The block numerical range of analytic operator functions

We introduce the block numerical range Wn(L) of an operator function L with respect to a decomposition H = H1⊕. . .⊕Hn of the underlying Hilbert space. Our main results include the spectral inclusion property and estimates of the norm of the resolvent for analytic L . They generalise, and improve, the corresponding results for the numerical range (which is the case n = 1) since the block numerical range is contained in, and may be much smaller than, the usual numerical range. We show that refinements of the decomposition entail inclusions between the corresponding block numerical ranges and that the block numerical range of the operator matrix function L contains those of its principal subminors. For the special case of operator polynomials, we investigate the boundedness of Wn(L) and we prove a Perron-Frobenius type result for the block numerical radius of monic operator polynomials with coefficients that are positive in Hilbert lattice sense.

Hygrical shrinkage stresses in tiling systems: Numerical modeling combined with field studies

To track down potential sites of material failure in the tile–mortar–substrate systems, locations and intensities of stress concentrations owing to drying-induced shrinkage are investigated. For this purpose, mechanical properties were measured on real systems and used as input parameters for numerical modeling of the effect of shrinkage of substrate and/or mortar using the finite element code Abaqus. On the base of different geometrical set-ups we demonstrate that stress concentrations in the mortar can become critical when (i) substantial mortar shrinkage occurs, (ii) substrate shrinkage can accumulate over considerable spatial distances, particularly (iii) in situations where the mortar layer is not separated from the substrate by a flexible waterproofing membrane. Hence material failure in the system tile–mortar–substrate can be prevented (or reduced) by (i) an application of the tiles after the major stages of substrate shrinkage, (ii) the use of elasto-plastic deformable tile adhesives which can react elastically on local stress concentrations, (iii) the implementation of flexible membranes, and (iv) a reduction of the field size by the installation of flexible joints.

A numerical model for inert gas transport in the lung based on fractal airway morphology

Patients suffering from cystic fibrosis (CF) show thick secretions, mucus plugging and bronchiectasis in bronchial and alveolar ducts. This results in substantial structural changes of the airway morphology and heterogeneous ventilation. Disease progression and treatment effects are monitored by so-called gas washout tests, where the change in concentration of an inert gas is measured over a single or multiple breaths. The result of the tests based on the profile of the measured concentration is a marker for the severity of the ventilation inhomogeneity strongly affected by the airway morphology. However, it is hard to localize underlying obstructions to specific parts of the airways, especially if occurring in the lung periphery. In order to support the analysis of lung function tests (e.g. multi-breath washout), we developed a numerical model of the entire airway tree, coupling a lumped parameter model for the lung ventilation with a 4th-order accurate finite difference model of a 1D advection-diffusion equation for the transport of an inert gas. The boundary conditions for the flow problem comprise the pressure and flow profile at the mouth, which is typically known from clinical washout tests. The natural asymmetry of the lung morphology is approximated by a generic, fractal, asymmetric branching scheme which we applied for the conducting airways. A conducting airway ends when its dimension falls below a predefined limit. A model acinus is then connected to each terminal airway. The morphology of an acinus unit comprises a network of expandable cells. A regional, linear constitutive law describes the pressure-volume relation between the pleural gap and the acinus. The cyclic expansion (breathing) of each acinus unit depends on the resistance of the feeding airway and on the flow resistance and stiffness of the cells themselves. Special care was taken in the development of a conservative numerical scheme for the gas transport across bifurcations, handling spatially and temporally varying advective and diffusive fluxes over a wide range of scales. Implicit time integration was applied to account for the numerical stiffness resulting from the discretized transport equation. Local or regional modification of the airway dimension, resistance or tissue stiffness are introduced to mimic pathological airway restrictions typical for CF. This leads to a more heterogeneous ventilation of the model lung. As a result the concentration in some distal parts of the lung model remains increased for a longer duration. The inert gas concentration at the mouth towards the end of the expirations is composed of gas from regions with very different washout efficiency. This results in a steeper slope of the corresponding part of the washout profile.

Numerical corrections to the strong coupling effective Polyakov-line action for finite T Yang-Mills theory

We consider a three-dimensional effective theory of Polyakov lines derived previously from lattice Yang-Mills theory and QCD by means of a resummed strong coupling expansion. The effective theory is useful for investigations of the phase structure, with a sign problem mild enough to allow simulations also at finite density. In this work we present a numerical method to determine improved values for the effective couplings directly from correlators of 4d Yang-Mills theory. For values of the gauge coupling up to the vicinity of the phase transition, the dominant short range effective coupling are well described by their corresponding strong coupling series. We provide numerical results also for the longer range interactions, Polyakov lines in higher representations as well as four-point interactions, and discuss the growing significance of non-local contributions as the lattice gets finer. Within this approach the critical Yang-Mills coupling β c is reproduced to better than one percent from a one-coupling effective theory on N τ = 4 lattices while up to five couplings are needed on N τ = 8 for the same accuracy.

Numerical study of the laser-tip coupling in surface plasmon assisted stacked-double-gate field emitter arrays

Recently, sub-wavelength-pitch stacked double-gate metal nanotip arrays have been proposed to realize high current, high brightness electron bunches for ultrabright cathodes for x-ray free-electron laser applications. With the proposed device structure, ultrafast field emission of photoexcited electrons is efficiently driven by vertical incident near infrared laser pulses, via near field coupling of the surface plasmon polariton resonance of the gate electrodes with the nanotip apex. In this work, in order to gain insight in the underlying physical processes, the authors report detailed numerical studies of the proposed device. The results indicate the importance of the interaction of the double-layer surface plasmon polariton, the position of the nanotip, as well as the incident angle of the near infrared laser pulses.

Comparison of co-located independent ground-based middle atmospheric wind and temperature measurements with numerical weather prediction models

High-resolution, ground-based and independent observations including co-located wind radiometer, lidar stations, and infrasound instruments are used to evaluate the accuracy of general circulation models and data-constrained assimilation systems in the middle atmosphere at northern hemisphere midlatitudes. Systematic comparisons between observations, the European Centre for Medium-Range Weather Forecasts (ECMWF) operational analyses including the recent Integrated Forecast System cycles 38r1 and 38r2, the NASA’s Modern-Era Retrospective Analysis for Research and Applications (MERRA) reanalyses, and the free-running climate Max Planck Institute–Earth System Model–Low Resolution (MPI-ESM-LR) are carried out in both temporal and spectral dom ains. We find that ECMWF and MERRA are broadly consistent with lidar and wind radiometer measurements up to ~40 km. For both temperature and horizontal wind components, deviations increase with altitude as the assimilated observations become sparser. Between 40 and 60 km altitude, the standard deviation of the mean difference exceeds 5 K for the temperature and 20 m/s for the zonal wind. The largest deviations are observed in winter when the variability from large-scale planetary waves dominates. Between lidar data and MPI-ESM-LR, there is an overall agreement in spectral amplitude down to 15–20 days. At shorter time scales, the variability is lacking in the model by ~10 dB. Infrasound observations indicate a general good agreement with ECWMF wind and temperature products. As such, this study demonstrates the potential of the infrastructure of the Atmospheric Dynamics Research Infrastructure in Europe project that integrates various measurements and provides a quantitative understanding of stratosphere-troposphere dynamical coupling for numerical weather prediction applications.

Numerical Magnitude Skills in 6-Years-Old Children: Exploring Specific Associations with Components of Executive Function

Little is known about how children learn to associate numbers with their corresponding magnitude and about individual characteristics contributing to performance differences on the numerical magnitude tasks within a relatively homogenous sample of 6-year-olds. The present study investigated the relationships between components of executive function and two different numerical magnitude skills in a sample of 162 kindergartners. The Symbolic Number Line was predicted by verbal updating and switching, whereas the Symbolic Magnitude Comparison was predicted by inhibition. Both symbolic tasks were predicted by visuo-spatial updating. Current findings suggest that visuo-spatial updating underlies young children’s retrieval and processing of numbers’ magnitude.

Case studies of the effects of a total solar eclipse on weather with varying degrees of cloud cover using a local numerical weather prediction model

The importance of renewable energies for the European electricity market is growing rapidly. This presents transmission grids and the power market in general with new challenges which stem from the higher spatiotemporal variability of power generation. This uncertainty is due to the fact that renewable power production results from weather phenomena, thus making it difficult to plan and control. We present a sensitivity study of a total solar eclipse in central Europe in March. The weather in Germany and Europe was modeled using the German Weather Service's local area models COSMO-DE and COSMO-EU, respectively (http://www.cosmo-model.org/). The simulations were performed with and without considering a solar eclipse for the following 3 situations: 1. An idealized, clear-sky situation for the entire model area (Europe, COSMO-EU) 2. A real weather situation with mostly cloudy skies (Germany, COSMO-DE) 3. A real weather situation with mostly clear skies (Germany, COSMO-DE) The data should help to evaluate the effects of a total solar eclipse on the weather in the planetary boundary layer. The results show that a total solar eclipse has significant effects particularly on the main variables for renewable energy production, such as solar irradiation and temperature near the ground.

Lagrangian back-tracing results for Kohnen station; output of time dependent numerical experiment with a 3D nested Antarctic ice sheet model

A nested ice flow model was developed for eastern Dronning Maud Land to assist with the dating and interpretation of the EDML deep ice core. The model consists of a high-resolution higher-order ice dynamic flow model that was nested into a comprehensive 3-D thermomechanical model of the whole Antarctic ice sheet. As the drill site is on a flank position the calculations specifically take into account the effects of horizontal advection as deeper ice in the core originated from higher inland. First the regional velocity field and ice sheet geometry is obtained from a forward experiment over the last 8 glacial cycles. The result is subsequently employed in a Lagrangian backtracing algorithm to provide particle paths back to their time and place of deposition. The procedure directly yields the depth-age distribution, surface conditions at particle origin, and a suite of relevant parameters such as initial annual layer thickness. This paper discusses the method and the main results of the experiment, including the ice core chronology, the non-climatic corrections needed to extract the climatic part of the signal, and the thinning function. The focus is on the upper 89% of the ice core (appr. 170 kyears) as the dating below that is increasingly less robust owing to the unknown value of the geothermal heat flux. It is found that the temperature biases resulting from variations of surface elevation are up to half of the magnitude of the climatic changes themselves.