arXiv subjects
Publications and source records attributed to Mark Allen.
We study a fractional analogue of a plasma problem arising from physics. Specifically, for a fixed bounded domain $Ω$ we study solutions to the eigenfunction equation \[ (- Δ)^s u = λ(u- γ)_+ \] with $u \equiv 0$ on $\partial Ω$.
We study regularity for a parabolic problem with fractional diffusion in space and a fractional time derivative. Our main result is a De Giorgi-Nash-Moser Holder regularity theorem for solutions in a divergence form equation. We also prove results regarding existence, uniqueness, and higher regularity in time.
We study minimizers of the functional $$ \int_{B_1^+}|\nabla u|^2 x_n^a\,d x +2\int_{B_1'} (λ_+ u^++λ_- u^-)\,d x', $$ for $a\in(-1,1)$. The problem arises in connection with heat flow with control on the boundary. It can also be seen as a non-local analogue of the, by now well studied, two-phase obstacle problem. Moreover, when $u$ does not change signs this is equivalent to the fractional obstacle problem. Our main results are the optimal regularity of the minimizer and the separation of the two free boundaries $Γ^+=\partial'\{u(\cdot,0)>0\}$ and $Γ^-=\partial'\{u(\cdot,0)<0\}$ when $a\geq 0$.
The Photometry Data Model (PhotDM) standard describes photometry filters, photometric systems, magnitude systems, zero points and its interrelation with the other IVOA data models through a simple data model. Particular attention is given necessarily to optical photometry where specifications of magnitude systems and photometric zero points are required to convert photometric measurements into physical flux density units.
We use the chemical evolution predictions of cosmological hydrodynamic simulations with our latest theoretical stellar population synthesis, photoionization and shock models to predict the strong line evolution of ensembles of galaxies from z=3 to the present day. In this paper, we focus on the brightest optical emission-line ratios, [NII]/H-alpha and [OIII]/H-beta. We use the optical diagnostic Baldwin-Phillips-Terlevich (BPT) diagram as a tool for investigating the spectral properties of ensembles of active galaxies. We use four redshift windows chosen to exploit new near-infrared multi-object spectrographs. We predict how the BPT diagram will appear in these four redshift windows given different sets of assumptions. We show that the position of star-forming galaxies on the BPT diagram traces the ISM conditions and radiation field in galaxies at a given redshift. Galaxies containing AGN form a mixing sequence with purely star-forming galaxies. This mixing sequence may change dramatically with cosmic time, due to the metallicity sensitivity of the optical emission-lines. Furthermore, the position of the mixing sequence may probe metallicity gradients in galaxies as a function of redshift, depending on the size of the AGN narrow line region. We apply our latest slow shock models for gas shocked by galactic-scale winds. We show that at high redshift, galactic wind shocks are clearly separated from AGN in line ratio space. Instead, shocks from galactic winds mimic high metallicity starburst galaxies. We discuss our models in the context of future large near-infrared spectroscopic surveys.
We study two phase problems posed over a two dimensional cone generated by a smooth curve $γ$ on the unit sphere. We show that when $length(γ)<2π$ the free boundary avoids the vertex of the cone. When $length(γ) \geq 2π$ we provide examples of minimizers such that the vertex belongs to the free boundary.
This paper studies local properties of a two phase free boundary problem for the fractional Laplacian. The main result states that the two free boundaries of the positive and negativity sets cannot touch.
We have derived disk scale lengths for 30374 non-interacting disk galaxies in all five SDSS bands. Virtual Observatory methods and tools were used to define, retrieve, and analyse the images for this unprecedentedly large sample classified as disk/spiral galaxies in the LEDA catalogue. Cross correlation of the SDSS sample with the LEDA catalogue allowed us to investigate the variation of the scale lengths for different types of disk/spiral galaxies. We further investigat asymmetry, concentration, and central velocity dispersion as indicators of morphological type, and are able to assess how the scale length varies with respect to galaxy type. We note however, that the concentration and asymmetry parameters have to be used with caution when investigating type dependence of structural parameters in galaxies. Here, we present the scale length derivation method and numerous tests that we have carried out to investigate the reliability of our results. The average r-band disk scale length is 3.79 kpc, with an RMS dispersion of 2.05 kpc, and this is a typical value irrespective of passband and galaxy morphology, concentration, and asymmetry. The derived scale lengths presented here are representative for a typical galaxy mass of $10^{10.8\pm 0.54} \rm{M}_\odot$, and the RMS dispersion is larger for more massive galaxies. Distributions and typical trends of scale lengths have also been derived in all the other SDSS bands with linear relations that indicate the relation that connect scale lengths in one passband to another. Such transformations could be used to test the results of forthcoming cosmological simulations of galaxy formation and evolution of the Hubble sequence.
The flybys of Jupiter by the Voyager spacecraft in 1979, and over two decades later by Cassini in 2000, have provided us with unique datasets from two different epochs, allowing the investigation of seasonal change in the atmosphere. In this paper we model zonal averages of thermal infrared spectra from the two instruments, Voyager 1 IRIS and Cassini CIRS, to retrieve the vertical and meridional profiles of temperature, and the abundances of the two minor hydrocarbons, acetylene (C2H2) and ethane (C2H6). The spatial variation of these gases is controlled by both chemistry and dynamics, and therefore their observed distribution gives us an insight into both processes. We find that the two gases paint quite different pictures of seasonal change. Whilst the 2-D cross-section of C2H6 abundance is slightly increased and more symmetric in 2000 (northern summer solstice) compared to 1979 (northern fall equinox), the major trend of equator to pole increase remains. For C2H2 on the other hand, the Voyager epoch exhibits almost no latitudinal variation, whilst the Cassini era shows a marked decrease polewards in both hemispheres. At the present time, these experimental findings are in advance of interpretation, as there are no published models of 2-D Jovian seasonal chemical variation available for comparison.
We present a new software tool to enable astronomers to easily compare observations of emission line ratios with those determined by photoionization and shock models, ITERA, the IDL Tool for Emission-line Ratio Analysis. This tool can plot ratios of emission lines predicted by models and allows for comparison of observed line ratios against grids of these models selected from model libraries associated with the tool. We provide details of the libraries of standard photoionization and shock models available with ITERA, and, in addition, present three example emission line ratio diagrams covering a range of wavelengths to demonstrate the capabilities of ITERA. ITERA, and associated libraries, is available from \url{http://www.brentgroves.net/itera.html}
We explore the environments of two radio galaxies at z~1.5, 7C1751+6809 and 7C1756+6520, using deep optical and near-infrared imaging. Our data cover 15'x15' fields around the radio galaxies. We develop and apply BzK color criteria to select cluster member candidates around the radio galaxies and find no evidence of an overdensity of red galaxies within 2Mpc of 7C1751+6809. In contrast, 7C1756+6520 shows a significant overdensity of red galaxies within 2Mpc of the radio galaxy, by a factor of 3.1 +/- 0.8 relative to the four MUSYC fields. At small separation (r<6''), this radio galaxy also has one z~1.4 evolved galaxy candidate, one z~1.4 star-forming galaxy candidate, and an AGN candidate (at indeterminate redshift). This is suggestive of several close-by companions. Several concentrations of red galaxies are also noticed in the full 7C1756+6520 field, forming a possible large-scale structure of evolved galaxies with a NW-SE orientation. We construct the color-magnitude diagram of red galaxies found near (r<2Mpc) 7C1756+6520, and find a clear red sequence that is truncated at Ks~21.5 (AB). We also find an overdensity of mid-IR selected AGN in the surroundings of 7C1756+6520. These results are suggestive of a proto-cluster at high redshift.
As a part of a Euro-VO research initiative, we have undertaken a programme aimed at studying the scale length of 54909 Sa-Sd spiral galaxies from the SDSS DR6 catalogue. We have retrieved u,g,r,i,z-band images for all galaxies in order to derive the light profiles. We also calculate asymmetry parameters to select non-disturbed disks for which we will derive exponential disk scale lengths. As images in different bands probe different optical depths and stellar populations, it is likely that a derived scale length value should depend on waveband, and our goal is to use the scale length variations with band pass, inclination, galaxy type, redshift, and surface brightness, in order to better understand the nature of spiral galaxies.
The Cassini measurements of C$_2$H$_2$ and C$_2$H$_6$ at $\sim$5 mbar provide a constraint on meridional transport in the stratosphere of Jupiter. We performed a two-dimensional photochemical calculation coupled with mass transport due to vertical and meridional mixing. The modeled profile of C$_2$H$_2$ at latitudes less than 70$^\circ$ follows the latitude dependence of the solar insolation, while that of C$_2$H$_6$ shows little latitude dependence, consistent with the measurements. In general, our model study suggests that the meridional transport timescale above 5-10 mbar altitude level is $\gtrsim$1000 years and the time could be as short as 10 years below 10 mbar level, in order to fit the Cassini measurements. The derived meridional transport timescale above the 5 mbar level is a hundred times longer than that obtained from the spreading of gas-phase molecules deposited after the impact of Shoemaker-Levy 9 comet. There is no explanation at this time for this discrepancy.
We report results from {\it XMM-Newton} observations of thirteen X-ray bright BL Lacertae objects, selected from the {\it Einstein} Slew Survey sample. The spectra are generally well fit by power-law models, with four objects having hard ($α<1; F_ν\propto ν^{-α}$) spectra that indicates synchrotron peaks at $>5$ keV. None of our spectra show line features, indicating that soft X-ray absorption ``notches'' must be rare amongst BL Lacs, rather than common or ubiquitous as had previously been asserted. We find significant curvature in most of the spectra. This curvature is almost certainly intrinsic, as it appears nearly constant from 0.5 to 6 keV, an observation which is inconsistent with the small columns seen in these sources.