swMATH - a new information service for mathematical software

An information service for mathematical software is presented. Publications and software are two closely connected facets of mathematical knowledge. This relation can be used to identify mathematical software and find relevant information about it. The approach and the state of the art of the information service are described here.Comment: see also: http://www.swmath.or

Adaptive Finite Element Methods for Rigid Particulate Flow Problems

Subject of this work is the numerical simulation of the motion of rigid particles in an incompressible viscous or viscoelastic fluid. What makes this task especially challenging is the fact that two different physical models are coupled: The fluid motion is described by a system of partial differential equations (Navier-Stokes equations), while the dynamics of the rigid particles is determined as the solution of a system of ordinary differential equations (Newton's laws of motion). In this work, numerical methods for some prototypical situations are developed, analyzed and validated; all of them are based on the finite element method (FEM). In this context, special emphasis is given to local grid adaptation. The goal is to obtain a high accuracy and, at the same time, to keep the computational effort as low as possible

Second Order Adaptive Boundary Conditions for Exterior Flow Problems: Non-Symmetric Stationary Flows in Two Dimensions

Abstract.: We consider the problem of solving numerically the stationary incompressible Navier-Stokes equations in an exterior domain in two dimensions. For numerical purposes we truncate the domain to a finite sub-domain, which leads to the problem of finding so called "artificial boundary conditions” to replace the boundary conditions at infinity. To solve this problem we construct - by combining results from dynamical systems theory with matched asymptotic expansion techniques based on the old ideas of Goldstein and Van Dyke - a smooth divergence free vector field depending explicitly on drag and lift and describing the solution to second and dominant third order, asymptotically at large distances from the body. The resulting expression appears to be new, even on a formal level. This improves the method introduced by the authors in a previous paper and generalizes it to non-symmetric flows. The numerical scheme determines the boundary conditions and the forces on the body in a self-consistent way as an integral part of the solution process. When compared with our previous paper where first order asymptotic expressions were used on the boundary, the inclusion of second and third order asymptotic terms further reduces the computational cost for determining lift and drag to a given precision by typically another order of magnitud

User-Centered Engineering of an Interactive Land Use Exploration Tool

In this paper we showcase a system for visualizing and predicting land-use data. The time series-based visualization application strives to improve science communication by facilitating the understanding of land-use change and is backed up by a machine learning-based land-use prediction application that imputes historic data and generates predictions of land use in the future. To present the project, we discuss the system's requirements which were developed by means of a User-Centered Engineering approach, elaborate on its current, early state of development and the corresponding results and finally discuss areas of potential improvement

Epigenetic dynamics of monocyte-to-macrophage differentiation

Background Monocyte-to-macrophage differentiation involves major biochemical and structural changes. In order to elucidate the role of gene regulatory changes during this process, we used high-throughput sequencing to analyze the complete transcriptome and epigenome of human monocytes that were differentiated in vitro by addition of colony-stimulating factor 1 in serum-free medium. Results Numerous mRNAs and miRNAs were significantly up- or down-regulated. More than 100 discrete DNA regions, most often far away from transcription start sites, were rapidly demethylated by the ten eleven translocation enzymes, became nucleosome-free and gained histone marks indicative of active enhancers. These regions were unique for macrophages and associated with genes involved in the regulation of the actin cytoskeleton, phagocytosis and innate immune response. Conclusions In summary, we have discovered a phagocytic gene network that is repressed by DNA methylation in monocytes and rapidly de-repressed after the onset of macrophage differentiation

Multiple Facets of Biodiversity Drive the Diversity-Stability Relationship

A significant body of evidence has demonstrated that biodiversity stabilizes ecosystem functioning over time in grassland ecosystems. However, the relative importance of different facets of biodiversity underlying the diversity–stability relationship remains unclear. Here we used data from 39 biodiversity experiments and structural equation modeling to investigate the roles of species richness, phylogenetic diversity, and both the diversity and community-weighted mean of functional traits representing the ‘fast–slow’ leaf economics spectrum in driving the diversity–stability relationship. We found that high species richness and phylogenetic diversity stabilize biomass production via enhanced asynchrony. Contrary to our hypothesis, low phylogenetic diversity also enhances ecosystem stability directly, albeit weakly. While the diversity of fast–slow functional traits has a weak effect on ecosystem stability, communities dominated by slow species enhance ecosystem stability by increasing mean biomass production relative to the standard deviation of biomass over time. Our results demonstrate that biodiversity influences ecosystem stability via a variety of facets, thus highlighting a more multicausal relationship than has been previously acknowledged

Adabtive boundary conditions for exterior flow problems

We consider the problem of solving numerically the stationary incompressible Navier-Stokes equations in an exterior domain in two dimensions. This corresponds to studying the stationary fluid flow past a body. The necessity to truncate for numerical purposes the infinite exterior domain to a finite domain leads to the problem of finding appropriate boundary conditions on the surface of the truncated domain. We solve this problem by providing a vector field describing the leading asymptotic behavior of the solution. This vector field is given in the form of an explicit expression depending on a real parameter. We show that this parameter can be determined from the total drag exerted on the body. Using this fact we set up a self-consistent numerical scheme that determines the parameter, and hence the boundary conditions and the drag, as part of the solution process. We compare the values of the drag obtained with our adaptive scheme with the results from using traditional constant boundary conditions. Computational times are typically reduced by several orders of magnitude

Second Order Adaptive Boundary Conditions for Exterior Flow Problems: Non-Symmetric Stationary Flows in Two Dimensions

We consider the problem of solving numerically the stationary incompressible Navier Stokes equations in an exterior domain in two dimensions. For numerical purposes we truncate the domain to a finite sub-domain, which leads to the problem of finding so called “artificial boundary conditions” to replace the boundary conditions at infinity. To solve this problem we construct by combining results from dynamical systems theory with matched asymptotic expansion techniques based on the old ideas of Goldstein and Van Dyke a smooth divergence free vector field depending explicitly on drag and lift and describing the solution to second and dominant third order, asymptotically at large distances from the body. The resulting expression appears to be new, even on a formal level. This improves the method introduced by the authors in a previous paper and generalizes it to non-symmetric flows. The numerical scheme determines the boundary conditions and the forces on the body in a self-consistent way as an integral part of the solution process. When compared with our previous paper where first order asymptotic expressions were used on the boundary, the inclusion of second and third order asymptotic terms further reduces the computational cost for determining lift and drag to a given precision by typically another order of magnitude