A note on multi-dimensional Camassa-Holm type systems on the torus

We present a $2n$-component nonlinear evolutionary PDE which includes the $n$-dimensional versions of the Camassa-Holm and the Hunter-Saxton systems as well as their partially averaged variations. Our goal is to apply Arnold's [V.I. Arnold, Sur la g\'eom\'etrie diff\'erentielle des groupes de Lie de dimension infinie et ses applications \`a l'hydrodynamique des fluides parfaits. Ann. Inst. Fourier (Grenoble) 16 (1966) 319-361], [D.G. Ebin and J.E. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid. Ann. of Math. 92(2) (1970) 102-163] geometric formalism to this general equation in order to obtain results on well-posedness, conservation laws or stability of its solutions. Following the line of arguments of the paper [M. Kohlmann, The two-dimensional periodic $b$-equation on the diffeomorphism group of the torus. J. Phys. A.: Math. Theor. 44 (2011) 465205 (17 pp.)] we present geometric aspects of a two-dimensional periodic $\mu$-$b$-equation on the diffeomorphism group of the torus in this context.Comment: 14 page

Precision high voltage divider for the KATRIN experiment

The Karlsruhe Tritium Neutrino Experiment (KATRIN) aims to determine the absolute mass of the electron antineutrino from a precise measurement of the tritium beta-spectrum near its endpoint at 18.6 keV with a sensitivity of 0.2 eV. KATRIN uses an electrostatic retardation spectrometer of MAC-E filter type for which it is crucial to monitor high voltages of up to 35 kV with a precision and long-term stability at the ppm level. Since devices capable of this precision are not commercially available, a new high voltage divider for direct voltages of up to 35 kV has been designed, following the new concept of the standard divider for direct voltages of up to 100 kV developed at the Physikalisch-Technische Bundesanstalt (PTB). The electrical and mechanical design of the divider, the screening procedure for the selection of the precision resistors, and the results of the investigation and calibration at PTB are reported here. During the latter, uncertainties at the low ppm level have been deduced for the new divider, thus qualifying it for the precision measurements of the KATRIN experiment.Comment: 22 pages, 12 figure

The geometry of the two-component Camassa-Holm and Degasperis-Procesi equations

We use geometric methods to study two natural two-component generalizations of the periodic Camassa-Holm and Degasperis-Procesi equations. We show that these generalizations can be regarded as geodesic equations on the semidirect product of the diffeomorphism group of the circle \Diff(S^1) with some space of sufficiently smooth functions on the circle. Our goals are to understand the geometric properties of these two-component systems and to prove local well-posedness in various function spaces. Furthermore, we perform some explicit curvature calculations for the two-component Camassa-Holm equation, giving explicit examples of large subspaces of positive curvature.Comment: 31 page

Necrotic tumor growth: an analytic approach

The present paper deals with a free boundary problem modeling the growth process of necrotic multi-layer tumors. We prove the existence of flat stationary solutions and determine the linearization of our model at such an equilibrium. Finally, we compute the solutions of the stationary linearized problem and comment on bifurcation.Comment: 14 pages, 3 figure

On the seasonal variability of eddy kinetic energy in the Gulf Stream region. Geophys

. [1] In the Gulf Stream region, eddy kinetic energy (EKE) peaks in summer while, as measured by the baroclinic eddy growth time scale, the ocean is most baroclinically unstable in late winter. We argue that the seasonally-varying Ekman pumping is unlikely to be responsible for the seasonal variation in growth time, and that the summer peak in EKE results from a reduction in dissipation in summer compared to winter. Citation: Zhai, X., R

The curvature of semidirect product groups associated with two-component Hunter-Saxton systems

In this paper, we study two-component versions of the periodic Hunter-Saxton equation and its $\mu$-variant. Considering both equations as a geodesic flow on the semidirect product of the circle diffeomorphism group \Diff(\S) with a space of scalar functions on $\S$ we show that both equations are locally well-posed. The main result of the paper is that the sectional curvature associated with the 2HS is constant and positive and that 2$\mu$HS allows for a large subspace of positive sectional curvature. The issues of this paper are related to some of the results for 2CH and 2DP presented in [J. Escher, M. Kohlmann, and J. Lenells, J. Geom. Phys. 61 (2011), 436-452].Comment: 19 page

Using knowledge for decision-making purposes

Abstract: Policy-related research in general, and Impact Assessments in particular, are too loosely connected to decision-making processes. The result is often sub-optimal or even undesirable, as one of two situations arises: 1) much research is done; however, those with the real power to make decisions do not make use of all of the resulting information, or 2) advocates of contrary opinions struggle with each other, using policy-related research as ammunition. To avoid these unwanted situations, the connection between the world of knowledge and the world of decisionmaking should be carefully constructed, by connecting the process of decision-making to the academic research and carefully developing research goals in response to the demands of decision-makers. By making these connections in a stepwise manner, knowledge may generate new insights and views for involved decision-makers and stakeholders, thus changing perceptions and problem definitions. In this way, these actors learn about the possibilities of several alternatives as well as each other’s perceptions, and thus can make educated decisions leading to the most desirable and socially acceptable solution. The way this proposed method works is illustrated using two cases in The Netherlands: the project “Mainport Rotterdam” (the enlargement of the port of Rotterdam), the project “A fifth runway for Amsterdam Airport (Schiphol)”