New Results in Sasaki-Einstein Geometry

This article is a summary of some of the author's work on Sasaki-Einstein geometry. A rather general conjecture in string theory known as the AdS/CFT correspondence relates Sasaki-Einstein geometry, in low dimensions, to superconformal field theory; properties of the latter are therefore reflected in the former, and vice versa. Despite this physical motivation, many recent results are of independent geometrical interest, and are described here in purely mathematical terms: explicit constructions of infinite families of both quasi-regular and irregular Sasaki-Einstein metrics; toric Sasakian geometry; an extremal problem that determines the Reeb vector field for, and hence also the volume of, a Sasaki-Einstein manifold; and finally, obstructions to the existence of Sasaki-Einstein metrics. Some of these results also provide new insights into Kahler geometry, and in particular new obstructions to the existence of Kahler-Einstein metrics on Fano orbifolds.Comment: 31 pages, no figures. Invited contribution to the proceedings of the conference "Riemannian Topology: Geometric Structures on Manifolds"; minor typos corrected, reference added; published version; Riemannian Topology and Geometric Structures on Manifolds (Progress in Mathematics), Birkhauser (Nov 2008

Effect of continuum couplings in fusion of halo 11^{11}Be on 208^{208}Pb around the Coulomb barrier

The effect of continuum couplings in the fusion of the halo nucleus $^{11}$Be on $^{208}$Pb around the Coulomb barrier is studied using a three-body model within a coupled discretised continuum channels (CDCC) formalism. We investigate in particular the role of continuum-continuum couplings. These are found to hinder total, complete and incomplete fusion processes. Couplings to the projectile $1p_{1/2}$ bound excited state redistribute the complete and incomplete fusion cross sections, but the total fusion cross section remains nearly constant. Results show that continuum-continuum couplings enhance the irreversibility of breakup and reduce the flux that penetrates the Coulomb barrier. Converged total fusion cross sections agree with the experimental ones for energies around the Coulomb barrier, but underestimate those for energies well above the Coulomb barrier.Comment: 15 pages, 7 figures, accepted in Phys. Rev.

The impact of reach averaging Manning's equation for an in-situ dataset of water surface elevation, width, and slope

The Surface Water and Ocean Topography Mission (SWOT) will generate global, spatially continuous maps of water surface elevation and extent for large inland water bodies when it launches in 2021. We present an analysis of water surface elevation, width, and bathymetry timeseries data from a medium-sized (average annual discharge 14 m3/s) river to explore Manning's equation, an empirical open channel flow equation, in the context of SWOT discharge algorithms. While this equation is in theory inapplicable to natural channels due to the non-uniform and spatially heterogeneous nature of river systems, we explored approaches to adapt it to this context using reach-averaged variables. At twenty sites along a 6.5 km stretch of the Olentangy River in Ohio, USA, we collected automated and manual measurements of water surface elevation and river width, undertook a full bathymetric survey of the study area, and built a hydraulic model. The stretch of river was divided into five reaches, and hydraulic variables were reach-averaged. Using these variables, we used a modified form of Manning's equation to compute a reach-averaged roughness coefficient. Reach-averaged roughness coefficients varied nonlinearly with discharge and were 2–10 times larger at low flow than at high flow in the in-situ data, ranging from 0.06 to 0.61 in one of the study reaches. These results were compared with the output of an unsteady flow simulation using a calibrated 1-D hydraulic model which was run with constant roughness coefficients at each cross section. When reach-averaged data was used, model-derived roughness coefficient also varied by more than an order of magnitude, with a range of 0.02–0.82 for one reach. For both in-situ and model-derived datasets, using a two-parameter roughness coefficient which scaled with a power law on either discharge or stage reduced discharge estimation error, with error for one reach dropping from 81% to 8% relative root-mean square error (rRMSE) in the in-situ data and 58% to 8% nRMSE in the modeled data. These results imply that spatial averaging of hydraulic variables leads to large variations in reach averaged Manning's n, which we term the reach's “effective resistance”, and suggest that this variability can be accounted for with a simple parameterization in estimates of discharge that use spatially averaged data

Search for charginos in e+e- interactions at sqrt(s) = 189 GeV

An update of the searches for charginos and gravitinos is presented, based on a data sample corresponding to the 158 pb^{-1} recorded by the DELPHI detector in 1998, at a centre-of-mass energy of 189 GeV. No evidence for a signal was found. The lower mass limits are 4-5 GeV/c^2 higher than those obtained at a centre-of-mass energy of 183 GeV. The (\mu,M_2) MSSM domain excluded by combining the chargino searches with neutralino searches at the Z resonance implies a limit on the mass of the lightest neutralino which, for a heavy sneutrino, is constrained to be above 31.0 GeV/c^2 for tan(beta) \geq 1.Comment: 22 pages, 8 figure

Hadronization properties of b quarks compared to light quarks in e+e- -> q qbar from 183 to 200 GeV

The DELPHI detector at LEP has collected 54 pb^{-1} of data at a centre-of-mass energy around 183 GeV during 1997, 158 pb^{-1} around 189 GeV during 1998, and 187 pb^{-1} between 192 and 200 GeV during 1999. These data were used to measure the average charged particle multiplicity in e+e- -> b bbar events, _{bb}, and the difference delta_{bl} between _{bb} and the multiplicity, _{ll}, in generic light quark (u,d,s) events: delta_{bl}(183 GeV) = 4.55 +/- 1.31 (stat) +/- 0.73 (syst) delta_{bl}(189 GeV) = 4.43 +/- 0.85 (stat) +/- 0.61 (syst) delta_{bl}(200 GeV) = 3.39 +/- 0.89 (stat) +/- 1.01 (syst). This result is consistent with QCD predictions, while it is inconsistent with calculations assuming that the multiplicity accompanying the decay of a heavy quark is independent of the mass of the quark itself.Comment: 13 pages, 2 figure

Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in √s = 7 TeV pp collisions with the ATLAS detector

A search for the direct production of charginos and neutralinos in final states with three electrons or muons and missing transverse momentum is presented. The analysis is based on 4.7 fb−1 of proton–proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in three signal regions that are either depleted or enriched in Z-boson decays. Upper limits at 95% confidence level are set in R-parity conserving phenomenological minimal supersymmetric models and in simplified models, significantly extending previous results