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