Burrow ventilation and associated porewater irrigation by the polychaete Marenzelleria viridis

Burrow ventilation of benthic infauna generates water currents that irrigate the interstices of the sediments surrounding the burrow walls. Such activities have associated effects on biogeochemical processes affecting ultimately important ecosystem processes. In this study, the ventilation and irrigation behavior of Marenzelleria viridis, an invasive polychaete species in Europe, was analyzed using different approaches. M. viridis showed to perform two types of ventilation: (1) muscular pumping of water out of the burrow and (2) cilia pumping of water into the burrow. Flowmeter measurements presented muscular pumping in time averaged rates of 0.15 ml min(-1). Oxygen needle electrodes positioned above the burrow openings revealed that muscular undulation of the worm body pumps anoxic water out of the burrow. On the other hand, microscope observations of the animal showed that ventilation of oxygen-rich water in the burrow occurs by ciliary action. The volume of water irrigated by M. viridis appears to vary linearly within the first 24 h incubation, with rates ranging from 0.003 to 0.01 ml min(-1). From those rates we could estimate that the time averaged rate of cilia ventilation should be about 0.16 ml min(-1). Since the cilia pumping into the burrow occurs in periods of 24 +/- 12 min and at 50-70% of the measured time, considerable amounts of water from deeper sediments may percolate upwards to the sediment surface. This water is rich in reduced compounds and nutrients and may have important associated ecological implications in the ecosystem (e.g. affecting redox conditions, organic matter degradation, benthic recruitment and primary production). (C) 2010 Elsevier B.V. All rights reserved.

Counting singularities via fitting ideals

The stable singularities of differential map germs constitute the main source of studying the geometric and topological behavior of these maps. In particular, one interesting problem is to find formulae which allow us to count the isolated stable singularities which appear in the discriminant of a stable deformation of a finitely determined map germ. Mond and Pellikaan showed how the Fitting ideals are related to such singularities and obtain a formula to count the number of ordinary triple points in map germs from C-2 to C-3, in terms of the Fitting ideals associated with the discriminant. In this article we consider map germs from (Cn+m, 0) to (C-m, 0), and obtain results to count the number of isolated singularities by means of the dimension of some associated algebras to the Fitting ideals. First in Corollary 4.5 we provide a way to compute the total sum of these singularities. In Proposition 4.9, for m = 3 we show how to compute the number of ordinary triple points. In Corollary 4.10 and with f of co-rank one, we show a way to compute the number of points formed by the intersection between a germ of a cuspidal edge and a germ of a plane. Furthermore, we show in some examples how to calculate the number of isolated singularities using these results.