Multiscale methods for second order elliptic equations based on non-overlapping domain decomposition schemes have great potential to take advantage of multi-core, state-of-the-art parallel computers. These methods typically involve solving local boundary value problems followed by the solution of a global interface problem. Known iterative procedures for the solution of the interface problem have typically slow convergence, increasing the overall cost of the multiscale solver. To overcome this problem we develop a scalable recursive solution method for such interface problem that replaces the global problem by a family of small interface systems associated with adjacent subdomains, in a hierarchy of nested subdomains. Then, we propose a novel parallel algorithm to implement our recursive formulation in multi-core devices using the Multiscale Robin Coupled Method by Guiraldello et al. (2018) [26], that can be seen as a generalization of several multiscale mixed methods. Through several numerical studies we show that the new algorithm is very fast and exhibits excellent strong and weak scalability. We consider very large problems, that can have billions of discretization cells, motivated by the numerical simulation of subsurface flows.

The present study analyzed how the economic, social and human mobility factors were responsible for dissemination of Covid -19 in Brazil and the Legal Amazon region. Human mobility was analyzed by four dimensions according to the network's hierarchies of: migration, pendular mobility, airlift, hydro and road routes and healthcare system. Manaus, capital of Amazon, was the first diffuser pole of cases; this may be explained by absence of public lockdown policies and restriction of mobility by river routes and airport system. In the face of the worsening of the pandemic, between March to May 2020, the previous migratory pattern of the urban population was accentuated to inland Amazonian cities that spread the virus towards remote areas of the Amazon. In addition, there was a pendular migratory movement to Manaus, which is the only center in the region with highly complex hospitals; this fact led to a strong migratory movement of populations seeking medical assistance. The analysis on migration revealed a close relation of the spatiotemporal behavior of Covid-19 spread and the migration network to Manaus. There were significant correlations related to fluvial or waterway transportation axis along the Amazon River which is the dominant route of the region. These pathways have long distances to be covered from one pole to another and were additional factors for the spread of the pandemic during the period studied and have long travel times that can be an important factor for COVID-19 further dissemination. We conclude that the wide dissemination of COVID-19 cases across the Legal Amazon was the result of multifactorial causes that include social inequities, vulnerability, high rate of mobility and migration, information failure and administrative and social management of the crisis.

This study aimed to quantify marine litter before and during the COVID pandemic found on urban touristic beaches closed to beachgoer access in northeastern Brazil. Litter identification and quantification was conducted during April, June, and August 2019, when 3583 items were sampled, and replicated during the same months in 2020, when access to the beaches studied was prohibited and a significant reduction in the amount of litter was found, 1812 items (49% decrease). Transects were used to monitor and classify litter according to its source, namely: autochthonous (litter that was locally discarded) and allochthonous (litter from other sites and sources). All beaches were classified as “very clean” and presented a smaller amount of litter during the beach closure period. The highest total marine litter reduction between the periods studied was 83%, while autochthonous litter in particular showed the most significant reduction, 88%. The comparison between the quantity and type of litter found in both periods showed greater specific anthropic pressure from beach users.

The southern skies and tall mountains of Latin America have cultivated a long history of astronomy on the continent. Today, the continent hosts over 80 observatories that are collaborative research centres for the region and the world. But what about other areas of physics? These have benefited from a culture of collaboration, but there are still challenges in fully developing the potential of research on the continent, such as insufficient researchers or resources. In this Viewpoint, seven physicists discuss the varying research landscapes of different areas of physics across the continent.

A wide range of approaches for batch processes monitoring can be found in the literature. This kind of process generates a very peculiar data structure, in which successive measurements of many process variables in each batch run are available. Traditional approaches do not take into account the time series nature of the data. The main reason is that the time series inference theory is not based on replications of time series, as it is in batch process data. It is based on the variability in a time domain. This fact demands some adaptations of this theory in order to accommodate the model coefficient estimates, considering jointly the batch to batch samples variability (batch domain) and the serial correlation in each batch (time domain). In order to address this issue, this paper proposes a new approach grounded in a group of control charts based on the classical ARMA model for monitoring and diagnostic of batch processes dynamics. The model coefficients are estimated (through the ordinary least square method) for each historical time series sample batch and modified Hotelling and t-Student distributions are derived and used to accommodate those estimates. A group of control charts based on that distributions are proposed for monitoring the new batches. Additionally, those groups of charts help to fault diagnosis, identifying the source of disturbances. Through simulated and real data we show that this approach seems to work well for both purposes.