Associative Submanifolds of the 7-Sphere

Associative submanifolds of the 7-sphere S^7 are 3-dimensional minimal submanifolds which are the links of calibrated 4-dimensional cones in R^8 called Cayley cones. Examples of associative 3-folds are thus given by the links of complex and special Lagrangian cones in C^4, as well as Lagrangian submanifolds of the nearly K\"ahler 6-sphere. By classifying the associative group orbits, we exhibit the first known explicit example of an associative 3-fold in S^7 which does not arise from other geometries. We then study associative 3-folds satisfying the curvature constraint known as Chen's equality, which is equivalent to a natural pointwise condition on the second fundamental form, and describe them using a new family of pseudoholomorphic curves in the Grassmannian of 2-planes in R^8 and isotropic minimal surfaces in S^6. We also prove that associative 3-folds which are ruled by geodesic circles, like minimal surfaces in space forms, admit families of local isometric deformations. Finally, we construct associative 3-folds satisfying Chen's equality which have an S^1-family of global isometric deformations using harmonic 2-spheres in S^6.Comment: 42 pages, v2: minor corrections, streamlined and improved exposition, published version; Proceedings of the London Mathematical Society, Advance Access published 17 June 201

How do drying and rewetting events affect nutrient fluxes and bacteria dynamics in subtropical estuarine sediments?

Drying and rewetting occur frequently in coastal marsh sediments due to oscillations of rising and falling tides, and episodic droughts and floods. Similarly, drying events also occur within freshwater systems due to changing precipitation patterns. However, little is known about how these events affect biogeochemical processes in sediments. In this study we examined the effects of drying on the release of nutrients from sediments to overlying waters, together with associated bacterial dynamics. We incubated dried and rewetted salt marsh sediments collected from the Nueces River mouth at the Nueces Salt Marsh (NSM) and from a freshwater section of the Mission River (MR) in South Texas. During the incubations, we quantified the nutrients released and changes of bacterial abundance and community structure in slurries of wet and dry sediments under anoxic conditions. Our results showed that ammonium concentrations increased steadily for both NSM and MR dry treatment incubations, reaching a maximum of 203 and 51 μM respectively, as compared to only 124 and 2 μM in the wet treatments. Phosphate concentrations steadily increased throughout the incubation in the NSM dry treatment, but not in the wet treatment where concentrations remained below 5 μM. In contrast, we observed an opposite trend in the MR sediment with phosphate concentrations in the dry treatment remaining below those in the wet treatment throughout the incubation. The atomic C/N ratios for NSM and MR sediments ranged from 10 to 14 for both MR and NSM treatments, however they were significantly lower in the supernatants of the NSM dry treatment (12). Although both NSM and MR had higher ammonium releases in the dry treatments than the wet ones, patterns in phosphate release and C/N ratios of dissolved organic matter differed in these two sediments, likely resulting from the differences in salinity and grain size distribution. Bacteria that developed in the slurry of NSM dried sediment included Bacillus, Anaerobacillus, Haloplasma, and Vibrio; these species were perhaps involved in decomposing sedimentary organic matter, including lysates from biota killed by the drying. The MR sediment slurry developed a different microbial community, where Gemmobacter, Rhodobacter, and Mycoplasma were most notable in the dried treatment. Overall, this study demonstrates that drying and rewetting events can increase nutrient fluxes out of marsh sediments and affect bacterial communities, important in estuarine biogeochemical processes. Information on this topic is important in the context of the increasing frequency of extreme droughts and floods and rising sea levels associated with global change.Marine Scienc

Tracking in dense environments and its inefficiency measurement using pixel dE/dxdE/dx

We present a measurement of the charged particle reconstruction inefficiency inside of jet cores, using data collected by the ATLAS experiment in 2015 of $pp$ collisions produced at the LHC, at a center-of-mass energy of 13 TeV. The determination of this inefficiency is important for jet energy scale and mass calibration, as well as multiple other performance studies and analyses. A data driven method is used, where the fraction of lost particle tracks is determined from energy deposition $dE/dx$ in the pixel detector. The fraction of lost tracks is found to be less than 5%, which is an improvement since the previous study, and agrees well within systematic uncertainties with a Monte Carlo simulation.Comment: Presented at PIXEL 2016 and prepared for submission to JINS