Optimization algorithms for the solution of the frictionless normal contact between rough surfaces

This paper revisits the fundamental equations for the solution of the frictionless unilateral normal contact problem between a rough rigid surface and a linear elastic half-plane using the boundary element method (BEM). After recasting the resulting Linear Complementarity Problem (LCP) as a convex quadratic program (QP) with nonnegative constraints, different optimization algorithms are compared for its solution: (i) a Greedy method, based on different solvers for the unconstrained linear system (Conjugate Gradient CG, Gauss-Seidel, Cholesky factorization), (ii) a constrained CG algorithm, (iii) the Alternating Direction Method of Multipliers (ADMM), and ($iv$) the Non-Negative Least Squares (NNLS) algorithm, possibly warm-started by accelerated gradient projection steps or taking advantage of a loading history. The latter method is two orders of magnitude faster than the Greedy CG method and one order of magnitude faster than the constrained CG algorithm. Finally, we propose another type of warm start based on a refined criterion for the identification of the initial trial contact domain that can be used in conjunction with all the previous optimization algorithms. This method, called Cascade Multi-Resolution (CMR), takes advantage of physical considerations regarding the scaling of the contact predictions by changing the surface resolution. The method is very efficient and accurate when applied to real or numerically generated rough surfaces, provided that their power spectral density function is of power-law type, as in case of self-similar fractal surfaces.Comment: 38 pages, 11 figure

X-ray Photons in the CO 2-1 'Lacuna' of NGC 2110

A recent ALMA study of the Seyfert 2 Active Galactic Nucleus (AGN) NGC 2110 by Rosario et al. (2019) has reported a remarkable lack of CO 2-1 emission from the circumnuclear region, where optical lines and H2 emission are observed, leading to the suggestion of excitation of the molecular clouds by the AGN. Since interaction with X-ray photons could be the cause of this excitation, we have searched the archival Chandra data for corroborating evidence. We report an extra-nuclear ~1'' (~170 pc) feature found in the soft (<1.0 keV) Chandra data of the Seyfert 2 Active Galactic Nucleus (AGN) NGC 2110. This feature is elongated to the north of the nucleus and its shape matches well that of the optical lines and H2 emission observed in this region, which is devoid of CO 2-1 emission. The Chandra image completes the emerging picture of a multi-phase circumnuclear medium excited by the X-rays from the AGN, with dense warm molecular clouds emitting in H2 but depleted of CO 2-1 emission.Comment: ApJ Letters - in pres

A new flaring high energy gamma-ray source

We report the detection of a new gamma-ray source in the Fermi-LAT sky using a source detection tool based on the Minimal Spanning Tree algorithm. The source, not reported in previous LAT catalogues but very recently observed in the X-rays and optical bands, is characterized by an increasing gamma-ray activity in 2012 June-September, reaching a weekly peak flux of (3.3+-0.6)*10^-7 photons cm^-2 s^-1. A search for a possible counterpart provides indication that it can be associated with the radio source NVSS J141828+354250 whose optical SDSS colours are typical of a blazar.Comment: 4 pages, 3 figures. Accepted for publication in Astronomy & Astrophysic