On a Dirichlet problem related to the invertibility of mappings arising in 2D grid generation problems

this paper depends strongly on a theorem of Carleman-HartmanWintner. This theorem is only true in two dimensional domains. In fact a straightforward generalization to more than two dimensional domains cannot be true. A counterexample to the proof of [15]forthe three dimensional case can be found by using a special harmonic function due to Kellogg [12]. This function is shown in [2]. A direct counterexample can be found in [13]. 2 Main result on smooth domain

On the invertibility of mappings arising in 2D grid generation problems

In adapting a grid for a Computational Fluid Dynamics problem one uses a mapping from the unit square onto itself that is the solution of an elliptic partial differential equation with rapidly varying coefficients. For a regular discretization this mapping has to be invertible. We will show that such result holds for general elliptic operators (in two dimensions). The Carleman-Hartman-Wintner Theorem will be fundamental in our proof. We will also explain why such a general result cannot be expected to hold for the (three-dimensional) cube

A sufficient condition for a discrete spectrum of the Kirchhoff plate with an infinite peak

Sufficient conditions for a discrete spectrum of the biharmonic equation in a two-dimensional peak-shaped domain are established. Different boundary conditions from Kirchhoff's plate theory are imposed on the boundary and the results depend both on the type of boundary conditions and the sharpness exponent of the peak.Comment: 12 pages, 1 figure, submitted to Math. Mech. Compl. Sy

Optimal estimates from below for biharmonic Green functions

Optimal pointwise estimates are derived for the biharmonic Green function under Dirichlet boundary conditions in arbitrary $C^{4,\gamma}$-smooth domains. Maximum principles do not exist for fourth order elliptic equations and the Green function may change sign. It prevents using a Harnack inequality as for second order problems and hence complicates the derivation of optimal estimates. The present estimate is obtained by an asymptotic analysis. The estimate shows that this Green function is positive near the singularity and that a possible negative part is small in the sense that it is bounded by the product of the squared distances to the boundary.Comment: 11 pages. To appear in "Proceedings of the AMS

Multistage Zeeman deceleration of atomic and molecular oxygen

Multistage Zeeman deceleration is a technique used to reduce the velocity of neutral molecules with a magnetic dipole moment. Here we present a Zeeman decelerator that consists of 100 solenoids and 100 magnetic hexapoles, that is based on a short prototype design presented recently [Phys. Rev. A 95, 043415 (2017)]. The decelerator features a modular design with excellent thermal and vacuum properties, and is robustly operated at a 10 Hz repetition rate. This multistage Zeeman decelerator is particularly optimized to produce molecular beams for applications in crossed beam molecular scattering experiments. We characterize the decelerator using beams of atomic and molecular oxygen. For atomic oxygen, the magnetic fields produced by the solenoids are used to tune the final longitudinal velocity in the 500 - 125 m/s range, while for molecular oxygen the velocity is tunable in the 350 - 150 m/s range. This corresponds to a maximum kinetic energy reduction of 95% and 80% for atomic and molecular oxygen, respectively.Comment: Latest version as accepted by Physical Review

Sharp Sobolev Inequalities for Vector Valued Maps

We discuss sharp Sobolev inequalities for vector valued maps.Comment: 25 page

On the many Dirichlet Laplacians on a non-convex polygon and their approximations by point interactions

By Birman and Skvortsov it is known that if \Omegasf is a planar curvilinear polygon with $n$ non-convex corners then the Laplace operator with domain H^2(\Omegasf)\cap H^1_0(\Omegasf) is a closed symmetric operator with deficiency indices $(n,n)$. Here we provide a Kre\u\i n-type resolvent formula for any self-adjoint extensions of such an operator, i.e. for the set of self-adjoint non-Friedrichs Dirichlet Laplacians on \Omegasf, and show that any element in this set is the norm resolvent limit of a suitable sequence of Friedrichs-Dirichlet Laplacians with $n$ point interactions.Comment: Slightly revised version. Accepted for publication in Journal of Functional Analysi

Betriebsstruktur und Grobfuttererzeugung ökologisch wirtschaftender Milchviehbetriebe in Deutschland

Die Erzeugung hochwertiger Grobfuttermittel spielt für die Rentabilität und Nachhaltigkeit der Milcherzeugung im ökologischen Landbau eine entscheidende Rolle. Grobfuttermittel beeinflussen die Gesundheit und Leistung des Milchviehs auf verschiedene Art und Weise. Zudem variieren die standörtlichen Bedingungen des Futterbaus sowie die avisierten Leistungsniveaus der Milchviehhaltung in der Praxis erheblich (Haas et al. 2001, Brinkmann & Winckler 2005, Müller-Lindenlauf et al. 2010). Ziel dieser Untersuchung ist es, die Variabilität der betrieblichen Konzepte der Grobfuttererzeugung überregional zu analysieren und etwaige Strategietypen zu identifizieren, die für weitergehende Analysen und Beratungsempfehlungen eine objektivierte Grundlage bieten