On the flow map for 2D Euler equations with unbounded vorticity

In Part I, we construct a class of examples of initial velocities for which the unique solution to the Euler equations in the plane has an associated flow map that lies in no Holder space of positive exponent for any positive time. In Part II, we explore inverse problems that arise in attempting to construct an example of an initial velocity producing an arbitrarily poor modulus of continuity of the flow map.Comment: http://iopscience.iop.org/0951-7715/24/9/013/ for published versio

Analysis of complex singularities in high-Reynolds-number Navier-Stokes solutions

Numerical solutions of the laminar Prandtl boundary-layer and Navier-Stokes equations are considered for the case of the two-dimensional uniform flow past an impulsively-started circular cylinder. We show how Prandtl's solution develops a finite time separation singularity. On the other hand Navier-Stokes solution is characterized by the presence of two kinds of viscous-inviscid interactions that can be detected by the analysis of the enstrophy and of the pressure gradient on the wall. Moreover we apply the complex singularity tracking method to Prandtl and Navier-Stokes solutions and analyze the previous interactions from a different perspective

Ammonia emissions from cattle urine and dung excreted on pasture

Twelve cattle were kept for three days in a circular area of 16 m radius on short pasture and fed with freshly-cut pasture. Ammonia (NH<sub>3</sub>) emissions from the urine and dung excreted by the cattle were measured with a micrometeorological mass-balance method, during the cattle presence and for 10 subsequent days. Daily-integrated emission rates peaked on Day 3 of the experiment (last day of cattle presence) and declined steadily for five days thereafter. Urine patches were the dominant sources for these emissions. On Day 9, a secondary emissions peak occurred, with dung pats likely to be the main sources. This interpretation is based on simultaneous observations of the pH evolution in urine patches and dung pats created next to the circular plot. Feed and dung samples were analysed to estimate the amounts of nitrogen (N) ingested and excreted. Total N volatilised as NH<sub>3</sub> was 19.8 (± 0.9)% of N intake and 22.4 (± 1.3)% of N excreted. The bimodal shape of the emissions time series allowed to infer separate estimates for volatilisation from urine and dung, respectively, with the result that urine accounted for 88.6 (± 2.6)% of the total NH<sub>3</sub> emissions. The emissions from urine represented 25.5 (± 2.0)% of the excreted urine-N, while the emissions from dung amounted to 11.6 (± 2.7)% of the deposited dung-N. Emissions from dung may have continued after Day 13 but were not resolved by the measurement technique. A simple resistance model shows that the magnitude of the emissions from dung is controlled by the resistance of the dung crust

Viscous-Inviscid Interactions in a Boundary-Layer Flow Induced by a Vortex Array

In this paper we investigate the asymptotic validity of boundary layer theory. For a flow induced by a periodic row of point-vortices, we compare Prandtl's solution to Navier-Stokes solutions at different $Re$ numbers. We show how Prandtl's solution develops a finite time separation singularity. On the other hand Navier-Stokes solution is characterized by the presence of two kinds of viscous-inviscid interactions between the boundary layer and the outer flow. These interactions can be detected by the analysis of the enstrophy and of the pressure gradient on the wall. Moreover we apply the complex singularity tracking method to Prandtl and Navier-Stokes solutions and analyze the previous interactions from a different perspective

First hints of new sensors

A mechanism by which plants detect and respond to oxygen starvation has been known for some years. Three recent papers suggest that we haven’t been seeing the full picture

The Inviscid Limit and Boundary Layers for Navier-Stokes Flows

The validity of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations modeling viscous incompressible flows converge to solutions of the Euler equations modeling inviscid incompressible flows as viscosity approaches zero, is one of the most fundamental issues in mathematical fluid mechanics. The problem is classified into two categories: the case when the physical boundary is absent, and the case when the physical boundary is present and the effect of the boundary layer becomes significant. The aim of this article is to review recent progress on the mathematical analysis of this problem in each category.Comment: To appear in "Handbook of Mathematical Analysis in Mechanics of Viscous Fluids", Y. Giga and A. Novotn\'y Ed., Springer. The final publication is available at http://www.springerlink.co

Uniform regularity for the Navier-Stokes equation with Navier boundary condition

We prove that there exists an interval of time which is uniform in the vanishing viscosity limit and for which the Navier-Stokes equation with Navier boundary condition has a strong solution. This solution is uniformly bounded in a conormal Sobolev space and has only one normal derivative bounded in $L^\infty$. This allows to get the vanishing viscosity limit to the incompressible Euler system from a strong compactness argument

Contribution of the cyclic nucleotide gated channel subunit, CNG-3, to olfactory plasticity in Caenorhabditis elegans.

In Caenorhabditis elegans, the AWC neurons are thought to deploy a cGMP signaling cascade in the detection of and response to AWC sensed odors. Prolonged exposure to an AWC sensed odor in the absence of food leads to reversible decreases in the animal's attraction to that odor. This adaptation exhibits two stages referred to as short-term and long-term adaptation. Previously, the protein kinase G (PKG), EGL-4/PKG-1, was shown necessary for both stages of adaptation and phosphorylation of its target, the beta-type cyclic nucleotide gated (CNG) channel subunit, TAX-2, was implicated in the short term stage. Here we uncover a novel role for the CNG channel subunit, CNG-3, in short term adaptation. We demonstrate that CNG-3 is required in the AWC for adaptation to short (thirty minute) exposures of odor, and contains a candidate PKG phosphorylation site required to tune odor sensitivity. We also provide in vivo data suggesting that CNG-3 forms a complex with both TAX-2 and TAX-4 CNG channel subunits in AWC. Finally, we examine the physiology of different CNG channel subunit combinations

High intensity neutrino oscillation facilities in Europe

The EUROnu project has studied three possible options for future, high intensity neutrino oscillation facilities in Europe. The first is a Super Beam, in which the neutrinos come from the decay of pions created by bombarding targets with a 4 MW proton beam from the CERN High Power Superconducting Proton Linac. The far detector for this facility is the 500 kt MEMPHYS water Cherenkov, located in the Fréjus tunnel. The second facility is the Neutrino Factory, in which the neutrinos come from the decay of μ+ and μ− beams in a storage ring. The far detector in this case is a 100 kt magnetized iron neutrino detector at a baseline of 2000 km. The third option is a Beta Beam, in which the neutrinos come from the decay of beta emitting isotopes, in particular He6 and Ne18, also stored in a ring. The far detector is also the MEMPHYS detector in the Fréjus tunnel. EUROnu has undertaken conceptual designs of these facilities and studied the performance of the detectors. Based on this, it has determined the physics reach of each facility, in particular for the measurement of CP violation in the lepton sector, and estimated the cost of construction. These have demonstrated that the best facility to build is the Neutrino Factory. However, if a powerful proton driver is constructed for another purpose or if the MEMPHYS detector is built for astroparticle physics, the Super Beam also becomes very attractive