High-order accurate methods for Nyström discretization of integral equations on smooth curves in the plane

Boundary integral equations and Nyström discretization provide a powerful tool for the solution of Laplace and Helmholtz boundary value problems. However, often a weakly-singular kernel arises, in which case specialized quadratures that modify the matrix entries near the diagonal are needed to reach a high accuracy. We describe the construction of four different quadratures which handle logarithmically-singular kernels. Only smooth boundaries are considered, but some of the techniques extend straightforwardly to the case of corners. Three are modifications of the global periodic trapezoid rule, due to Kapur–Rokhlin, to Alpert, and to Kress. The fourth is a modification to a quadrature based on Gauss–Legendre panels due to Kolm–Rokhlin; this formulation allows adaptivity. We compare in numerical experiments the convergence of the four schemes in various settings, including low- and high-frequency planar Helmholtz problems, and 3D axisymmetric Laplace problems. We also find striking differences in performance in an iterative setting. We summarize the relative advantages of the schemes.     

Analysis of the quantum numbers J(PC) of the X(3872) particle

We present an analysis of angular distributions and correlations of the X(3872) particle in the exclusive decay mode X(3872)-->J/psipi+ pi- with J/psi-->mu+ mu-. We use 780 pb-1 of data from pp[over ] collisions at sqrt[s]=1.96 TeV collected with the CDF II detector at the Fermilab Tevatron. We derive constraints on spin, parity, and charge conjugation parity of the X(3872) particle by comparing measured angular distributions of the decay products with predictions for different J(PC) hypotheses. The assignments J(PC)=1++ and 2-+ are the only ones consistent with the data.     

Measurement of the top-quark mass in all-hadronic decays in pp collisions at CDF II

We present a measurement of the top-quark mass Mtop in the all-hadronic decay channel tt-->W+bW-b-->q1q2bq3q4b. The analysis is performed using 310 pb-1 of sqrt[s]=1.96 TeV pp[over ] collisions collected with the CDF II detector using a multijet trigger. The mass measurement is based on an event-by-event likelihood which depends on both the sample purity and the value of the top-quark mass, using 90 possible jet-to-parton assignments in the six-jet final state. The joint likelihood of 290 selected events yields a value of Mtop=177.1+/-4.9(stat)+/-4.7(syst) GeV/c2.     

A Novel Bismuth‐Based Metal–Organic Framework for High Volumetric Methane and Carbon Dioxide Adsorption

Solvothermal reaction of H₄L (L=biphenyl‐3,3′,5,5′‐tetracarboxylate) and Bi(NO₃)₃ ? (H₂O)₅ in a mixture of DMF/MeCN/H₂O in the presence of piperazine and nitric acid at 100 °C for 10 h affords the solvated metal–organic polymer [Bi₂(L)_1.5(H₂O)₂] ? (DMF)_3.5 ? (H₂O)₃ (NOTT‐220‐solv). A single crystal X‐ray structure determination confirms that it crystallises in space group P2/c and has a neutral and non‐interpenetrated structure comprising binuclear {Bi₂} centres bridged by tetracarboxylate ligands. NOTT‐220‐solv shows a 3,6‐connected network having a framework topology with a {4 ? 6²}₂{4² ? 6⁵ ? 8⁸}{6² ? 8} point symbol. The desolvated material NOTT‐220a shows exceptionally high adsorption uptakes for CH₄ and CO₂ on a volumetric basis at moderate pressures and temperatures with a CO₂ uptake of 553 g L^?1 (20 bar, 293 K) with a saturation uptake of 688 g L^?1 (1 bar, 195 K). The corresponding CH₄ uptake was measured as 165 V(STP)/V (20 bar, 293 K) and 189 V(STP/V) (35 bar, 293 K) with a maximum CH₄ uptake for NOTT‐220a recorded at 20 bar and 195 K to be 287 V(STP)/V, while H₂ uptake of NOTT‐220a at 20 bar, 77 K is 42 g L^?1. These gas uptakes have been modelled by grand canonical Monte Carlo (GCMC) and density functional theory (DFT) calculations, which confirm the experimental data and give insights into the nature of the binding sites of CH₄ and CO₂ in this porous hybrid material.     

One Guest or Two? A Crystallographic and Solution Study of Guest Binding in a Cubic Coordination Cage

A crystallographic investigation of a series of host–guest complexes in which small-molecule organic guests occupy the central cavity of an approximately cubic M₈L₁₂ coordination cage has revealed some unexpected behaviour. Whilst some guests form 1:1 H⋅G complexes as we have seen before, an extensive family of bicyclic guests—including some substituted coumarins and various saturated analogues—form 1:2 H⋅G₂ complexes in the solid state, despite the fact that solution titrations are consistent with 1:1 complex formation, and the combined volume of the pair of guests significantly exceeds the Rebek 55±9 % packing for optimal guest binding, with packing coefficients of up to 87 %. Re-examination of solution titration data for guest binding in two cases showed that, although conventional fluorescence titrations are consistent with 1:1 binding model, alternative forms of analysis—Job plot and an NMR titration—at higher concentrations do provide evidence for 1:2 H⋅G₂ complex formation. The observation of guests binding in pairs in some cases opens new possibilities for altered reactivity of bound guests, and also highlights the recently articulated difficulties associated with determining stoichiometry of supramolecular complexes in solution.     

Monomeric Chini‐Type Triplatinum Clusters Featuring Dianionic and Radical‐Anionic π*‐Systems

Owing to their unique topologies and abilities to self‐assemble into a variety of extended and aggregated structures, the binary platinum carbonyl clusters [Pt₃(CO)₆]_n^2? (“Chini clusters”) continue to draw significant interest. Herein, we report the isolation and structural characterization of the trinuclear electron‐transfer series [Pt₃(μ‐CO)₃(CNAr^Dipp2)₃]^n? (n=0, 1, 2), which represents a unique set of monomeric Pt₃ clusters supported by π‐acidic ligands. Spectroscopic, computational, and synthetic investigations demonstrate that the highest‐occupied molecular orbitals of the mono‐ and dianionic clusters consist of a combined π*‐framework of the CO and CNAr^Dipp2 ligands, with negligible Pt character. Accordingly, this study provides precedent for an ensemble of carbonyl and isocyanide ligands to function in a redox non‐innocent manner.     

Programmed discrimination of qbits with added classical information

We investigate some properties of programmed quantum-state discriminators with simple programs. Bergou et al. [Phys. Rev. A 73, 062334 (2006)] have considered programmable devices which are supplied with two distinct but unknown program qbits and one data qbit which is certain to be identical to one or other of the program qbits. The task is to discriminate between the first and the second possibility. In this paper, we consider this state-discrimination problem when there is some additional classical information available. We find that in the minimum error discrimination mode, the probability of correct discrimination is increased by each type of classical information. The same is broadly true of unambiguous discrimination, with the chance of success improving when the overlap between the program qbits is reduced.     

Search for new heavy particles in the WZ0 final state in pp collisions at square root[s] = 1.8 TeV

We present the first general search for new heavy particles, X, which decay via X --> WZ0 --> e(nu)+jj as a function of M(X) and Gamma(X) in pp collisions at square root[s] = 1.8 TeV. No evidence is found for production of X in 110 pb(-1) of data collected by the Collider Detector at Fermilab. General cross section limits are set at the 95% C.L. as a function of mass and width of the new particle. The results are further interpreted as mass limits on the production of new heavy charged vector bosons which decay via W' --> WZ0 in an extended gauge model as a function of the width, Gamma(W'), and mixing factor between the W' and the standard model W bosons.