Toward an internally consistent astronomical distance scale

Accurate astronomical distance determination is crucial for all fields in astrophysics, from Galactic to cosmological scales. Despite, or perhaps because of, significant efforts to determine accurate distances, using a wide range of methods, tracers, and techniques, an internally consistent astronomical distance framework has not yet been established. We review current efforts to homogenize the Local Group's distance framework, with particular emphasis on the potential of RR Lyrae stars as distance indicators, and attempt to extend this in an internally consistent manner to cosmological distances. Calibration based on Type Ia supernovae and distance determinations based on gravitational lensing represent particularly promising approaches. We provide a positive outlook to improvements to the status quo expected from future surveys, missions, and facilities. Astronomical distance determination has clearly reached maturity and near-consistency.Comment: Review article, 59 pages (4 figures); Space Science Reviews, in press (chapter 8 of a special collection resulting from the May 2016 ISSI-BJ workshop on Astronomical Distance Determination in the Space Age

Localized non-diffusive asymptotic patterns for nonlinear parabolic equations with gradient absorption

International audienceWe study the large-time behaviour of the solutions u of the evolution equation involving nonlinear diffusion and gradient absorption $\partial_t u − \Delta_p u + |\nabla u|^q = 0$. We consider the problem posed for $x\in\mathbb{R}^N$ and $t>0$ with non-negative and compactly supported initial data. We take the exponent $p > 2$ which corresponds to slow $p$-Laplacian diffusion, and the exponent $q$ in the superlinear range $1<q<p−1$. In this range the influence of the Hamilton-Jacobi term $|\nabla u|^q$ is determinant, and gives rise to the phenomenon of localization. The large time behaviour is described in terms of a suitable self-similar solution that solves a Hamilton-Jacobi equation. The shape of the corresponding spatial pattern is rather conical instead of bell-shaped or parabolic