Symbolic algorithms for the Painlevé test, special solutions, and recursion operators for nonlinear PDEs

This paper discusses the algorithms and implementations of three MATHEMATICA packages for the study of integrability and the computation of closed-form solutions of nonlinear polynomial PDEs. The first package, PainleveTest.m, symbolically performs the Painlevé integrability test. The second package, PDESpecialSolutions.m, computes exact solutions expressible in hyperbolic or elliptic functions. The third package, PDERecursionOperator.m, generates and tests recursion operators

Symbolic Computation of Polynomial Conserved Densities, Generalized Symmetries, and Recursion Operators for Nonlinear Differential-Difference Equations

Algorithms for the symbolic computation of polynomial conserved densities, fluxes, generalized symmetries, and recursion operators for systems of nonlinear differential-difference equations are presented. In the algorithms we use discrete versions of the Fréchet and variational derivatives, as well as discrete Euler and homotopy operators. The algorithms are illustrated for prototypical nonlinear polynomial lattices, including the Kac-van Moerbeke (Volterra) and Toda lattices. Results are shown for the modified Volterra and Ablowitz-Ladik lattices

Cluster Morphologies and Model-independent Y_(SZ) Estimates from Bolocam Sunyaev-Zel'dovich Images

We present initial results from our ongoing program to image the Sunyaev-Zel'dovich (SZ) effect in galaxy clusters at 143 GHz using Bolocam; five clusters and one blank field are described in this manuscript. The images have a resolution of 58 arcsec and a radius of ≃ 6-7 arcmin, which is approximately r_(500)-2r_(500) for these clusters. We effectively high-pass filter our data in order to subtract noise sourced by atmospheric fluctuations, but we are able to obtain unbiased images of the clusters by deconvolving the effects of this filter. The beam-smoothed rms is ≃ 10 μK_(CMB) in these images; with this sensitivity, we are able to detect the SZ signal to beyond r_(500) in binned radial profiles. We have fit our images to beta and Nagai models, fixing spherical symmetry or allowing for ellipticity in the plane of the sky, and we find that the best-fit parameter values are in general consistent with those obtained from other X-ray and SZ data. Our data show no clear preference for the Nagai model or the beta model due to the limited spatial dynamic range of our images. However, our data show a definitive preference for elliptical models over spherical models, quantified by an F ratio of ≃ 20 for the two models. The weighted mean ellipticity of the five clusters is ϵ = 0.27 ± 0.03, consistent with results from X-ray data. Additionally, we obtain model-independent estimates of Y_(500), the integrated SZ y-parameter over the cluster face to a radius of r_(500), with systematics-dominated uncertainties of ≃ 10%. Our Y_(500) values, which are free from the biases associated with model-derived Y_(500) values, scale with cluster mass in a way that is consistent with both self-similar predictions and expectations of a ≃ 10% intrinsic scatter

Development of lanthanum nickelate as a cathode for use in intermediate temperature solid oxide fuel cells

The performance of lanthanum nickelate, La2NiO4+δ (LNO), as a cathode in IT-SOFCs with the electrolyte cerium gadolinium oxide, Ce0.9Gd0.1O2−δ (CGO), has been investigated by AC impedance spectroscopy of symmetrical cells. A significant reduction in the area specific resistance (ASR) has been achieved with a layered cathode structure consisting of a thin compact LNO layer between the dense electrolyte and porous electrode. This decrease in ASR is believed to be a result of contact at the electrolyte/cathode boundary enhancing the oxygen ion transfer to the electrolyte. An ASR of 1.0 Ω cm2 at 700 °C was measured in a symmetrical cell with this layered structure, compared to an ASR of 7.4 Ω cm2 in a cell without the compact layer. In addition, further improvements were observed by enhancing the cell current collection and it is anticipated that a symmetrical cell consisting of a layered structure with adequate current collection would lower these ASR values further

CLASH: accurate photometric redshifts with 14 HST bands in massive galaxy cluster cores

We present accurate photometric redshifts for galaxies observed by the Cluster Lensing And Supernova survey with Hubble (CLASH). CLASH observed 25 massive galaxy cluster cores with the Hubble Space Telescope in 16 filters spanning 0.2–1.7 μm. Photometry in such crowded fields is challenging. Compared to our previously released catalogues, we make several improvements to the photometry, including smaller apertures, intracluster light subtraction, point spread function matching and empirically measured uncertainties. We further improve the Bayesian photometric redshift estimates by adding a redder elliptical template and by inflating the photometric uncertainties of the brightest galaxies. The resulting photometric redshift accuracies are dz/(1+z) ∼ 0.8, 1.0 and 2.0 per cent for galaxies with I-band F814W AB magnitudes < 18, 20 and 23, respectively. These results are consistent with our expectations. They improve on our previously reported accuracies by a factor of 4 at the bright end and a factor of 2 at the faint end. Our new catalogue includes 1257 spectroscopic redshifts, including 382 confirmed cluster members. We also provide stellar mass estimates. Finally, we include lensing magnification estimates of background galaxies based on our public lens models. Our new catalogue of all 25 CLASH clusters is available via Mikulski Archive for Space Telescopes. The analysis techniques developed here will be useful in other surveys of crowded fields, including the Frontier Fields and surveys carried out with Javalambre-Physics of the Accelerated Universe Astrophysical Survey and James Webb Space Telescope

CLASH: The Concentration-Mass Relation of Galaxy Clusters

We present a new determination of the concentration–mass (c–M) relation for galaxy clusters based on our comprehensive lensing analysis of 19 X-ray selected galaxy clusters from the Cluster Lensing and Supernova Survey with Hubble (CLASH). Our sample spans a redshift range between 0.19 and 0.89. We combine weak-lensing constraints from the Hubble Space Telescope (HST) and from ground-based wide-field data with strong lensing constraints from HST. The results are reconstructions of the surface-mass density for all CLASH clusters on multi-scale grids. Our derivation of Navarro–Frenk–White parameters yields virial masses between 0.53 × 10^(15) M_⊙ h and 1.76 × 10^(15) M_⊙ h and the halo concentrations are distributed around c_(200c) ∼ 3.7 with a 1σ significant negative slope with cluster mass. We find an excellent 4% agreement in the median ratio of our measured concentrations for each cluster and the respective expectation from numerical simulations after accounting for the CLASH selection function based on X-ray morphology. The simulations are analyzed in two dimensions to account for possible biases in the lensing reconstructions due to projection effects. The theoretical c–M relation from our X-ray selected set of simulated clusters and the c–M relation derived directly from the CLASH data agree at the 90% confidence level