Long-term planning versus short-term planning in the asymptotical location problem

Given the probability measure $\nu$ over the given region $\Omega\subset \R^n$, we consider the optimal location of a set $\Sigma$ composed by $n$ points \Om in order to minimize the average distance \Sigma\mapsto \int_\Om \dist(x,\Sigma) d\nu (the classical optimal facility location problem). The paper compares two strategies to find optimal configurations: the long-term one which consists in placing all $n$ points at once in an optimal position, and the short-term one which consists in placing the points one by one adding at each step at most one point and preserving the configuration built at previous steps. We show that the respective optimization problems exhibit qualitatively different asymptotic behavior as $n\to\infty$, although the optimization costs in both cases have the same asymptotic orders of vanishing.Comment: for more pictures and some movies as well, see http://www.sissa.it/~brancoli

Spin-Peierls transition with strong structural fluctuations in the vanadium oxide VOSb2_{2}O4_{4}

We report on the magnetic susceptibility and electron spin resonance measurements on polycrystalline samples of the vanadium oxide VOSb$_{2}$O$_{4}$, a quasi-one dimensional S=1/2 Heisenberg system. We show that the susceptibility vanishes at zero temperature, as in a gapped system, and we argue that this is due to a spin-Peierls transition with strong structural fluctuations.Comment: 5 pages, 4 figure

Orbital frustration at the origin of the magnetic behavior in LiNiO2

We report on the ESR, magnetization and magnetic susceptibility measurements performed over a large temperature range, from 1.5 to 750 K, on high-quality stoichiometric LiNiO2. We find that this compound displays two distinct temperature regions where its magnetic behavior is anomalous. With the help of a statistical model based on the Kugel'-Khomskii Hamiltonian, we show that below T_of ~ 400 K, an orbitally-frustrated state characteristic of the triangular lattice is established. This then gives a solution to the long-standing controversial problem of the magnetic behavior in LiNiO2.Comment: 5 pages, 5 figures, RevTex, accepted in PR

Semiclassical treatment of logarithmic perturbation theory

The explicit semiclassical treatment of logarithmic perturbation theory for the nonrelativistic bound states problem is developed. Based upon $\hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions for the one-dimensional anharmonic oscillator is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and exited states have been obtained. As an example, the perturbation expansions for the energy eigenvalues of the harmonic oscillator perturbed by $\lambda x^{6}$ are considered.Comment: 6 pages, LATEX 2.09 using IOP style

Summary of the CMS Discovery Potential for the MSSM SUSY Higgses

This work summarises the present understanding of the expected MSSM SUSY Higgs reach for CMS. Many of the studies presented here result from detailed detector simulations incorporating final CMS detector design and response. With 30 fb-1 the h -> gamma,gamma and h -> bb channels allow to cover most of the MSSM parameter space. For the massive A,H,H+ MSSM Higgs states the channels A,H -> tau,tau and H+ -> tau,nu turn out to be the most profitable ones in terms of mass reach and parameter space coverage. Consequently CMS has made a big effort to trigger efficiently on taus. Provided neutralinos and sleptons are not too heavy, there is an interesting complementarity in the reaches for A,H -> tau,tau and A,H -> chi,chi.Comment: 19 pages, 27 figure

Direct Measurement of Effective Magnetic Diffusivity in Turbulent Flow of Liquid Sodium

The first direct measurements of effective magnetic diffusivity in turbulent flow of electro-conductive fluids (the so-called beta-effect) under magnetic Reynolds number Rm >> 1 are reported. The measurements are performed in a nonstationary turbulent flow of liquid sodium, generated in a closed toroidal channel. The peak level of the Reynolds number reached Re \approx 3 10^6, which corresponds to the magnetic Reynolds number Rm \approx 30. The magnetic diffusivity of the liquid metal was determined by measuring the phase shift between the induced and the applied magnetic fields. The maximal deviation of magnetic diffusivity from its basic (laminar) value reaches about 50% .Comment: 5 pages, 6 figuser, accepted in PR