Homogenization of the one-dimensional wave equation

We present a method for two-scale model derivation of the periodic homogenization of the one-dimensional wave equation in a bounded domain. It allows for analyzing the oscillations occurring on both microscopic and macroscopic scales. The novelty reported here is on the asymptotic behavior of high frequency waves and especially on the boundary conditions of the homogenized equation. Numerical simulations are reported

Species of Eurydice (Isopoda, Flabellifera) from southern Brazil

This paper reports species of Eurydice (Isopoda, Flabellifera) occurring on the continental shelf of southern Brazil, from lat. 22º00'S. Three species are recorded. E. littoralis (Moore, 1902), is a new occurrence from Brazil. Detailed illustrations and new morphologi cal data are furnished for this species hitherto inadequately described. E. elongata sp. n. and E. emarginata sp. n., are new to science. The flagellar process on the antenna 2, reported in three species of Eurydice, seems to be an exclusively male characteristic, and probably it will also occur in the males of most of the already described species. Genus and species diagnosis are provided, together with a classification key for all species recorded up to date from southern Brazil. All available distributional and ecological infor mation completes the account of each species.No presente trabalho faz-se um levantamento das especies do gênero Eurydice (Isopoda, Flabellifera) ocorrendo na plataforma continental centrosul do Brasil, a partir da Lat. 22º00'S. Tres espécies são assinaladas para a região: E. littoralis (Moore, 1902), E. elongata sp. n. e E. emarginata sp.n. Novos dados morfológicos e detalhadas ilustrações são apresentadas para a espécie E. littoralis. O processo flagelar da antena 2, observado em três espécies de Eurydice, parece constituir uma característica exclusiva dos machos, donde se pressupõe possa também ser encontrado em outros machos de espécies já descritas. São fornecidas diagnoses para o gênero e espécie, assim como urna chave de classificação para todas as espécies tratadas. Tanto quanto possível, observações ecológicas completam a descrição das espécies

Numerical methods for stochastic partial differential equations with multiples scales

A new method for solving numerically stochastic partial differential equations (SPDEs) with multiple scales is presented. The method combines a spectral method with the heterogeneous multiscale method (HMM) presented in [W. E, D. Liu, and E. Vanden-Eijnden, Comm. Pure Appl. Math., 58(11):1544--1585, 2005]. The class of problems that we consider are SPDEs with quadratic nonlinearities that were studied in [D. Blomker, M. Hairer, and G.A. Pavliotis, Nonlinearity, 20(7):1721--1744, 2007.] For such SPDEs an amplitude equation which describes the effective dynamics at long time scales can be rigorously derived for both advective and diffusive time scales. Our method, based on micro and macro solvers, allows to capture numerically the amplitude equation accurately at a cost independent of the small scales in the problem. Numerical experiments illustrate the behavior of the proposed method.Comment: 30 pages, 5 figures, submitted to J. Comp. Phy

First Sagittarius A* Event Horizon Telescope Results. II. EHT and Multiwavelength Observations, Data Processing, and Calibration

We present Event Horizon Telescope (EHT) 1.3 mm measurements of the radio source located at the position of the supermassive black hole Sagittarius A* (Sgr A*), collected during the 2017 April 5–11 campaign. The observations were carried out with eight facilities at six locations across the globe. Novel calibration methods are employed to account for Sgr A*'s flux variability. The majority of the 1.3 mm emission arises from horizon scales, where intrinsic structural source variability is detected on timescales of minutes to hours. The effects of interstellar scattering on the image and its variability are found to be subdominant to intrinsic source structure. The calibrated visibility amplitudes, particularly the locations of the visibility minima, are broadly consistent with a blurred ring with a diameter of ∼50 μas, as determined in later works in this series. Contemporaneous multiwavelength monitoring of Sgr A* was performed at 22, 43, and 86 GHz and at near-infrared and X-ray wavelengths. Several X-ray flares from Sgr A* are detected by Chandra, one at low significance jointly with Swift on 2017 April 7 and the other at higher significance jointly with NuSTAR on 2017 April 11. The brighter April 11 flare is not observed simultaneously by the EHT but is followed by a significant increase in millimeter flux variability immediately after the X-ray outburst, indicating a likely connection in the emission physics near the event horizon. We compare Sgr A*’s broadband flux during the EHT campaign to its historical spectral energy distribution and find that both the quiescent emission and flare emission are consistent with its long-term behavior