Substructuring of a Signorini-type problem and Robin's method for the Richards equation in heterogeneous soil

We prove a substructuring result for variational inequalities. It concerns but is not restricted to the Richards equation in heterogeneous soil, and it includes boundary conditions of Signorini’s type. This generalizes existing results for the linear case and leads to interface conditions known from linear variational equalities: continuity of Dirichlet and flux values in a weak sense. In case of the Richards equation, these are the continuity of the physical pressure and of the water flux, which is hydrologically reasonable. We use these interface conditions in a heterogeneous problem with piecewise constant soil parameters, which we address by the Robin method. We prove that, for a certain time discretization, the homogeneous problems in the subdomains including Robin and Signorini-type boundary conditions can be solved by convex minimization. As a consequence, we are able to apply monotone multigrid in the discrete setting as an efficient and robust solver for the local problems. Numerical results demonstrate the applicability of our approach

Heterogeneous domain decomposition of surface and porous media flow

We present a heterogeneous domain decomposition approach to the Richards equation coupled with surface water flow. Assuming piecewise constant soil parameters in the constitutive equations for saturation and relative permeability, we present a novel domain decomposition approch to the Richards equation involving on fast and robust subdomain solver based on optimization techniques. The coupling of ground and surface water is resolved by a Dirichlet - Neumann-type iteration

Fast and robust numerical solution of the Richards equation in homogeneous soil

We derive and analyze a solver-friendly finite element discretization of a time discrete Richards equation based on Kirchhoff transformation. It can be interpreted as a classical finite element discretization in physical variables with nonstandard quadrature points. Our approach allows for nonlinear outflow or seepage boundary conditions of Signorini type. We show convergence of the saturation and, in the nondegenerate case, of the discrete physical pressure. The associated discrete algebraic problems can be formulated as discrete convex minimization problems and, therefore, can be solved efficiently by monotone multigrid methods. In numerical examples for two and three space dimensions we observe $L^2$-convergence rates of order $\mathcal{O}(h^2)$ and $H^1$-convergence rates of order $\mathcal{O}(h)$ as well as robust convergence behavior of the multigrid method with respect to extreme choices of soil parameters

On nonlinear Dirichlet-Neumann Algorithms for jumping nonlinearities. In: Domain Decomposition Methods in Science and Engineering XVI

We consider a quasilinear elliptic transmission problem where the nonlinearity changes discontinuously across two subdomains. By a reformulation of the problem via Kirchhoff transformation we first obtain linear problems on the subdomains together with nonlinear transmission conditions and then a nonlinear Steklov–Poincar´e interface equation. We introduce a Dirichlet–Neumann iteration for this problem and prove convergence to a unique solution in one space dimension. Finally we present numerical results in two space dimensions suggesting that the algorithm can be applied successfully in more general cases

Heterogeneous substructuring methods for coupled surface and subsurface flow

The exchange of ground- and surface water plays a crucial role in a variety of practically relevant processes ranging from flood protection measures to preservation of ecosystem health in natural and human-impacted water resources systems

Prediction of Instability in Rotor-Seal Systems using Forward Whirl Magnetic Bearing Excitation

To separate different fluids and pressure levels in high-speed turbomachinery or pumps, mostly contactless seals are used. The leakage flow inside the seal gap applies forces to the vibrating rotor system in deflectional and tangential directions, that are dependent on the rotational speed. Above a speed limit, mainly tangential seal forces can lead to self-excited vibrations and, ultimately, rotor instability. This is similar to the “oil whip” phenomenon in journal bearings. To predict the speed limit, two methods are shown and compared: Simulations based on the bulk flow assumptions and an experimental method. To demonstrate the application, a test rig is used. The experimental method uses measured transfer functions, utilizing an active magnetic bearing for forward whirl excitation in the safe operational range. The speed limit can be predicted by analyzing and extrapolating the vibrational behavior of the rotor-seal system

Classification of Children's Handwriting Errors for the Design of an Educational Co-writer Robotic Peer

In this paper, we propose a taxonomy of handwriting errors exhibited by children as a way to build adequate strategies for integration with a co-writing peer. The exploration includes the collection of letters written by children in an initial study, which were then revised in a second study. The second study also analyses the "peer-learning" (PL) and "peer-tutoring" (PT) learning methods in an educational scenario, where a pair of children perform a collaborative writing activity in the presence of a robot facilitator. The data obtained in the first two studies allowed us to create a "taxonomy of handwriting errors". A set of writing errors were selected and implemented in an educational activity for validation. This activity constituted a third study, wherein we systematically induced the errors into a Nao robot's handwriting using the {PT} method - A teacher-child corrects the handwriting errors of the learner-robot. The preliminary results suggest that the children in general showed awareness to the writing errors and were able to perceive the writing abilities of the robot

Bacterial community structure and function shift across a northern boreal forest fire chronosequence

Soil microbial responses to fire are likely to change over the course of forest recovery. Investigations on long-term changes in bacterial dynamics following fire are rare. We characterized the soil bacterial communities across three different times post fire in a 2 to 152-year fire chronosequence by Illumina MiSeq sequencing, coupled with a functional gene array (GeoChip). The results showed that the bacterial diversity did not differ between the recently and older burned areas, suggesting a concomitant recovery in the bacterial diversity after fire. The differences in bacterial communities over time were mainly driven by the rare operational taxonomic units (OTUs <0.1%). Proteobacteria (39%), Acidobacteria (34%) and Actinobacteria (17%) were the most abundant phyla across all sites. Genes involved in C and N cycling pathways were present in all sites showing high redundancy in the gene profiles. However, hierarchical cluster analysis using gene signal intensity revealed that the sites with different fire histories formed separate clusters, suggesting potential differences in maintaining essential biogeochemical soil processes. Soil temperature, pH and water contents were the most important factors in shaping the bacterial community structures and function. This study provides functional insight on the impact of fire disturbance on soil bacterial community.Peer reviewe

Comparative susceptibility of eastern cottontails and New Zealand white rabbits to classical rabbit haemorrhagic disease virus (RHDV) and RHDV2

Rabbit haemorrhagic disease virus (RHDV) is associated with high morbidity and mortality in the European rabbit (Oryctolagus cuniculus). In 2010, a genetically distinct RHDV named RHDV2 emerged in Europe and spread to many other regions, including North America in 2016. Prior to this study it was unknown if eastern cottontails (ECT(s); Sylvilagus floridanus), one of the most common wild lagomorphs in the United States, were susceptible to RHDV2. In this study, 10 wild-caught ECTs and 10 New Zealand white rabbits (NZWR(s); O. cuniculus) were each inoculated orally with either RHDV (RHDVa/GI.1a; n = 5 per species) or RHDV2 (a recombinant GI.1bP-GI.2; n = 5 per species) and monitored for the development of disease. Three of the five ECTs that were infected with RHDV2 developed disease consistent with RHD and died at 4 and 6 days post-inoculation (DPI). The RHDV major capsid protein/antigen (VP60) was detected in the livers of three ECTs infected with RHDV2, but none was detected in the ECTs infected with RHDV. Additionally, RHD viral RNA was detected in the liver, spleen, intestine and blood of ECTs infected with RHDV2, but not in the ECTs infected with RHDV. RHD viral RNA was detected in urine, oral swabs and rectal swabs in at least two of five ECTs infected with RHDV2. One ECT inoculated with RHDV2 seroconverted and developed a high antibody titre by the end of the experimental period (21 DPI). ECTs inoculated with the classic RHDV did not seroconvert. In comparison, NZWRs inoculated with RHDV2 exhibited high mortality (five of five) at 2 DPI and four of five NZWRs inoculated with RHDV either died or were euthanized at 2 DPI indicating both of these viruses were highly pathogenic to this species. This experiment indicates that ECTs are susceptible to RHDV2 and can shed viral RNA, thereby suggesting this species could be involved in the epidemiology of this virus

SOS: A Screening Instrument to Identify Children with Handwriting Impairments

Poor handwriting has been shown to be associated with developmental disorders such as Developmental Coordination Disorder, Attention Deficit Hyperactivity Disorder, autism, and learning disorders. Handwriting difficulties could lead to academic underachievement and poor self-esteem. Therapeutic intervention has been shown to be effective in treating children with poor handwriting, making early identification critical. The SOS test (Systematic Screening for Handwriting Difficulties) has been developed for this purpose. A child copies a sample of writing within 5 min. Handwriting quality is evaluated using six criteria and writing speed is measured. The Dutch SOS test was administered to 860 Flemish children (7-12 years). Inter-and intrarater reliability was excellent. Test-retest reliability was moderate. A correlation coefficient of 0.70 between SOS and "Concise Assessment Methods of Children Handwriting" test (Dutch version) confirmed convergent validity. The SOS allowed discrimination between typically developing children and children in special education, males and females, and different age groups