Radiating stars with composite matter distributions

In this paper we study the junction conditions for a generalised matter distribution in a radiating star. The internal matter distribution is a composite distribution consisting of barotropic matter, null dust and a null string fluid in a shear-free spherical spacetime. The external matter distribution is a combination of a radiation field and a null string fluid. We find the boundary condition for the composite matter distribution at the stellar surface which reduces to the familiar Santos result with barotropic matter. Our result is extended to higher dimensions. We also find the boundary condition for the general spherical geometry in the presence of shear and anisotropy for a generalised matter distribution.

Revisiting the Lognormal Modelling of Shadowing Effects during Wireless Communications by Means of the α-μ/α-μ Composite Distribution

Properly modeling the shadowing effects during wireless transmissions is crucial to perform the network quality assessment. From a mathematical point of view, using composite distributions allows one to combine both fast fading and slow fading stochastic phenomena. Numerous statistical distributions have been used to account for the fast fading effects. On the other hand, even though several studies indicate the adequacy of the Lognormal distributon (LNd) as a shadowing model, they also reveal this distribution renders some analytic tractability issues. Past works include the combination of Rayleigh and Weibull distributions with LNd. Due to the difficulty inherent to obtaining closed form expressions for the probability density functions involved, other authors approximated LNd as a Gamma distribution, creating Nakagami-m/Gamma and Rayleigh/Gamma composite distributions. In order to better mimic the LNd, approximations using the inverse Gamma and the inverse Nakagami-m distributions have also been considered. Although all these alternatives were discussed, it is still an open question how to effectively use the LNd in the compound models and still get closed-form results. We present a novel understanding on how the α-μ distribution can be reduced to a LNd by a limiting procedure, overcoming the analytic intractability inherent to Lognormal fading processes. Interestingly, new closed-form and series representations for the PDF and CDF of the composite distributions are derived. We build computational codes to evaluate all the expression hereby derived as well as model real field trial results by the equations developed. The accuracy of the codes and of the model are remarkable.

First Light And Reionisation Epoch Simulations (FLARES) II: The Photometric Properties of High-Redshift Galaxies

We present the photometric properties of galaxies in the First Light and Reionisation Epoch Simulations (Flares). The simulations trace the evolution of galaxies in a range of overdensities through the Epoch of Reionistion (EoR). With a novel weighting scheme we combine these overdensities, extending significantly the dynamic range of observed composite distribution functions compared to periodic simulation boxes. Flares predicts a significantly larger number of intrinsically bright galaxies, which can be explained through a simple model linking dust-attenuation to the metal content of the interstellar medium, using a line-of-sight (LOS) extinction model. With this model we present the photometric properties of the Flares galaxies for z ∈ [5, 10]. We show that the ultraviolet (UV) luminosity function (LF) matches the observations at all redshifts. The function is fit by Schechter and double power-law forms, with the latter being favoured at these redshifts by the Flares composite UV LF. We also present predictions for the UV continuum slope as well as the attenuation in the UV. The impact of environment on the UV LF is also explored, with the brightest galaxies forming in the densest environments. We then present the line luminosity and equivalent widths of some prominent nebular emission lines arising from the galaxies, finding rough agreement with available observations. We also look at the relative contribution of obscured and unobscured star formation, finding comparable contributions at these redshifts.

First Light And Reionization Epoch Simulations (FLARES) – I. Environmental dependence of high-redshift galaxy evolution

ABSTRACT We introduce the First Light And Reionisation Epoch Simulations (FLARES), a suite of zoom simulations using the EAGLE model. We resimulate a range of overdensities during the Epoch of Reionization (EoR) in order to build composite distribution functions, as well as explore the environmental dependence of galaxy formation and evolution during this critical period of galaxy assembly. The regions are selected from a large $(3.2 \, \mathrm{cGpc})^{3}$ parent volume, based on their overdensity within a sphere of radius 14 h−1 cMpc. We then resimulate with full hydrodynamics, and employ a novel weighting scheme that allows the construction of composite distribution functions that are representative of the full parent volume. This significantly extends the dynamic range compared to smaller volume periodic simulations. We present an analysis of the galaxy stellar mass function (GSMF), the star formation rate distribution function (SFRF), and the star-forming sequence (SFS) predicted by FLARES, and compare to a number of observational and model constraints. We also analyse the environmental dependence over an unprecedented range of overdensity. Both the GSMF and the SFRF exhibit a clear double-Schechter form, up to the highest redshifts (z = 10). We also find no environmental dependence of the SFS normalization. The increased dynamic range probed by FLARES will allow us to make predictions for a number of large area surveys that will probe the EoR in coming years, carried out on new observatories such as Roman and Euclid.

Bias correction of daily precipitation over South Korea from the long-term reanalysis using a composite Gamma-Pareto distribution approach

Long-term precipitation data plays an important role in climate impact studies, but the observation for a given catchment is very limited. To significantly expand our sample size for the extreme rainfall analysis, we considered ERA-20c, a century-long reanalysis daily precipitation provided by the European Centre for Medium-Range Weather Forecasts (ECMWF). Preliminary studies have already indicated that ERA-20c can reproduce the mean reasonably well, but rainfall intensity is underestimated while wet-day frequency is overestimated. Thus, we first adopted a relatively simple approach to adjust the frequency of wet-days by imposing an optimal threshold. Moreover, we introduced a quantile mapping approach based on a composite distribution of a generalized Pareto distribution for the upper tail (e.g. 95th and 99th percentile), and a gamma distribution for the interior part of the distribution. The proposed composite distributions provide a significant reduction of the biases over the conventional method for the extremes. We suggested an interpolation method for the set of parameters of bias correction approach in ungauged catchments. A comparison of the corrected precipitation using spatially interpolated parameters shows that the proposed modelling scheme, particularly with the 99th percentile, can reliably reduce the systematic bias.

Methods for generating coherent distortion risk measures

This paper presents methods for generating new distortion functions utilising distribution functions and composite distribution functions. To ensure the coherency of the corresponding distortion risk measures, the concavity of the proposed distortion functions is established by restricting the parameter space of the generating distribution. Closed-form expressions for risk measures are derived for some cases. Numerical and graphical results are presented to demonstrate the effects of parameter values on the risk measures for exponential, Pareto and log-normal losses. In addition, we apply the proposed distortion functions to derive risk measures for a segregated fund guarantee.