An L^2-Index Theorem for Dirac Operators on S^1 * R^3

An expression is found for the $L^2$-index of a Dirac operator coupled to a connection on a $U_n$ vector bundle over $S^1\times{\mathbb R}^3$. Boundary conditions for the connection are given which ensure the coupled Dirac operator is Fredholm. Callias' index theorem is used to calculate the index when the connection is independent of the coordinate on $S^1$. An excision theorem due to Gromov, Lawson, and Anghel reduces the index theorem to this special case. The index formula can be expressed using the adiabatic limit of the $\eta$-invariant of a Dirac operator canonically associated to the boundary. An application of the theorem is to count the zero modes of the Dirac operator in the background of a caloron (periodic instanton).Comment: 14 pages, Latex, to appear in the Journal of Functional Analysi

To Tell the Truth, Memory Isn\u27t That Good

To Tell the Truth, Memory Isn\u27t That Goo

To Tell the Truth, Memory Isn\u27t That Good

To Tell the Truth, Memory Isn\u27t That Goo

Enhancement of charged macromolecule capture by nanopores in a salt gradient

Nanopores spanning synthetic membranes have been used as key components in proof-of-principle nanofluidic applications, particularly those involving manipulation of biomolecules or sequencing of DNA. The only practical way of manipulating charged macromolecules near nanopores is through a voltage difference applied across the nanopore-spanning membrane. However, recent experiments have shown that salt concentration gradients applied across nanopores can also dramatically enhance charged particle capture from a low concentration reservoir of charged molecules at one end of the nanopore. This puzzling effect has hitherto eluded a physically consistent theoretical explanation. Here, we propose an electrokinetic mechanism of this enhanced capture that relies on the electrostatic potential near the pore mouth. For long pores with diameter much greater than the local screening length, we obtain accurate analytic expressions showing how salt gradients control the local conductivity which can lead to increased local electrostatic potentials and charged analyte capture rates. We also find that the attractive electrostatic potential may be balanced by an outward, repulsive electroosmotic flow (EOF) that can in certain cases conspire with the salt gradient to further enhance the analyte capture rate.Comment: 10 pages, 6 Figure

Cover Crop Selection and Management for Agronomic Farming Systems

Cover crops can extend the season of active nutrient uptake and living soil cover and thereby reduce nutrient losses in water and sediment. The conversion of the prairies or other native vegetation ecosystems to summer annual grain crops resulted in a shortening of the season of living plant cover and nutrient uptake. Summer annual grain crops, like corn and soybean, accumulate water and nutrients and provide living cover for only about four months (mid-May to mid-September), whereas in natural systems, some living plants are actively accumulating nutrients and water whenever the ground is not frozen (at least 7 months; April-October). As a result, soil nutrients in summer annual cropping systems are susceptible to losses in part because there are periods during each year when active plant uptake and soil cover are absent

Effects of Streambed Morphology and Biofilm Growth on the Transient Storage of Solutes

Microbial biofilms are the prime site of nutrient and contaminant removal in streams. It is therefore essential to understand how biofilms affect hydrodynamic exchange, solute transport, and retention in systems where geomorphology and induced hydrodynamics shape their growth and structure. We experimented with large-scale streamside flumes with streambed landscapes constructed from graded bedforms of constant height and wavelength. Each flume had a different bedform height and was covered with a layer of gravel as substratum for benthic microbial biofilms. Biofilms developed different biomass and physical structures in response to the hydrodynamic conditions induced by the streambed morphology. Step injections of conservative tracers were performed at different biofilm growth stages. The experimental breakthrough curves were analyzed with the STIR model, using a residence time approach to characterize the retention effects associated with biofilms. The retained mass of the solute increased with biofilm biomass and the biofilm-associated retention was furthermore related to bedform height. We tentatively relate this behavior to biofilm structural differentiation induced by bed morphology, which highlights the strong linkage between geomorphology, hydrodynamics, and biofilms in natural streams and provide important clues for stream restoration

The First Two Years of Electromagnetic Follow-Up with Advanced LIGO and Virgo

We anticipate the first direct detections of gravitational waves (GWs) with Advanced LIGO and Virgo later this decade. Though this groundbreaking technical achievement will be its own reward, a still greater prize could be observations of compact binary mergers in both gravitational and electromagnetic channels simultaneously. During Advanced LIGO and Virgo's first two years of operation, 2015 through 2016, we expect the global GW detector array to improve in sensitivity and livetime and expand from two to three detectors. We model the detection rate and the sky localization accuracy for binary neutron star (BNS) mergers across this transition. We have analyzed a large, astrophysically motivated source population using real-time detection and sky localization codes and higher-latency parameter estimation codes that have been expressly built for operation in the Advanced LIGO/Virgo era. We show that for most BNS events the rapid sky localization, available about a minute after a detection, is as accurate as the full parameter estimation. We demonstrate that Advanced Virgo will play an important role in sky localization, even though it is anticipated to come online with only one-third as much sensitivity as the Advanced LIGO detectors. We find that the median 90% confidence region shrinks from ~500 square degrees in 2015 to ~200 square degrees in 2016. A few distinct scenarios for the first LIGO/Virgo detections emerge from our simulations.Comment: 17 pages, 11 figures, 5 tables. For accompanying data, see http://www.ligo.org/scientists/first2year

Dirichlet process Gaussian-mixture model:an application to localizing coalescing binary neutron stars with gravitational-wave observations

We reconstruct posterior distributions for the position (sky area and distance) of a simulated set of binary neutron star gravitational-waves signals observed with Advanced LIGO and Advanced Virgo. We use a Dirichlet process Gaussian-mixture model, a fully Bayesian non-parametric method that can be used to estimate probability density functions with a flexible set of assumptions. The ability to reliably reconstruct the source position is important for multimessenger astronomy, as recently demonstrated with GW170817. We show that for detector networks comparable to the early operation of Advanced LIGO and Advanced Virgo, typical localization volumes are similar to 10(4)-10(5 similar to)Mpc(3) corresponding to similar to 10(2)-10(3) potential host galaxies. The localization volume is a strong function of the network signal-to-noise ratio, scaling roughly proportional to e(net)(-6). Fractional localizations improve with the addition of further detectors to the network. Our Dirichlet process Gaussian-mixture model can be adopted for localizing events detected during future gravitational-wave observing runs and used to facilitate prompt multimessenger follow-up