2,759 research outputs found
Critical sets of nonlinear Sturm-Liouville operators of Ambrosetti-Prodi type
The critical set C of the operator F:H^2_D([0,pi]) -> L^2([0,pi]) defined by
F(u)=-u''+f(u) is studied. Here X:=H^2_D([0,pi]) stands for the set of
functions that satisfy the Dirichlet boundary conditions and whose derivatives
are in L^2([0,pi]). For generic nonlinearities f, C=\cup C_k decomposes into
manifolds of codimension 1 in X. If f''0, the set C_j is shown to be
non-empty if, and only if, -j^2 (the j-th eigenvalue of u -> u'') is in the
range of f'. The critical components C_k are (topological) hyperplanes.Comment: 6 pages, no figure
Heating and acceleration of coronal and chromospheric ions during solar flares
One-dimensional, electrostatic, particle-in-cell simulations are used to explore two mechanisms proposed to explain turbulent broadening of soft x ray emission lines of heavy ions observed during solar flares and the presence of blue-shifted components. Results from the simulations are in qualitative agreement with the observations
Chromospheric-coronal coupling during solar flares: Current systems and particle acceleration
Two-dimensional (three velocity) electrostatic particle simulations are used to investigate the particle heating and acceleration associated with the impulsive phase of a solar flare. A crossfield current in the high corona (which is presumably driven by reconnection processes) is used to initiate the flare. Due to the differential motion of the electrons and ions, currents, and associated quasi-static electric fields are generated with the primary current and balancing return current being on adjacent field lines. These currents extend from the corona down into the chromosphere. Electrons can be accelerated to energies exceeding 100 keV on short time scales via the quasi-static fields and wave-particle interactions. The spectra of these electrons has a broken power-law distribution which hardens in time. The spatially separate primary and return currents are closed by the cross-field acceleration of the ambient ions into the primary current regions. These ions are then accelerated upwards into the corona by the same quasi-static electric field accelerating the electrons downwards. This acceleration can account for the broadened stationary and weak blue shifted component seen in soft x ray line emissions and enhancements in heavy ion abundances seen in the solar wind in associations with solar flares
Resolving on 100 pc scales the UV-continuum in Lyman- emitters between redshift 2 to 3 with gravitational lensing
We present a study of seventeen LAEs at redshift 23 gravitationally
lensed by massive early-type galaxies (ETGs) at a mean redshift of
approximately 0.5. Using a fully Bayesian grid-based technique, we model the
gravitational lens mass distributions with elliptical power-law profiles and
reconstruct the UV-continuum surface brightness distributions of the background
sources using pixellated source models. We find that the deflectors are close
to, but not consistent with isothermal models in almost all cases, at the
-level. We take advantage of the lensing magnification (typically
20) to characterise the physical and morphological properties of
these LAE galaxies. From reconstructing the ultra-violet continuum emission, we
find that the star-formation rates range from 0.3 to 8.5 M yr
and that the galaxies are typically composed of several compact and diffuse
components, separated by 0.4 to 4 kpc. Moreover, they have peak star-formation
rate intensities that range from 2.1 to 54.1 M yr kpc.
These galaxies tend to be extended with major axis ranging from 0.2 to 1.8 kpc
(median 561 pc), and with a median ellipticity of 0.49. This morphology is
consistent with disk-like structures of star-formation for more than half of
the sample. However, for at least two sources, we also find off-axis components
that may be associated with mergers. Resolved kinematical information will be
needed to confirm the disk-like nature and possible merger scenario for the
LAEs in the sample.Comment: 19 pages, 7 figures, accepted for publication on MNRA
ALMA imaging of SDP.81 - I. A pixelated reconstruction of the far-infrared continuum emission
We present a sub-50 pc-scale analysis of the gravitational lens system SDP.81
at redshift 3.042 using Atacama Large Millimetre/submillimetre Array (ALMA)
science verification data. We model both the mass distribution of the
gravitational lensing galaxy and the pixelated surface brightness distribution
of the background source using a novel Bayesian technique that fits the data
directly in visibility space. We find the 1 and 1.3 mm dust emission to be
magnified by a factor of u_tot = 17.6+/-0.4, giving an intrinsic total
star-formation rate of 315+/-60 M_sol/yr and a dust mass of 6.4+/-1.5*10^8
M_sol. The reconstructed dust emission is found to be non-uniform, but composed
of multiple regions that are heated by both diffuse and strongly clumped
star-formation. The highest surface brightness region is a ~1.9*0.7 kpc
disk-like structure, whose small extent is consistent with a potential
size-bias in gravitationally lensed starbursts. Although surrounded by extended
star formation, with a density of 20-30+/-10 M_sol/yr/kpc^2, the disk contains
three compact regions with densities that peak between 120-190+/-20
M_sol/yr/kpc^2. Such star-formation rate densities are below what is expected
for Eddington-limited star-formation by a radiation pressure supported
starburst. There is also a tentative variation in the spectral slope of the
different star-forming regions, which is likely due to a change in the dust
temperature and/or opacity across the source.Comment: MNRAS accepted 2015 April 1
A novel search for gravitationally lensed radio sources in wide-field VLBI imaging from the mJIVE-20 survey
We present a novel pilot search for gravitational lenses in the mJIVE-20
survey, which observed radio sources selected from FIRST with the
VLBA at an angular resolution of 5 mas. We have taken the visibility data for
an initial sources that were detected by the mJIVE-20 observations and
re-mapped them to make wide-field images, selecting fourteen sources that had
multiple components separated by mas, with a flux-ratio of
: and a surface brightness consistent with gravitational lensing.
Two of these candidates are re-discoveries of gravitational lenses found as
part of CLASS. The remaining twelve candidates were then re-observed at 1.4 GHz
and then simultaneously at 4.1 and 7.1 GHz with the VLBA to measure the
spectral index and surface brightness of the individual components as a
function of frequency. Ten were rejected as core-jet or core-hotspot(s)
systems, with surface brightness distributions and/or spectral indices
inconsistent with gravitational lensing, and one was rejected after lens
modelling demonstrated that the candidate lensed images failed the parity test.
The final lens candidate has an image configuration that is consistent with a
simple lens mass model, although further observations are required to confirm
the lensing nature. Given the two confirmed gravitational lenses in the
mJIVE-20 sample, we find a robust lensing-rate of :() for a
statistical sample of 635 radio sources detected on mas-scales, which is
consistent with that found for CLASS.Comment: 31 pages, 22 figures; accepted for publication in MNRA
The Toda hierarchy and the KdV hierarchy
The Toda hierarchy of size is well known to be analogous to the KdV
hierarchy at goes to infinity. This paper shows that given a periodic
function, there is a canonical way of defining the initial data for the Toda
lattice equations so that the evolution of this data under the Toda lattice
hierarchy looks asymptotically like the evolution of under the KdV
hierarchy. Further, the conserved quantities of and those of the Toda
hierarchy match.Comment: AMSTe
ISSUES IN NONMARKET VALUATION AND POLICY APPLICATION: A RETROSPECTIVE GLANCE
While issues in estimating nonmarket values continue to cause concern, resource economists have more reason now than ever before to be optimistic. More progress toward improved measurement has been made in the past six years than in the previous quarter century since development of the contingent valuation and travel cost methods. The new challenge is to learn how to adjust past studies to estimate nonmarket values for future policy analysis. The process involves developing an understanding of the important variables that explain the observed difference in estimates. This paper illustrates how the results thus far could be adjusted to develop some tentative estimates of the recreation-use value of Forest Service resources.Research Methods/ Statistical Methods, Resource /Energy Economics and Policy,
THE VALUE OF SPORT FISHING IN THE SNAKE RIVER BASIN OF CENTRAL IDAHO
The value of sportfishing in the Snake River Basin in Central Idaho was measured using a two-stage/disequilibrium travel model. The two-stage/disequilibrium model does not require monetization of recreationists? travel time as required of traditional equilibrium labor market travel cost models. The model was estimated using Poisson regression, appropriate for count data when over-dispersion is absent, and adjusted for endogenous stratification (self selection bias) . Contrary to expectations that anglers living close to the sites with low values would be over represented in the sample, the endogenous stratification adjustment caused estimated consumers surplus to decline from 35 after adjustment. The average number of sportfishing trips per year was 6.72, resulting in an average annual willingness-to-pay of $236 per year per angler.Resource /Energy Economics and Policy,
ALMA imaging of SDP.81 - II. A pixelated reconstruction of the CO emission lines
We present a sub-100 pc-scale analysis of the CO molecular gas emission and
kinematics of the gravitational lens system SDP.81 at redshift 3.042 using
Atacama Large Millimetre/submillimetre Array (ALMA) science verification data
and a visibility-plane lens reconstruction technique. We find clear evidence
for an excitation dependent structure in the unlensed molecular gas
distribution, with emission in CO (5-4) being significantly more diffuse and
structured than in CO (8-7). The intrinsic line luminosity ratio is r_8-7/5-4 =
0.30 +/- 0.04, which is consistent with other low-excitation starbursts at z ~
3. An analysis of the velocity fields shows evidence for a star-forming disk
with multiple velocity components that is consistent with a
merger/post-coalescence merger scenario, and a dynamical mass of M(< 1.56 kpc)
= 1.6 +/- 0.6 x 10^10 M_sol . Source reconstructions from ALMA and the Hubble
Space Telescope show that the stellar component is offset from the molecular
gas and dust components. Together with Karl G. Jansky Very Large Array CO (1-0)
data, they provide corroborative evidence for a complex ~2 kpc-scale starburst
that is embedded within a larger ~15 kpc structure.Comment: MNRAS accepted, 6th July 201
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