Step energies and equilibrium shape of strained monolayer islands

Using a simple atomistic model of anharmonic nearest-neighbors interaction, we have calculated the step energies of strained hexagonal monolayer islands. These have been found to decrease with the absolute value of the misfit due to the strain relaxation at steps. The effect is significantly more pronounced in the case of positive misfit owing to the stronger repulsive interatomic forces. Furthermore, (111)-faceted steps are favored at positive misfit (compressed islands) and, to a lesser extent, (100)-faceted steps at negative misfits (tensile islands). The result is rationalized in terms of the different bonding geometries at step edges and a comparison with experiments is included. Thus, the equilibrium shape transforms from regular hexagons at zero misfit to threefold symmetric hexagons with increasing misfit.Comment: 6 pages, 5 figures, 1 table. Improved, finally accepted version including a new figure, a new table and several minor modifications resulting from discussions with referee

Prospects for transient gravitational waves at r-mode frequencies associated with pulsar glitches

t Glitches in pulsars are likely to trigger oscillation modes in the fluid interior of neutron stars. We examined these oscillations specifically at r-mode frequencies. The excited r-modes will emit gravitational waves and can have long damping time scales (minutes - days). We use simple estimates of how much energy the glitch might put into the r-mode and assess the detectability of the emitted gravitational waves with future interferometers

Top dimensional group of the basic intersection cohomology for singular riemannian foliations

It is known that, for a regular riemannian foliation on a compact manifold, the properties of its basic cohomology (non-vanishing of the top-dimensional group and Poincar\'e Duality) and the tautness of the foliation are closely related. If we consider singular riemannian foliations, there is little or no relation between these properties. We present an example of a singular isometric flow for which the top dimensional basic cohomology group is non-trivial, but its basic cohomology does not satisfy the Poincar\'e Duality property. We recover this property in the basic intersection cohomology. It is not by chance that the top dimensional basic intersection cohomology groups of the example are isomorphic to either 0 or $\mathbb{R}$. We prove in this Note that this holds for any singular riemannian foliation of a compact connected manifold. As a Corollary, we get that the tautness of the regular stratum of the singular riemannian foliation can be detected by the basic intersection cohomology.Comment: 11 pages. Accepted for publication in the Bulletin of the Polish Academy of Science

Quantum Singular Value Decomposer

We present a variational quantum circuit that produces the Singular Value Decomposition of a bipartite pure state. The proposed circuit, that we name Quantum Singular Value Decomposer or QSVD, is made of two unitaries respectively acting on each part of the system. The key idea of the algorithm is to train this circuit so that the final state displays exact output coincidence from both subsystems for every measurement in the computational basis. Such circuit preserves entanglement between the parties and acts as a diagonalizer that delivers the eigenvalues of the Schmidt decomposition. Our algorithm only requires measurements in one single setting, in striking contrast to the $3^n$ settings required by state tomography. Furthermore, the adjoints of the unitaries making the circuit are used to create the eigenvectors of the decomposition up to a global phase. Some further applications of QSVD are readily obtained. The proposed QSVD circuit allows to construct a SWAP between the two parties of the system without the need of any quantum gate communicating them. We also show that a circuit made with QSVD and CNOTs acts as an encoder of information of the original state onto one of its parties. This idea can be reversed and used to create random states with a precise entanglement structure.Comment: 6 + 1 pages, 5 figure

Chemical Abundances from the Continuum

The calculation of solar absolute fluxes in the near-UV is revisited, discussing in some detail recent updates in theoretical calculations of bound-free opacity from metals. Modest changes in the abundances of elements such as Mg and the iron-peak elements have a significant impact on the atmospheric structure, and therefore self-consistent calculations are necessary. With small adjustments to the solar photospheric composition, we are able to reproduce fairly well the observed solar fluxes between 200 and 270 nm, and between 300 and 420 nm, but find too much absorption in the 270-290 nm window. A comparison between our reference 1D model and a 3D time-dependent hydrodynamical simulation indicates that the continuum flux is only weakly sensitive to 3D effects, with corrections reaching <10% in the near-UV, and <2% in the optical.Comment: 10 pages, 5 figures, to appear in the proceedings of the conference A Stellar Journey, a symposium in celebration of Bengt Gustafsson's 65th birthday, June 23-27, 2008, Uppsal