Self-adjointness of two-dimensional Dirac operators on corner domains

We investigate the self-adjointness of the two-dimensional Dirac operator D, with quantum-dot and Lorentz-scalar i-shell boundary conditions, on piecewise C2 domains (with finitely many corners). For both models, we prove the existence of a unique self-adjoint realization whose domain is included in the Sobolev space H1=2, the formal form domain of the free Dirac operator. The main part of our paper consists of a description of the domain of the adjoint operator D in terms of the domain of D and the set of harmonic functions that verify some mixed boundary conditions. Then, we give a detailed study of the problem on an infinite sector, where explicit computations can be made: we find the self-adjoint extensions for this case. The result is then translated to general domains by a coordinate transformation

Reconstructing the Initial Density Field of the Local Universe: Method and Test with Mock Catalogs

Our research objective in this paper is to reconstruct an initial linear density field, which follows the multivariate Gaussian distribution with variances given by the linear power spectrum of the current CDM model and evolves through gravitational instability to the present-day density field in the local Universe. For this purpose, we develop a Hamiltonian Markov Chain Monte Carlo method to obtain the linear density field from a posterior probability function that consists of two components: a prior of a Gaussian density field with a given linear spectrum, and a likelihood term that is given by the current density field. The present-day density field can be reconstructed from galaxy groups using the method developed in Wang et al. (2009a). Using a realistic mock SDSS DR7, obtained by populating dark matter haloes in the Millennium simulation with galaxies, we show that our method can effectively and accurately recover both the amplitudes and phases of the initial, linear density field. To examine the accuracy of our method, we use $N$-body simulations to evolve these reconstructed initial conditions to the present day. The resimulated density field thus obtained accurately matches the original density field of the Millennium simulation in the density range 0.3 <= rho/rho_mean <= 20 without any significant bias. Especially, the Fourier phases of the resimulated density fields are tightly correlated with those of the original simulation down to a scale corresponding to a wavenumber of ~ 1 h/Mpc, much smaller than the translinear scale, which corresponds to a wavenumber of ~ 0.15 h\Mpc.Comment: 43 pages, 15 figures, accepted for publication in Ap

Healthy people with nature in mind

BACKGROUND: The global disease burden resulting from climate change is likely to be substantial and will put further strain on public health systems that are already struggling to cope with demand. An up- stream solution, that of preventing climate change and associated adverse health effects, is a promising approach, which would create win-win-situations where both the environment and human health benefit. One such solution would be to apply methods of behaviour change to prompt pro-environmentalism, which in turn benefits health and wellbeing. DISCUSSION: Based on evidence from the behavioural sciences, we suggest that, like many social behaviours, pro- environmental behaviour can be automatically induced by internal or external stimuli. A potential trigger for such automatic pro-environmental behaviour would be natural environments themselves. Previous research has demonstrated that natural environments evoke specific psychological and physiological reactions, as demonstrated by self-reports, epidemiological studies, brain imaging techniques, and various biomarkers. This suggests that exposure to natural environments could have automatic behavioural effects, potentially in a pro-environmental direction, mediated by physiological reactions. Providing access and fostering exposure to natural environments could then serve as a public health tool, together with other measures, by mitigating climate change and achieving sustainable health in sustainable ecosystems. However, before such actions are implemented basic research is required to elucidate the mechanisms involved, and applied investigations are needed to explore real world impacts and effect magnitudes. As environmental research is still not sufficiently integrated within medical or public health studies there is an urgent need to promote interdisciplinary methods and investigations in this critical field. Health risks posed by anthropogenic climate change are large, unevenly distributed, and unpredictable. To ameliorate negative impacts, pro-environmental behaviours should be fostered. Potentially this could be achieved automatically through exposure to favourable natural environments, with an opportunity for cost-efficient nature-based solutions that provide benefits for both the environment and public health

Properties of Galaxy Groups in the SDSS: I.-- The Dependence of Colour, Star Formation, and Morphology on Halo Mass

Using a large galaxy group catalogue constructed from the SDSS, we investigate the correlation between various galaxy properties and halo mass. We split the population of galaxies in early types, late types, and intermediate types, based on their colour and specific star formation rate. At fixed luminosity, the early type fraction increases with increasing halo mass. Most importantly, this mass dependence is smooth and persists over the entire mass range probed, without any break or feature at any mass scale. We argue that the previous claim of a characteristic feature on galaxy group scales is an artefact of the environment estimators used. At fixed halo mass, the luminosity dependence of the type fractions is surprisingly weak: galaxy type depends more strongly on halo mass than on luminosity. We also find that the early type fraction decreases with increasing halo-centric radius. Contrary to previous studies, we find that this radial dependence is also present in low mass haloes. The properties of satellite galaxies are strongly correlated with those of their central galaxy. In particular, the early type fraction of satellites is significantly higher in a halo with an early type central galaxy than in a halo of the same mass but with a late type central galaxy. This phenomenon, which we call `galactic conformity', is present in haloes of all masses and for satellites of all luminosities. Finally, the fraction of intermediate type galaxies is always ~20 percent, independent of luminosity, independent of halo mass, independent of halo-centric radius, and independent of whether the galaxy is a central galaxy or a satellite galaxy. We discuss the implications of all these findings for galaxy formation and evolution.Comment: 28 pages, 15 figures. Submitted for publication in MNRA

Mixing in anharmonic potential well

We prove phase-space mixing for solutions to Liouville’s equation for integrable systems. Under a natural non-harmonicity condition, we obtain weak convergence of the distribution function with rate ⟨time⟩−1. In one dimension, we also study the case where this condition fails at a certain energy, showing that mixing still holds but with a slower rate. When the condition holds and functions have higher regularity, the rate can be faster

Evidence for a 3 x 10^8 solar mass black hole in NGC 7052 from HST observations of the nuclear gas disk

We present an HST study of the nuclear region of the E4 radio galaxy NGC 7052, which has a nuclear disk of dust and gas. The WFPC2 was used to obtain B, V and I broad-band images and an H_alpha+[NII] narrow-band image. The FOS was used to obtain H_alpha+[NII] spectra along the major axis, using a 0.26 arcsec diameter circular aperture. The observed rotation velocity of the ionized gas is V = 155 +/- 17 km/s at r = 0.2 arcsec from the nucleus. The Gaussian dispersion of the emission lines increases from sigma = 70 km/s at r=1 arcsec, to sigma = 400 km/s on the nucleus. To interpret the gas kinematics we construct axisymmetric models in which the gas and dust reside in a disk in the equatorial plane of the stellar body. It is assumed that the gas moves on circular orbits, with an intrinsic velocity dispersion due to turbulence. The circular velocity is calculated from the combined gravitational potential of the stars and a possible nuclear black hole (BH). Models without a BH predict a rotation curve that is shallower than observed (V_pred = 92 km/s at r = 0.2 arcsec), and are ruled out at > 99% confidence. Models with a BH of 3.3^{+2.3}_{-1.3} x 10^8 solar masses provide an acceptable fit. NGC 7052 can be added to the list of active galaxies for which HST spectra of a nuclear gas disk provide evidence for the presence of a central BH. The BH masses inferred for M87, M84, NGC 6251, NGC 4261 and NGC 7052 span a range of a factor 10, with NGC 7052 falling on the low end. By contrast, the luminosities of these galaxies are identical to within 25%. Any relation between BH mass and luminosity, as suggested by independent arguments, must therefore have a scatter of at least a factor 10.Comment: 39 pages, LaTeX, with 16 PostScript figures. Submitted to the Astronomical Journal. Postscript version with higher resolution figures available from http://sol.stsci.edu/~marel/abstracts/abs_R22.htm

Quantifying the sustainability of agriculture

The rural sustainability index is a scientifically based tool to quantify the performance of agriculture. The sustainability of crop production is quantified from three perspectives; people, planet and profit. Within each perspective, one condition was selected that must be met to warrant agriculture. These are: No hazardous work should be used within the crop production chain; agricultural crops should not be grown on land allocated to nature by national law or regulations and, when a GM-crop is present or is introduced in a region, it should not harm development opportunities of other farmers. If these excluding conditions are met, the sustainability of agriculture is assessed through five performance indicators on school attendance, water use and consumption, fertilizer use, pesticide use, and farm income. For each of the five indicators, critical values and target values have been given that limit the transition range between non-sustainable and sustainable production. The five indicators are combined into a sustainability index. The index aims at improving the socio-economic position of farmers while protecting the environment