The Degasperis-Procesi equation as a non-metric Euler equation

In this paper we present a geometric interpretation of the periodic Degasperis-Procesi equation as the geodesic flow of a right invariant symmetric linear connection on the diffeomorphism group of the circle. We also show that for any evolution in the family of $b$-equations there is neither gain nor loss of the spatial regularity of solutions. This in turn allows us to view the Degasperis-Procesi and the Camassa-Holm equation as an ODE on the Fr\'echet space of all smooth functions on the circle.Comment: 17 page

Pilot Experiments with Electrodialysis and Ozonation for the Production of a Fertilizer from Urine

Pilot tests were performed with a process combination of electrodialysis and ozonation for the removal of micropollutants and the concentration of nutrients in urine. In continuous and batch experiments, maximum concentration factors up to 3.5 and 4.1 were obtained, respectively. The desalination capacity did not decrease significantly during continuous operation periods of several weeks. Membrane cleaning after 195 days resulted in approximately 35% increase in desalination rate. The Yeast Estrogen Screen (YES), a bioassay that selectively detects oestrogenic compounds, confirmed that about 90% of the oestrogenic activity was removed by electrodialysis. HPLC analysis showed that ibuprofen was removed to a high extent, while other micropollutants were below the detection limit. In view of the fact that ibuprofen is among the most rapidly transported micropollutants in electrodialysis processes, this result indicates that electrodialysis provides an effective barrier for micropollutants. Standardised plant growth tests were performed in the field with the salt solution resulting from the treatment by electrodialysis and subsequent ozonation. The results show that the plant height is comparable to synthetic fertilisers, but the crop yield is slightly lower. The latter is probably caused by volatilisation losses during field application, which can be prevented by improved application technologies

The geometry of a vorticity model equation

We provide rigorous evidence of the fact that the modified Constantin-Lax-Majda equation modeling vortex and quasi-geostrophic dynamics describes the geodesic flow on the subgroup of orientation-preserving diffeomorphisms fixing one point, with respect to right-invariant metric induced by the homogeneous Sobolev norm $H^{1/2}$ and show the local existence of the geodesics in the extended group of diffeomorphisms of Sobolev class $H^{k}$ with $k\ge 2$.Comment: 24 page

Many-body approach to proton emission and the role of spectroscopic factors

The process of proton emission from nuclei is studied by utilizing the two-potential approach of Gurvitz and Kalbermann in the context of the full many-body problem. A time-dependent approach is used for calculating the decay width. Starting from an initial many-body quasi-stationary state, we employ the Feshbach projection operator approach and reduce the formalism to an effective one-body problem. We show that the decay width can be expressed in terms of a one-body matrix element multiplied by a normalization factor. We demonstrate that the traditional interpretation of this normalization as the square root of a spectroscopic factor is only valid for one particular choice of projection operator. This causes no problem for the calculation of the decay width in a consistent microscopic approach, but it leads to ambiguities in the interpretation of experimental results. In particular, spectroscopic factors extracted from a comparison of the measured decay width with a calculated single-particle width may be affected.Comment: 17 pages, Revte