Abrupt Climate Change during the Last Glacial-Interglacial Transition (LGIT) in the Southern Hemisphere

This proposal will fund the development of a continuous, isotopically-dated paleochironomid and pollen record of deglacial climate fluctuations from lake sediments located in climatically sensitive sites along the Southern Alps, New Zealand. Detailed investigations will be carried out for the Last Glacial-Interglacial Transition (LGIT) at Boundary Stream Tarn, Quagmire Tarn, and Kettlehole Bog to establish the sequence of deglacial climate events and to facilitate comparisons with other well-dated northern and southern records. The primary scientific objectives of the project are to determine: 1) the pattern and magnitude of past climate change; 2) whether changes recorded show an in-phase or out-of-phase relationship with the Northern Hemisphere; and 3) whether the Antarctic signature extends into the southwest Pacific region. These results will facilitate differentiation among viable hypotheses concerning abrupt global climate change. Detailed chironomid analysis, interpreted by a newly developed chironomid-temperature transfer function, will be carried out on Quagmire Tarn and Kettlehole Bog LGIT-age sediment and pollen analysis will be conducted on Quagmire Tarn. This project will provide the opportunity for three undergraduate students to conduct independent research. The project will also enhance greater understanding in global paleoclimatology and provide opportunities for collaboration among researchers through the publication of a photographic key to fossil chironomids

Kinetic instability of drift-Alfven waves in solar corona and stochastic heating

The solar atmosphere is structured and inhomogeneous both horizontally and vertically. The omnipresence of coronal magnetic loops implies gradients of the equilibrium plasma quantities like the density, magnetic field and temperature. These gradients are responsible for the excitation of drift waves that grow both within the two-component fluid description (in the presence of collisions and without it) and within the two-component kinetic descriptions (due to purely kinetic effects). In the present work the effects of the density gradient in the direction perpendicular to the magnetic field vector are investigated within the kinetic theory, in both electrostatic and electromagnetic regimes. The electromagnetic regime implies the coupling of the gradient-driven drift wave with the Alfven wave. The growth rates for the two cases are calculated and compared. It is found that, in general, the electrostatic regime is characterized by stronger growth rates, as compared with the electromagnetic perturbations. Also discussed is the stochastic heating associated with the drift wave. The released amount of energy density due to this heating should be more dependent on the magnitude of the background magnetic field than on the coupling of the drift and Alfven waves. The stochastic heating is expected to be much higher in regions with a stronger magnetic field. On the whole, the energy release rate caused by the stochastic heating can be several orders of magnitude above the value presently accepted as necessary for a sustainable coronal heating.Comment: To appear in ApJ (2010

Suppression of energetic electron transport in flares by double layers

During flares and coronal mass ejections, energetic electrons from coronal sources typically have very long lifetimes compared to the transit times across the systems, suggesting confinement in the source region. Particle-in-cell simulations are carried out to explore the mechanisms of energetic electron transport from the corona to the chromosphere and possible confinement. We set up an initial system of pre-accelerated hot electrons in contact with ambient cold electrons along the local magnetic field, and let it evolve over time. Suppression of transport by a nonlinear, highly localized electrostatic electric field (in the form of a double layer) is observed after a short phase of free-streaming by hot electrons. The double layer (DL) emerges at the contact of the two electron populations. It is driven by an ion-electron streaming instability due to the drift of the back-streaming return current electrons interacting with the ions. The DL grows over time and supports a significant drop in temperature and hence reduces heat flux between the two regions that is sustained for the duration of the simulation. This study shows transport suppression begins when the energetic electrons start to propagate away from a coronal acceleration site. It also implies confinement of energetic electrons with kinetic energies less than the electrostatic energy of the DL for the DL lifetime, which is much longer than the electron transit time through the source region

RISK-RETURN ANALYSIS OF INCORPORATING ANNUAL LEGUMES AND LAMB GRAZING WITH DRYLAND CROP ROTATIONS

Profitability and risk, 1988-2001, are examined for lamb-grazed field pea as a fallow alternative with wheat, or an extended wheat-sunflower-millet rotation. Switching from conventional wheat-fallow to an extended rotation with grazed-peas increases profitability (2.3% to 7.3%), and reduces risk (below 0% target in only 2 versus 7 of 14 years).Crop Production/Industries,