The significance of sedimentation and sediments to phytoplankton growth in drinking-water reservoirs

In the mesotrophic-eutrophic Saidenbach Reservoir in Saxony, the nanoplankton and cyanobacteria have increased at the expense of diatom dominance, due to a doubling of the external phosphorus load in the last 15 years. However, the phosphorus sedimentation flux is still very high (up to 80% of the input), corresponding to more than 2 g m2 d-1 in terms of dry weight. There is a strong correlation between the abundance of diatoms in the euphotic zone and their sedimentation flux (with a delay of about 2 weeks). Only about 25% of the deposited material could be clearly attributed to plankton biomass; the remainder resulted from flocculation and precipitation processes or directly from the inflow of clay minerals. The ash content of the deposited material was high (73%). Thus the sedimentation flux can be considered to operate as an internal water-treatment/oligotrophication process within the lake. The neighbouring Neunzehnhain Reservoir still has a very clear water with a transparency up to 18 m depth. Though the sediment was not much lower than Saidenbach sediment in total phosphorus and total numbers of bacteria, sulphide was always absent and the ratio of Fe 2+ to Fe 3+ was very low in the upper (0- 5 cm) layer. Thus the external and internal phosphorus loads do not attain the critical level necessary to induce a ”phosphorus - phytoplankton” feedback loop

Higher-order signature cocycles for subgroups of mapping class groups and homology cylinders

We define families of invariants for elements of the mapping class group of S, a compact orientable surface. Fix any characteristic subgroup H of pi_1(S) and restrict to J(H), any subgroup of mapping classes that induce the identity modulo H. To any unitary representation, r of pi_1(S)/H we associate a higher-order rho_r-invariant and a signature 2-cocycle sigma_r. These signature cocycles are shown to be generalizations of the Meyer cocycle. In particular each rho_r is a quasimorphism and each sigma_r is a bounded 2-cocycle on J(H). In one of the simplest non-trivial cases, by varying r, we exhibit infinite families of linearly independent quasimorphisms and signature cocycles. We show that the rho_r restrict to homomorphisms on certain interesting subgroups. Many of these invariants extend naturally to the full mapping class group and some extend to the monoid of homology cylinders based on S.Comment: 38 pages. This is final version for publication in IMRN, deleted some material and many references (sorry-at referee's insistence

Knot concordance and homology cobordism

We consider the question: "If the zero-framed surgeries on two oriented knots in the 3-sphere are integral homology cobordant, preserving the homology class of the positive meridians, are the knots themselves concordant?" We show that this question has a negative answer in the smooth category, even for topologically slice knots. To show this we first prove that the zero-framed surgery on K is Z-homology cobordant to the zero-framed surgery on many of its winding number one satellites P(K). Then we prove that in many cases the tau and s-invariants of K and P(K) differ. Consequently neither tau nor s is an invariant of the smooth homology cobordism class of the zero-framed surgery. We also show, that a natural rational version of this question has a negative answer in both the topological and smooth categories, by proving similar results for K and its (p,1)-cables.Comment: 15 pages, 8 figure

Entanglement versus Correlations in Spin Systems

We consider pure quantum states of $N\gg 1$ spins or qubits and study the average entanglement that can be \emph{localized} between two separated spins by performing local measurements on the other individual spins. We show that all classical correlation functions provide lower bounds to this \emph{localizable entanglement}, which follows from the observation that classical correlations can always be increased by doing appropriate local measurements on the other qubits. We analyze the localizable entanglement in familiar spin systems and illustrate the results on the hand of the Ising spin model, in which we observe characteristic features for a quantum phase transition such as a diverging entanglement length.Comment: 4 page