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-α\alpha emitters between redshift 2 to 3 with gravitational lensing

We present a study of seventeen LAEs at redshift 2$<z<$3 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 $2\sigma$-level. We take advantage of the lensing magnification (typically $\mu\simeq$ 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$_{\odot}$ yr$^{-1}$ 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$_{\odot}$ yr$^{-1}$ kpc$^{-2}$. 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 $24\,903$ radio sources selected from FIRST with the VLBA at an angular resolution of 5 mas. We have taken the visibility data for an initial $3\,640$ 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 $\geq100$ mas, with a flux-ratio of $\leq15$:$1$ 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 $1$:($318\pm225$) 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 $N$ is well known to be analogous to the KdV hierarchy at $N$ goes to infinity. This paper shows that given $f$ 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 $f$ under the KdV hierarchy. Further, the conserved quantities of $f$ and those of the Toda hierarchy match.Comment: AMSTe

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 $42 per person per trip before adjustment for endogenous stratification to$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,

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,

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