Numerical solution of partial differential equations with variable coefficients with an operational approach to the tau method

AbstractWe discuss the numerical solution of linear partial differential equations with variable coefficients by means of an operational approach to Ortiz' recursive formulation of the Tau method.We discuss a procedure which makes it possible to determine the coefficients of a bivariate Tau approximant by means of a reduced set of matrix operations. It involves no discretization of the variables, approximate quadratures or the use of special trial functions.Error surfaces exhibit a remarkable equioscillatory behaviour

The number of extrema of the error function of a class of methods for differential equations

AbstractWe give sharp estimates for the number of extrema of the error of approximation of functions implicitly defined by linear and nonlinear differential equations, and by systems of differential equations when the latter are approximated using the Tau Method. Our estimates are deduced using the concept of length of a maximal monotone partition relative to a given function. This work is related to interesting previous work of Pittnauer [1] and to more recent work of El-Daou and Ortiz [2]. Our estimation techniques use explicitly analytical results from the Tau Method, relating the approximation error to the perturbation term. Recent work of El-Daou and Ortiz [3,4] and El-Daou, Ortiz and Samara [5], showed the possibility of simulating with the Tau Method, through a suitable choice of the perturbation term, of a variety of other, apparently diverse, numerical techniques. Among them Galerkin's method, polynomial expansion techniques, spectral methods, collocation and finite difference methods. Therefore, although our results are formulated in the language of the Tau Method, they are immediately applicable to a wider class of numerical methods for the approximate solution of differential equations

Benchmark low-mass objects in Moving Groups

This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In order to compile a sample of ultracool dwarfs that will serve as benchmarks for testing theoretical formation and evolutionary models, we selected low-mass cool (>M7) objects that are potentially members of five known young Moving Groups in the solar neighbourhood. We have studied the kinematics of the sample, finding that 49 targets belong to the young disk area, from which 36 are kinematic member of one of the five moving groups under study. Some of the identified low-mass members have been spectroscopically characterised (T-eff, log g) and confirmed as young members through a detailed study of age indicators

Application of mineralogical, petrological and geochemical tools for evaluating the palaeohdrogeological evolution of the PADAMOT study sites

The role of Work Package (WP) 2 of the PADAMOT project – ‘Palaeohydrogeological Data Measurements’ - has been to study late-stage fracture mineral and water samples from groundwater systems in Spain, Sweden, United Kingdom and the Czech Republic, with the aim of understanding the recent palaeohydrogeological evolution of these groundwater systems. In particular, the project sought to develop and evaluate methods for obtaining information about past groundwater evolution during the Quaternary (about the last 2 million years) by examining how the late-stage mineralization might record mineralogical, petrographical and geochemical evidence of how the groundwater system may have responded to past geological and climatological changes. Fracture-flow groundwater systems at six European sites were studied: • Melechov Hill, in the Bohemian Massif of the Czech Republic: a shallow (0-100 m) dilute groundwater flow system within the near-surface weathering zone in fractured granitic rocks; • Cloud Hill, in the English Midlands: a (~100 m) shallow dilute groundwater flow system in fractured and dolomitized Carboniferous limestone; • Los Ratones, in southwest Spain: an intermediate depth (0-500 m) dilute groundwater flow system in fractured granitic rocks; • Laxemar, in southeast Sweden: a deep (0-1000 m) groundwater flow system in fractured granitic rocks. This is a complex groundwater system with potential recharge and flushing by glacial, marine, lacustrine and freshwater during the Quaternary; • Sellafield, northwest England: a deep (0-2000 m) groundwater flow system in fractured Ordovician low-grade metamorphosed volcaniclastic rocks and discontinuous Carboniferous Limestone, overlain by a Permo-Triassic sedimentary sequence with fracture and matrix porosity. This is a complex coastal groundwater system with deep hypersaline sedimentary basinal brines, and deep saline groundwaters in crystalline basement rocks, overlain by a shallow freshwater aquifer system. The site was glaciated several times during the Quaternary and may have been affected by recharge from glacial meltwater; • Dounreay, northeast Scotland: a deep (0-1400 m) groundwater flow system in fractured Precambrian crystalline basement overlain by fractured Devonian sedimentary rocks. This is within the coastal discharge area of a complex groundwater system, comprising deep saline groundwater hosted in crystalline basement, overlain by a fracture-controlled freshwater sedimentary aquifer system. Like Sellafield, this area experienced glaciation and may potentially record the impact of glacial meltwater recharge. In addition, a study has been made of two Quaternary sedimentary sequences in Andalusia in southeastern Spain to provide a basis of estimating the palaeoclimatic history of the region that could be used in any reconstruction of the palaeoclimatic history at the Los Ratones site: • The Cúllar-Baza lacustrine sequence records information about precipitation and palaeotemperature regimes, derived largely from the analysis of the stable isotope (δ18O and δ13C) signatures from biogenic calcite (ostracod shells). • The Padul Peat Bog sequence provided information on past vegetation cover and palaeogroundwater inputs based on the study of fossil pollen and biomarkers as proxies for past climate change. Following on from the earlier EC 4th Framework EQUIP project, the focus of the PADAMOT studies has been on calcite mineralization. Calcite has been identified as a late stage mineral, closely associated with hydraulically-conductive fractures in the present-day groundwater systems at the Äspö-Laxemar, Sellafield, Dounreay and Cloud Hill sites. At Los Ratones and Melechov sites late-stage mineralization is either absent or extremely scarce, and both the quantity and fine crystal size of any late-stage fracture mineralization relevant to Quaternary palaeohydrogeological investigations is difficult to work with. The results from the material investigated during the PADAMOT studies indicate that the fracture fillings at these sites are related to hydrothermal activity, and so do not have direct relevance as Quaternary indicators. Neoformed calcite has not been found at these two sites at the present depth of the investigations. Furthermore, the HCO3 - concentration in all the Los Ratones groundwaters is mainly controlled by complex carbonate dissolution. The carbonate mineral saturation indices do not indicate precipitation conditions, and this is consistent with the fact that neoformed calcite, ankerite or dolomite have not been observed petrographically

Incompatibility Systems in Switchgrass

Switchgrass (Panicum virgatum L.), a cross-pollinated perennial, produces very little or no seed when self-pollinated, indicating the presence of self-incompatibility mechanisms. Knowledge of self-incompatibility mechanisms is required to use germplasm effectively in a breeding program. The objective of this study was to characterize features of the incompatibility systems in switchgrass. Seed set and seed characteristics of reciprocal matings of tetraploid, octaploid, and tetraploid x octaploid plants were used as measures of incompatibility. Both bagged mutual pollination and manual emasculation and pollination methods were used to make crosses. The percentages of self-compatibility in the tetraploid and octaploid parent plants were 0.35 and 1.39%, respectively. Prefertilization incompatibility in switchgrass is apparently under gametophytic control, since there were significant differences in percentage of compatible pollen as measured by percentage of total seed set between reciprocal matings within ploidy levels. Results indicated that the prefertilization incompatibility system in switchgrass is similar to the S-Z incompatibility system found in other members of the Poaceae. A postfertilization incompatibility system also exists that inhibits intermatings among octaploid and tetraploid plants. In these interploidy crosses, two very distinctive types of abnormal seed were found. When the female parent was the tetraploid plant, the resulting seed was small and shriveled, while when the female parent was the octaploid, small seed with floury endosperm was obtained. These results are similar to those obtained for endosperm incompatibility due to the endosperm balance number system found in other species

Self-consistent calculation of total energies of the electron gas using many-body perturbation theory

The performance of many-body perturbation theory for calculating ground-state properties is investigated. We present fully numerical results for the electron gas in three and two dimensions in the framework of the GW approximation. The overall agreement with very accurate Monte Carlo data is excellent, even for those ranges of densities for which the GW approach is often supposed to be unsuitable. The latter seems to be due to the fulfillment of general conservation rules. These results open further prospects for accurate calculations of ground-state properties circumventing the limitations of standard density-functional theory

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

Consenso colombiano de atención, diagnóstico y manejo de la infección por SARS-COV-2/COVID-19 en establecimientos de atención de la salud Recomendaciones basadas en consenso de expertos e informadas en la evidencia

The “Asociación Colombiana de Infectología” (ACIN) and the “Instituto de Evaluación de Nuevas Tecnologías de la Salud” (IETS) created a task force to develop recommendations for Covid 19 health care diagnosis, management and treatment informed, and based, on evidence. Theses reccomendations are addressed to the health personnel on the Colombian context of health services. © 2020 Asociacion Colombiana de Infectologia. All rights reserved

RICORS2040 : The need for collaborative research in chronic kidney disease

Chronic kidney disease (CKD) is a silent and poorly known killer. The current concept of CKD is relatively young and uptake by the public, physicians and health authorities is not widespread. Physicians still confuse CKD with chronic kidney insufficiency or failure. For the wider public and health authorities, CKD evokes kidney replacement therapy (KRT). In Spain, the prevalence of KRT is 0.13%. Thus health authorities may consider CKD a non-issue: very few persons eventually need KRT and, for those in whom kidneys fail, the problem is 'solved' by dialysis or kidney transplantation. However, KRT is the tip of the iceberg in the burden of CKD. The main burden of CKD is accelerated ageing and premature death. The cut-off points for kidney function and kidney damage indexes that define CKD also mark an increased risk for all-cause premature death. CKD is the most prevalent risk factor for lethal coronavirus disease 2019 (COVID-19) and the factor that most increases the risk of death in COVID-19, after old age. Men and women undergoing KRT still have an annual mortality that is 10- to 100-fold higher than similar-age peers, and life expectancy is shortened by ~40 years for young persons on dialysis and by 15 years for young persons with a functioning kidney graft. CKD is expected to become the fifth greatest global cause of death by 2040 and the second greatest cause of death in Spain before the end of the century, a time when one in four Spaniards will have CKD. However, by 2022, CKD will become the only top-15 global predicted cause of death that is not supported by a dedicated well-funded Centres for Biomedical Research (CIBER) network structure in Spain. Realizing the underestimation of the CKD burden of disease by health authorities, the Decade of the Kidney initiative for 2020-2030 was launched by the American Association of Kidney Patients and the European Kidney Health Alliance. Leading Spanish kidney researchers grouped in the kidney collaborative research network Red de Investigación Renal have now applied for the Redes de Investigación Cooperativa Orientadas a Resultados en Salud (RICORS) call for collaborative research in Spain with the support of the Spanish Society of Nephrology, Federación Nacional de Asociaciones para la Lucha Contra las Enfermedades del Riñón and ONT: RICORS2040 aims to prevent the dire predictions for the global 2040 burden of CKD from becoming true