Comparison results for the Stokes equations

This paper enfolds a medius analysis for the Stokes equations and compares different finite element methods (FEMs). A first result is a best approximation result for a P1 non-conforming FEM. The main comparison result is that the error of the P2-P0-FEM is a lower bound to the error of the Bernardi-Raugel (or reduced P2-P0) FEM, which is a lower bound to the error of the P1 non-conforming FEM, and this is a lower bound to the error of the MINI-FEM. The paper discusses the converse direction, as well as other methods such as the discontinuous Galerkin and pseudostress FEMs. Furthermore this paper provides counterexamples for equivalent convergence when different pressure approximations are considered. The mathematical arguments are various conforming companions as well as the discrete inf-sup condition

Impact of model parameter optimisation on the properties of ensemble forecasts

Numerical weather prediction models are the backbone of modern weather forecasting. They discretise and approximate the continuous multi-scale atmosphere into computable chunks. Thus, small-scale and complex processes must be parametrised rather than explicitly calculated. This introduces parameters estimated by empirical methods best fit the observed nature. However, the changes to the parameters are changing the properties of the model itself. This work quantifies the impact parameter optimisation has on ensemble forecasts. OpenEPS allows running automated ensemble forecasts in a scientific setting. Here, it uses the OpenIFS model at T255L91 resolution with a 20 min timestep to create 10-day forecasts, which are initialised every week in the period from 1.12.2016 to 30.11.2017. Four different experiments are devised to study the impact on the forecast. The experiments only differ in the parameter values supplied to OpenIFS, all other boundary conditions are held constant. The parameters for the experiments are obtained using the EPPES optimisation tool with different goals. The first experiment minimises the cost function by supplying knowledge regarding the ensemble initial perturbation. The second experiment takes a set of parameters with a worse cost function value. Experiments three and four replicate experiments one and two with the difference that the ensemble initial perturbations are not provided to EPPES. The quality of an ensemble forecast is quantified with a series of metrics. Root mean squared error, spread, and continuous ranked probability score are used with ERA5 reanalysis data as the reference, while the filter likelihood score is providing a direct comparison with observations. The results are summarised in comprehensive scorecards. This work shows that optimising parameters decreases the root mean square error and continuous ranked probability score of the ensemble forecast. However, if the initial perturbations are included in the optimisation the spread of the ensemble is strongly limited. It also could be shown that this effect is reversed if the parameters are tuned with a worse cost function. Nonetheless, when excluding the initial perturbations from the optimisation process, then a better model can be achieved without sacrificing the ensemble spread

Analysis of Mobile Agents using Invariants of Object Nets

Mobility induces new challenges for dynamic systems, which need a new conceptional treatment: systems, that deal for example with mobile agents, need extended security concepts to handle the risks, induced by foreign, untrusted agents. In this contribution we use object nets to model mobile systems. Object nets are Petri nets which have Petri nets as tokens – an approach known as the nets-withinnets paradigm. Object nets are called elementary if the net system has a two levelled structure. In this work we apply structural analysis methods for object nets – namely place invariants – to a simple case study modelling mobile agents

Dynamics of Natural Killer cell receptor revealed by quantitative analysis of photoswitchable protein

Natural Killer (NK) cell activation is dynamically regulated by numerous activating and inhibitory surface receptors that accumulate at the immune synapse. Quantitative analysis of receptor dynamics has been limited by methodologies which rely on indirect measurements such as fluorescence recovery after photobleaching. Here, we report a novel approach to study how proteins traffic to and from the immune synapse using NK cell receptors tagged with the photoswitchable fluorescent protein tdEosFP, which can be irreversibly photoswitched from a green to red fluorescent state by ultraviolet light. Thus, following a localized switching event, the movement of the photoswitched molecules can be temporally and spatially resolved by monitoring fluorescence in two regions of interest. By comparing images with mathematical models, we evaluated the diffusion coefficient of the receptor KIR2DL1 (0.23 +- 0.06 micron^2/s) and assessed how synapse formation affects receptor dynamics. Our data conclude that the inhibitory NK cell receptor KIR2DL1 is continually trafficked into the synapse and remains surprisingly stable there. Unexpectedly however, in NK cells forming synapses with multiple target cells simultaneously, KIR2DL1 at one synapse can relocate to another synapse. Thus, our results reveal a previously undetected inter-synaptic exchange of protein.Comment: 25 pages, 5 figure

Continuum multiscale modeling of absorption processes in micro- and nanocatalysts

In this paper, we propose a novel, semi-analytic approach for the two-scale, computational modeling of concentration transport in packed bed reactors. Within the reactor, catalytic pellets are stacked, which alter the concentration evolution. Firstly, the considered experimental setup is discussed and a naive one-scale approach is presented. This one-scale model motivates, due to unphysical fitted values, to enrich the computational procedure by another scale. The computations on the second scale, here referred to as microscale, are based on a proper investigation of the diffusion process in the catalytic pellets from which, after continuum-consistent considerations, a sink term for the macroscopic advection–diffusion–reaction process can be identified. For the special case of a spherical catalyst pellet, the parabolic partial differential equation at the microscale can be reduced to a single ordinary differential equation in time through a semi-analytic approach. After the presentation of our model, we show results for its calibration against the macroscopic response of a simple standard mass transport experiment. Based thereon, the effective diffusion parameters of the catalyst pellets can be identified. © 2022, The Author(s)

Nonlinearities in shadowgraphy experiments on non-equilibrium fluctuations in polymer solutions

Giant thermal and solutal non-equilibrium fluctuations are observed in shadowgraphy experiments on liquid mixtures subjected to a temperature gradient. For large temperature differences, both the temperature and the composition dependence of the relevant thermophysical parameters and the nonlinear terms in the diffusion equation need to be taken into account, leading to a nonlinear concentration profile. For temperature differences exceeding the inverse of the Soret coefficient, in our example approximately 10 K, the usual data evaluation yields increasingly wrong diffusion and Soret coefficients that are off by almost a factor of two for a temperature difference of 50 K. A local model that treats the measured shadowgraph signal as a superposition of the contributions from every layer of the sample is able to capture the essential trend and yields a good agreement with experimental data. The results are important for the application of shadowgraphy as a tool for the measurement of Soret and diffusion coefficients, where large temperature gradients promise a good signal-to-noise ratio

Increasing Evapotranspiration on Extensive Green Roofs by Changing Substrate Depths, Construction, and Additional Irrigation

Urban environments are characterized by dense development and paved ground with reduced evapotranspiration rates. These areas store sensible and latent heat, providing the base for typical urban heat island effects. Green roof installations are one possible strategy to reintroduce evaporative surfaces into cities. If green roofs are irrigated, they can contribute to urban water management and evapotranspiration can be enhanced. As part of two research projects, lysimeter measurements were used to determine the real evapotranspiration rates on the research roof of the University of Applied Sciences in Neubrandenburg, Germany. In this paper, we address the results from 2017, a humid and cool summer, and 2018, a century summer with the highest temperatures and dryness over a long period of time, measured in Northeast Germany. The lysimeter measurements varied between the normal green roof layer (variation of extensive green roof constructions) and a special construction with an extra retention layer and damming. The results show that the average daily evapotranspiration rates can be enhanced from 3 to 5 L/m2/day under optimized conditions. A second test on a real green roof with irrigation was used to explain the cooling effects of the surface above a café building in Berlin