Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations

We present new interior regularity criteria for suitable weak solutions of the 3-D Navier-Stokes equations: a suitable weak solution is regular near an interior point $z$ if either the scaled $L^{p,q}_{x,t}$-norm of the velocity with $3/p+2/q\leq 2$, $1\leq q\leq \infty$, or the $L^{p,q}_{x,t}$-norm of the vorticity with $3/p+2/q\leq 3$, $1 \leq q < \infty$, or the $L^{p,q}_{x,t}$-norm of the gradient of the vorticity with $3/p+2/q\leq 4$, $1 \leq q$, $1 \leq p$, is sufficiently small near $z$

Effects of submerged vegetation on water clarity across climates

A positive feedback between submerged vegetation and water clarity forms the backbone of the alternative state theory in shallow lakes. The water clearing effect of aquatic vegetation may be caused by different physical, chemical, and biological mechanisms and has been studied mainly in temperate lakes. Recent work suggests differences in biotic interactions between (sub)tropical and cooler lakes might result in a less pronounced clearing effect in the (sub)tropics. To assess whether the effect of submerged vegetation changes with climate, we sampled 83 lakes over a gradient ranging from the tundra to the tropics in South America. Judged from a comparison of water clarity inside and outside vegetation beds, the vegetation appeared to have a similar positive effect on the water clarity across all climatic regions studied. However, the local clearing effect of vegetation decreased steeply with the contribution of humic substances to the underwater light attenuation. Looking at turbidity on a whole-lake scale, results were more difficult to interpret. Although lakes with abundant vegetation (>30%) were generally clear, sparsely vegetated lakes differed widely in clarity. Overall, the effect of vegetation on water clarity in our lakes appears to be smaller than that found in various Northern hemisphere studies. This might be explained by differences in fish communities and their relation to vegetation. For instance, unlike in Northern hemisphere studies, we find no clear relation between vegetation coverage and fish abundance or their diet preference. High densities of omnivorous fish and coinciding low grazing pressures on phytoplankton in the (sub)tropics may, furthermore, weaken the effect of vegetation on water clarity

Biaxial Testing of Elastomers: Experimental Setup, Measurement and Experimental Optimisation of Specimen’s Shape

The present article deals with the setup and the control of a biaxial tension test device for characterising the material properties of elastomers. After a short introduction into the experimental setup a brief explanation of the benefits of a biaxial tension test is given. Furthermore the analysis of this test will be discussed. Therefore, the used optical field measurement by digital image correlation for analysing the strains is shortly introduced to the reader. Additionally, the basic concepts of the calculation of an inverse boundary problem for identifying the material’s parameters are imposed. However the main focus is laid on the experimental optimisation of the specimen’s geometry, whereupon a nearly hyperelastic, incompressible silicone is used to get the experimental results. The resulting geometry will be specially fitted to the requirements of elastomers. The tested geometries and the evaluation of the experiments will be explained as well as the resulting quality factor for the suitability of a specimen’s shape. After all, a short validation of the foregoing considerations will be presented

Implementation of the strongly pronounced non-linear viscoelasticity of an incompressible filled rubber

Filled rubber materials regularly show a pronounced non-linear viscoelasticity with very long relaxation times. In this contribution, a phenomenological description for an incompressible carbon black-filled EPDM (ethylene propylene diene monomer) is given, which also shows the abovementioned characteristic behaviour. In order to represent the non-linear viscoelastic material, the relaxation times of the model are chosen not as constant material parameters but as process-dependent functions. This contribution presents two different realisations of the model’s implementation. At first, this work provides an implementation of the material model, which is able to describe complex geometries and loading conditions. In this realisation, the three-dimensional model is implemented in the open source finite element library deal.II for finite deformations. Hence, real applications can be represented. In an alternative numerical solution, the model is reduced to the single case of uniaxial tension. The model is simplified to scalar equations, which are quite easy to handle for the implementation. This procedure provides a more simple identification process, but it presents the roblem that the model character is extremely restricted for the individual case of uniaxial tension. For the numerical realisation, at first, special attention has to be turned on the determination of the inelastic part of the kinematics. A detailed evaluation of the necessary evolution equations is provided in this contribution. Finally, he results of the different implementations are compared with respect to different loading conditions, like relaxation tests or cyclic loading

On admissibility criteria for weak solutions of the Euler equations

We consider solutions to the Cauchy problem for the incompressible Euler equations satisfying several additional requirements, like the global and local energy inequalities. Using some techniques introduced in an earlier paper we show that, for some bounded compactly supported initial data, none of these admissibility criteria singles out a unique weak solution. As a byproduct we show bounded initial data for which admissible solutions to the p-system of isentropic gas dynamics in Eulerian coordinates are not unique in more than one space dimension.Comment: 33 pages, 1 figure; v2: 35 pages, corrected typos, clarified proof

Climate-dependent CO2 emissions from lakes

Inland waters, just as the world's oceans, play an important role in the global carbon cycle. While lakes and reservoirs typically emit CO2, they also bury carbon in their sediment. The net CO2 emission is largely the result of the decomposition or preservation of terrestrially supplied carbon. What regulates the balance between CO2 emission and carbon burial is not known, but climate change and temperature have been hypothesized to influence both processes. We analyzed patterns in carbon dioxide partial pressure (pCO2) in 83 shallow lakes over a large climatic gradient in South America and found a strong, positive correlation with temperature. The higher pCO2 in warmer lakes may be caused by a higher, temperature-dependent mineralization of organic carbon. This pattern suggests that cool lakes may start to emit more CO2 when they warm up because of climate ch

Universal Guard Problems

We provide a spectrum of results for the Universal Guard Problem, in which one is to obtain a small set of points ("guards") that are "universal" in their ability to guard any of a set of possible polygonal domains in the plane. We give upper and lower bounds on the number of universal guards that are always sufficient to guard all polygons having a given set of n vertices, or to guard all polygons in a given set of k polygons on an n-point vertex set. Our upper bound proofs include algorithms to construct universal guard sets of the respective cardinalities

Thresholds Are in the Eye of the Beholder: Plants and Wildlife Respond Differently to Short‐Term Cattle Corrals

Rangelands are governed by threshold dynamics, and factors such as drought, wildfire, and herbivory can drive change across thresholds and between ecological states. Most work on this topic has focused on shifts in a single response variable, vegetation, and little research has considered how to reconcile responses of more than one variable to determine whether a system has undergone a genuine state change. In sub‐Saharan Africa, mobile overnight livestock corrals (bomas) can be used by managers to precipitate ecological transitions from areas dominated by bare ground to productive ecosystem hotspots (glades) that are attractive to wild herbivores. We asked how long bomas must be occupied by cattle before undergoing a state change, considering both plant and animal response variables, to glade ecosystem hotspots. We tested five durations of boma occupation: 0, 4, 7, 14, and 28 days. Each treatment was replicated five times, and we assessed vegetation as well as herbivore dung (as a proxy of use) at multiple time points over 3 yr following boma abandonment. Vegetation in 7‐, 14‐, and 28‐d boma duration treatments appeared to undergo a complete transition to glade‐like plant communities, whereas the shortest 4‐d treatment had not converted to a glade plant community by year 3. Wildlife responses appeared to lag behind vegetation responses, with transitions to glade‐like herbivore use occurring only in the longest duration (14‐ and 28‐d) treatments. Our results show that different response variables, when considered individually, may provide incomplete or misleading information about state changes. Although shorter‐occupied bomas might be effective for reducing bare ground, they may not attract enough wild herbivores to constitute crossing into an alternative state. Understanding threshold dynamics associated not only with vegetation responses but with a broader suite of response variables is challenging, but will provide a more complete representation of ecosystem function and greater opportunity for more successful ecosystem management