A Cantor set of tori with monodromy near a focus-focus singularity

We write down an asymptotic expression for action coordinates in an integrable Hamiltonian system with a focus-focus equilibrium. From the singularity in the actions we deduce that the Arnol'd determinant grows infinitely large near the pinched torus. Moreover, we prove that it is possible to globally parametrise the Liouville tori by their frequencies. If one perturbs this integrable system, then the KAM tori form a Whitney smooth family: they can be smoothly interpolated by a torus bundle that is diffeomorphic to the bundle of Liouville tori of the unperturbed integrable system. As is well-known, this bundle of Liouville tori is not trivial. Our result implies that the KAM tori have monodromy. In semi-classical quantum mechanics, quantisation rules select sequences of KAM tori that correspond to quantum levels. Hence a global labeling of quantum levels by two quantum numbers is not possible.Comment: 11 pages, 2 figure

Unoccupied states of individual silver clusters and chains on Ag(111)

Size-selected silver clusters on Ag(111) were fabricated with the tip of a scanning tunneling microscope. Unoccupied electron resonances give rise to image contrast and spectral features which shift toward the Fermi level with increasing cluster size. Linear assemblies exhibit higher resonance energies than equally sized compact assemblies. Density functional theory calculations reproduce the observed energies and enable an assignment of the resonances to hybridized atomic 5s and 5p orbitals with silver substrate states.Comment: 9 pages, 8 figure

Dissipative Boussinesq System of Equations in the B\'enard-Marangoni Phenomenon

By using the long-wave approximation, a system of coupled evolution equations for the bulk velocity and the surface perturbations of a B\'enard-Marangoni system is obtained. It includes nonlinearity, dispersion and dissipation, and it can be interpreted as a dissipative generalization of the usual Boussinesq system of equations. As a particular case, a strictly dissipative version of the Boussinesq system is obtained. Finnaly, some speculations are made on the nature of the physical phenomena described by this system of equations.Comment: 15 Pages, REVTEX (Version 3.0), no figure

Geometric Satake, Springer correspondence, and small representations

For a simply-connected simple algebraic group $G$ over \C, we exhibit a subvariety of its affine Grassmannian that is closely related to the nilpotent cone of $G$, generalizing a well-known fact about $GL_n$. Using this variety, we construct a sheaf-theoretic functor that, when combined with the geometric Satake equivalence and the Springer correspondence, leads to a geometric explanation for a number of known facts (mostly due to Broer and Reeder) about small representations of the dual group.Comment: Version 2: minor revisions, 33 page

Aromaticity in a Surface Deposited Cluster: Pd4_4 on TiO2_2 (110)

We report the presence of \sigma-aromaticity in a surface deposited cluster, Pd$_4$ on TiO$_2$ (110). In the gas phase, Pd$_4$ adopts a tetrahedral structure. However, surface binding promotes a flat, \sigma-aromatic cluster. This is the first time aromaticity is found in surface deposited clusters. Systems of this type emerge as a promising class of catalyst, and so realization of aromaticity in them may help to rationalize their reactivity and catalytic properties, as a function of cluster size and composition.Comment: 4 pages, 3 figure

Large-scale pharmacogenomic study of sulfonylureas and the QT, JT and QRS intervals: CHARGE Pharmacogenomics Working Group

Sulfonylureas, a commonly used class of medication used to treat type 2 diabetes, have been associated with an increased risk of cardiovascular disease. Their effects on QT interval duration and related electrocardiographic phenotypes are potential mechanisms for this adverse effect. In 11 ethnically diverse cohorts that included 71 857 European, African-American and Hispanic/Latino ancestry individuals with repeated measures of medication use and electrocardiogram (ECG) measurements, we conducted a pharmacogenomic genome-wide association study of sulfonylurea use and three ECG phenotypes: QT, JT and QRS intervals. In ancestry-specific meta-analyses, eight novel pharmacogenomic loci met the threshold for genome-wide significance (P<5 × 10−8), and a pharmacokinetic variant in CYP2C9 (rs1057910) that has been associated with sulfonylurea-related treatment effects and other adverse drug reactions in previous studies was replicated. Additional research is needed to replicate the novel findings and to understand their biological basis