1,574 research outputs found
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 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
Attracted Diffusion-Limited Aggregation
In this paper, we present results of extensive Monte Carlo simulations of
diffusion-limited aggregation (DLA) with a seed placed on an attractive plane
as a simple model in connection with the electrical double layers. We compute
the fractal dimension of the aggregated patterns as a function of the
attraction strength \alpha. For the patterns grown in both two and three
dimensions, the fractal dimension shows a significant dependence on the
attraction strength for small values of \alpha, and approaches to that of the
ordinary two-dimensional (2D) DLA in the limit of large \alpha. For
non-attracting case with \alpha=1, our results in three dimensions reproduce
the patterns of 3D ordinary DLA, while in two dimensions our model leads to
formation of a compact cluster with dimension two. For intermediate \alpha, the
3D clusters have quasi-2D structure with a fractal dimension very close to that
of the ordinary 2D-DLA. This allows one to control morphology of a growing
cluster by tuning a single external parameter \alpha.Comment: 6 pages, 6 figures, to appear in Phys. Rev. E (2012
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