The paradox of the clumps mathematically explained

The lumpy distribution of species along a continuous one-dimensional niche axis recently found by Scheffer and van Nes (Scheffer and van Ness 2006) is explained mathematically. We show that it emerges simply from the eigenvalue and eigenvectors of the community matrix. Both the transient patterns—lumps and gaps between them—as well as the asymptotic equilibrium are explained. If the species are evenly distributed along the niche axis, the emergence of these patterns can be demonstrated analytically. The more general case, of randomly distributed species, shows only slight deviations and is illustrated by numerical simulation. This is a robust result whenever the finiteness of the niche is taken into account: it can be extended to different analytic dependence of the interaction coefficients with the distance on the niche axis (i.e., different kernel interactions), different boundary conditions, etc. We also found that there is a critical value both for the width of the species distribution s and the number of species n below which the clusterization disappear

Resilience: Accounting for the Noncomputable

Plans to solve complex environmental problems should always consider the role of surprise. Nevertheless, there is a tendency to emphasize known computable aspects of a problem while neglecting aspects that are unknown and failing to ask questions about them. The tendency to ignore the noncomputable can be countered by considering a wide range of perspectives, encouraging transparency with regard to conflicting viewpoints, stimulating a diversity of models, and managing for the emergence of new syntheses that reorganize fragmentary knowledg

Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations

We present new interior regularity criteria for suitable weak solutions of the 3-D Navier-Stokes equations: a suitable weak solution is regular near an interior point $z$ if either the scaled $L^{p,q}_{x,t}$-norm of the velocity with $3/p+2/q\leq 2$, $1\leq q\leq \infty$, or the $L^{p,q}_{x,t}$-norm of the vorticity with $3/p+2/q\leq 3$, $1 \leq q < \infty$, or the $L^{p,q}_{x,t}$-norm of the gradient of the vorticity with $3/p+2/q\leq 4$, $1 \leq q$, $1 \leq p$, is sufficiently small near $z$

Use of open-top chambers to study the effect of climate change in aquatic ecosystems

The aim of this research was to explore the possibility to use inexpensive open-top chambers (OTCs) as passive artificial warming devices in experimental aquatic studies. Our results show that OTCs give a significant temperature increase compared with the control. The measured increase (up to an average of 2.3°C) corresponds with predicted climatic warming. Due to their open top, the light quantity and quality is only minimally reduced. We found that OTCs are especially suited for studying the effect of climate change in small waters as the vertical temperature gradients remain unchanged. They can also easily be transported to remote environments. We discuss other advantages and disadvantages of these devices for aquatic studies and compare them with other warming devices

A geometric condition implying energy equality for solutions of 3D Navier-Stokes equation

We prove that every weak solution $u$ to the 3D Navier-Stokes equation that belongs to the class $L^3L^{9/2}$ and \n u belongs to $L^3L^{9/5}$ localy away from a 1/2-H\"{o}lder continuous curve in time satisfies the generalized energy equality. In particular every such solution is suitable.Comment: 10 page

Effects of aquatic vegetation type on denitrification

In a microcosm 15N enrichment experiment we tested the effect of floating vegetation (Lemna sp.) and submerged vegetation (Elodea nuttallii) on denitrification rates, and compared it to systems without macrophytes. Oxygen concentration, and thus photosynthesis, plays an important role in regulating denitrification rates and therefore the experiments were performed under dark as well as under light conditions. Denitrification rates differed widely between treatments, ranging from 2.8 to 20.9 µmol N m-2 h-1, and were strongly affected by the type of macrophytes present. These differences may be explained by the effects of macrophytes on oxygen conditions. Highest denitrification rates were observed under a closed mat of floating macrophytes where oxygen concentrations were low. In the light, denitrification was inhibited by oxygen from photosynthesis by submerged macrophytes, and by benthic algae in the systems without macrophytes. However, in microcosms with floating vegetation there was no effect of light, as the closed mat of floating plants caused permanently dark conditions in the water column. Nitrate removal was dominated by plant uptake rather than denitrification, and did not differ between systems with submerged or floating plant

Partial Regularity of solutions to the Four-dimensional Navier-Stokes equations at the first blow-up time

The solutions of incompressible Navier-Stokes equations in four spatial dimensions are considered. We prove that the two-dimensional Hausdorff measure of the set of singular points at the first blow-up time is equal to zero.Comment: 19 pages, a comment regarding five or higher dimensional case is added in Remark 1.3. accepted by Comm. Math. Phy