A proof of the Grothendieck-Serre conjecture on principal bundles over regular local rings containing infinite fields

Let R be a regular local ring, containing an infinite field. Let G be a reductive group scheme over R. We prove that a principal G-bundle over R is trivial, if it is trivial over the fraction field of R.Comment: Section "Formal loops and affine Grassmannians" is removed as this is now covered in arXiv:1308.3078. Exposition is improved and slightly restructured. Some minor correction

Decadal timescale shift in the ^14C record of a central equatorial Pacific coral

Coral skeletal radiocarbon records reflect seawater Δ^14C and are useful for reconstructing the history of water mass movement and ventilation in the tropical oceans. Here, we reconstructed the inter-annual variability in central equatorial Pacific surface water Δ^14C from 1922–1956 using near-monthly 14C measurements in a Porites sp. coral skeleton (FI5A) from the windward side of Fanning Island (3°54'32"N, 159°18'88"W). The most pronounced feature in this record is a large, positive shift in the Δ^14C between 1947 and 1956 that coincides with the switch of the Pacific Decadal Oscillation (PDO) from a positive to a negative phase in the mid-1940s. Although the absolute Δ^14C values from 1950–1955 in FI5A differ from the Δ^14C values of another coral core collected from the opposite side of the island, both records show a large, positive shift in their Δ^14C records at that time. The relative increase in the Δ^14C of each record is consistent with the premise that a common mechanism is controlling the Δ^14C records within each coral record. Overall, the Fanning Δ^14C data support the notion that a significant amount of subtropical seawater is arriving at the Equator, but does not allow us to determine the mechanism for its transport

Spin properties of dense near-surface ensembles of nitrogen-vacancy centres in diamond

We present a study of the spin properties of dense layers of near-surface nitrogen-vacancy (NV) centres in diamond created by nitrogen ion implantation. The optically detected magnetic resonance contrast and linewidth, spin coherence time, and spin relaxation time, are measured as a function of implantation energy, dose, annealing temperature and surface treatment. To track the presence of damage and surface-related spin defects, we perform in situ electron spin resonance spectroscopy through both double electron-electron resonance and cross-relaxation spectroscopy on the NV centres. We find that, for the energy ($4-30$~keV) and dose ($5\times10^{11}-10^{13}$~ions/cm$^2$) ranges considered, the NV spin properties are mainly governed by the dose via residual implantation-induced paramagnetic defects, but that the resulting magnetic sensitivity is essentially independent of both dose and energy. We then show that the magnetic sensitivity is significantly improved by high-temperature annealing at $\geq1100^\circ$C. Moreover, the spin properties are not significantly affected by oxygen annealing, apart from the spin relaxation time, which is dramatically decreased. Finally, the average NV depth is determined by nuclear magnetic resonance measurements, giving $\approx10$-17~nm at 4-6 keV implantation energy. This study sheds light on the optimal conditions to create dense layers of near-surface NV centres for high-sensitivity sensing and imaging applications.Comment: 12 pages, 7 figure

Aerosol Climatology Over Nile Delta Based on MODIS, MISR and OMI Satellite Data

Since 1999 Cairo and the Nile delta region have suffered from air pollution episodes called the “black cloud” during the fall season. These have been attributed to either burning of agriculture waste or long-range transport of desert dust. Here we present a detailed analysis of the optical and microphysical aerosol properties, based on satellite data. Monthly mean values of Moderate Resolution Imaging Spectroradiometer (MODIS) aerosol optical depth (AOD) at 550 nm were examined for the 10 yr period from 2000–2009. Significant monthly variability is observed in the AOD with maxima in April or May (_0.5) and October (_0.45), and a minimum in December and January (_0.2). Monthly mean values of UV Aerosol Index (UVAI) retrieved by the Ozone Monitoring Instrument (OMI) for 4 yr (2005–2008) exhibit the same AOD pattern. The carbonaceous aerosols during the black cloud periods are confined to the planetary boundary layer (PBL), while dust aerosols exist over a wider range of altitudes, as shown by Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) aerosol profiles. The monthly climatology of Multi-angle Imaging Spectro-Radiometer (MISR) data show that the aerosols during the black cloud periods are spherical with a higher percentage of small and medium size particles, whereas the spring aerosols are mostly large non-spherical particles. All of the results show that the air quality in Cairo and the Nile delta region is subject to a complex mixture of air pollution types, especially in the fall season, when biomass burning contributes to a background of urban pollution and desert dust

Formal Hecke algebras and algebraic oriented cohomology theories

In the present paper we generalize the construction of the nil Hecke ring of Kostant-Kumar to the context of an arbitrary algebraic oriented cohomology theory of Levine-Morel and Panin-Smirnov, e.g. to Chow groups, Grothendieck's K_0, connective K-theory, elliptic cohomology, and algebraic cobordism. The resulting object, which we call a formal (affine) Demazure algebra, is parameterized by a one-dimensional commutative formal group law and has the following important property: specialization to the additive and multiplicative periodic formal group laws yields completions of the nil Hecke and the 0-Hecke rings respectively. We also introduce a deformed version of the formal (affine) Demazure algebra, which we call a formal (affine) Hecke algebra. We show that the specialization of the formal (affine) Hecke algebra to the additive and multiplicative periodic formal group laws gives completions of the degenerate (affine) Hecke algebra and the usual (affine) Hecke algebra respectively. We show that all formal affine Demazure algebras (and all formal affine Hecke algebras) become isomorphic over certain coefficient rings, proving an analogue of a result of Lusztig.Comment: 28 pages. v2: Some results strengthened and references added. v3: Minor corrections, section numbering changed to match published version. v4: Sign errors in Proposition 6.8(d) corrected. This version incorporates an erratum to the published versio

Superfluid Helium Tanker (SFHT) study

Replenishment of superfluid helium (SFHe) offers the potential of extending the on-orbit life of observatories, satellite instruments, sensors and laboratories which operate in the 2 K temperature regime. A reference set of resupply customers was identified as representing realistic helium servicing requirements and interfaces for the first 10 years of superfluid helium tanker (SFHT) operations. These included the Space Infrared Telescope Facility (SIRTF), the Advanced X-ray Astrophysics Facility (AXAF), the Particle Astrophysics Magnet Facility (Astromag), and the Microgravity and Materials Processing Sciences Facility (MMPS)/Critical Point Phenomena Facility (CPPF). A mixed-fleet approach to SFHT utilization was considered. The tanker permits servicing from the Shuttle cargo bay, in situ when attached to the OMV and carried to the user spacecraft, and as a depot at the Space Station. A SFHT Dewar ground servicing concept was developed which uses a dedicated ground cooling heat exchanger to convert all the liquid, after initial fill as normal fluid, to superfluid for launch. This concept permits the tanker to be filled to a near full condition, and then cooled without any loss of fluid. The final load condition can be saturated superfluid with any desired ullage volume, or the tank can be totally filed and pressurized. The SFHT Dewar and helium plumbing system design has sufficient component redundancy to meet fail-operational, fail-safe requirements, and is designed structurally to meet a 50 mission life usage requirement. Technology development recommendations were made for the selected SFHT concept, and a Program Plan and cost estimate prepared for a phase C/D program spanning 72 months from initiation through first launch in 1997

Spatiotemporal Characteristics of the Near-Surface Turbulent Cascade at the Submesoscale in the Drake Passage.

Submesoscale currents and internal gravity waves achieve an intense turbulent cascade near the ocean surface [depth of 0–O(100) m], which is thought to give rise to significant energy sources and sinks for mesoscale eddies. Here, we characterize the contributions of nonwave currents (NWCs; including eddies and fronts) and internal gravity waves (IGWs; including near-inertial motions, lee waves, and the internal wave continuum) to near-surface submesoscale turbulence in the Drake Passage. Using a numerical simulation, we combine Lagrangian filtering and a Helmholtz decomposition to identify NWCs and IGWs and to characterize their dynamics (rotational versus divergent). We show that NWCs and IGWs contribute in different proportions to the inverse and forward turbulent kinetic energy cascades, based on their dynamics and spatiotemporal scales. Purely rotational NWCs cause most of the inverse cascade, while coupled rotational–divergent components of NWCs and coupled NWC–IGWs cause the forward cascade. The cascade changes direction at a spatial scale at which motions become increasingly divergent. However, the forward cascade is ultimately limited by the motions’ spatiotemporal scales. The bulk of the forward cascade (80%–95%) is caused by NWCs and IGWs of small spatiotemporal scales (L < 10 km; T < 6 h), which are primarily rotational: submesoscale eddies, fronts, and the internal wave continuum. These motions also cause a significant part of the inverse cascade (30%). Our results highlight the requirement for high spatiotemporal resolutions to diagnose the properties and large-scale impacts of near-surface submesoscale turbulence accurately, with significant implications for ocean energy cycle study strategies

A TQFT associated to the LMO invariant of three-dimensional manifolds

We construct a Topological Quantum Field Theory (in the sense of Atiyah) associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from the category of 3-dimensional manifolds with parametrized boundary, satisfying some additional conditions, to an algebraic-combinatorial category. It is built together with its truncations with respect to a natural grading, and we prove that these TQFTs are non-degenerate and anomaly-free. The TQFT(s) induce(s) a (series of) representation(s) of a subgroup ${\cal L}_g$ of the Mapping Class Group that contains the Torelli group. The N=1 truncation produces a TQFT for the Casson-Walker-Lescop invariant.Comment: 28 pages, 13 postscript figures. Version 2 (Section 1 has been considerably shorten, and section 3 has been slightly shorten, since they will constitute a separate paper. Section 4, which contained only announce of results, has been suprimated; it will appear in detail elsewhere. Consequently some statements have been re-numbered. No mathematical changes have been made.