The origin of the core-level binding energy shifts in nanoclusters

We investigate the shifts of the core-level binding energies in small gold nanoclusters by using {\it ab initio} density functional theory calculations. The shift of the 4$f$ states is calculated for magic number nanoclusters in a wide range of sizes and morphologies. We find a non-monotonous behavior of the core-level shift in nanoclusters depending on the size. We demonstrate that there are three main contributions to the Au 4$f$ shifts, which depend sensitively on the interatomic distances, coordination and quantum confinement. They are identified and explained by the change of the on-site electrostatic potential.Comment: 7 pages, 9 figure

Immunizing Conic Quadratic Optimization Problems Against Implementation Errors

We show that the robust counterpart of a convex quadratic constraint with ellipsoidal implementation error is equivalent to a system of conic quadratic constraints. To prove this result we first derive a sharper result for the S-lemma in case the two matrices involved can be simultaneously diagonalized. This extension of the S-lemma may also be useful for other purposes. We extend the result to the case in which the uncertainty region is the intersection of two convex quadratic inequalities. The robust counterpart for this case is also equivalent to a system of conic quadratic constraints. Results for convex conic quadratic constraints with implementation error are also given. We conclude with showing how the theory developed can be applied in robust linear optimization with jointly uncertain parameters and implementation errors, in sequential robust quadratic programming, in Taguchi’s robust approach, and in the adjustable robust counterpart.Conic Quadratic Program;hidden convexity;implementation error;robust optimization;simultaneous diagonalizability;S-lemma

Numerical solution of Fredholm integral equation of the first kind

Numerical solution of first kind Fredholm integral equatio

Pinpointing the massive black hole in the Galactic Center with gravitationally lensed stars

A new statistical method for pinpointing the massive black hole (BH) in the Galactic Center on the IR grid is presented and applied to astrometric IR observations of stars close to the BH. This is of interest for measuring the IR emission from the BH, in order to constrain accretion models; for solving the orbits of stars near the BH, in order to measure the BH mass and to search for general relativistic effects; and for detecting the fluctuations of the BH away from the dynamical center of the stellar cluster, in order to study the stellar potential. The BH lies on the line connecting the two images of any background source it gravitationally lenses, and so the intersection of these lines fixes its position. A combined search for a lensing signal and for the BH shows that the most likely point of intersection coincides with the center of acceleration of stars orbiting the BH. This statistical detection of lensing by the BH has a random probability of ~0.01. It can be verified by deep IR stellar spectroscopy, which will determine whether the most likely lensed image pair candidates (listed here) have identical spectra.Comment: 4 pages, 2 figures, submitted to ApJ

Exciton-polariton emission from organic semiconductor optical waveguides

We photo-excite slab polymer waveguides doped with J-aggregating dye molecules and measure the leaky emission from strongly coupled waveguide exciton polariton modes at room temperature. We show that the momentum of the waveguide exciton polaritons can be controlled by modifying the thickness of the excitonic waveguide. Non-resonantly pumped excitons in the slab excitonic waveguide decay into transverse electric and transverse magnetic strongly coupled exciton waveguide modes with radial symmetry. These leak to cones of light with radial and azimuthal polarizations

Phase Noise Modeling of Opto-Mechanical Oscillators

We build upon and derive a precise far from carrier phase noise model for radiation pressure driven opto-mechanical oscillators and show that calculations based on our model accurately match published phase noise data for such oscillators. Furthermore, we derive insights based on the equations presented and calculate phase noise for an array of coupled disk resonators, showing that it is possible to achieve phase noise as low as -80 dBc/Hz at 1 kHz offset for a 54 MHz opto-mechanical oscillator

Beaming Binaries - a New Observational Category of Photometric Binary Stars

The new photometric space-borne survey missions CoRoT and Kepler will be able to detect minute flux variations in binary stars due to relativistic beaming caused by the line-of-sight motion of their components. In all but very short period binaries (P>10d), these variations will dominate over the ellipsoidal and reflection periodic variability. Thus, CoRoT and Kepler will discover a new observational class: photometric beaming binary stars. We examine this new category and the information that the photometric variations can provide. The variations that result from the observatory heliocentric velocity can be used to extract some spectral information even for single stars.Comment: 15 pages, 4 figures, accpeted for publication in The Astrophysical Journa