Finite times to equipartition in the thermodynamic limit

We study the time scale T to equipartition in a 1D lattice of N masses coupled by quartic nonlinear (hard) springs (the Fermi-Pasta-Ulam beta model). We take the initial energy to be either in a single mode gamma or in a package of low frequency modes centered at gamma and of width delta-gamma, with both gamma and delta-gamma proportional to N. These initial conditions both give, for finite energy densities E/N, a scaling in the thermodynamic limit (large N), of a finite time to equipartition which is inversely proportional to the central mode frequency times a power of the energy density E/N. A theory of the scaling with E/N is presented and compared to the numerical results in the range 0.03 <= E/N <= 0.8.Comment: Plain TeX, 5 `eps' figures, submitted to Phys. Rev.

The ESO Spectroscopic facility

We present the concept of a novel facility dedicated to massively-multiplexed spectroscopy. The telescope has a very wide field Cassegrain focus optimised for fibre feeding. With a Field of View (FoV) of 2.5 degrees diameter and a 11.4m pupil, it will be the largest etendue telescope. The large focal plane can easily host up to 16.000 fibres. In addition, a gravity invariant focus for the central 10 arc-minutes is available to host a giant integral field unit (IFU). The 3 lenses corrector includes an ADC, and has good performance in the 360-1300 nm wavelength range. The top level science requirements were developed by a dedicated ESO working group, and one of the primary cases is high resolution spectroscopy of GAIA stars and, in general, how our Galaxy formed and evolves. The facility will therefore be equipped with both, high and low resolution spectrographs. We stress the importance of developing the telescope and instrument designs simultaneously. The most relevant R\&D aspect is also briefly discussed.Comment: 6 pages 4 figures , presented at IAU Symposium 334 "rediscovering our galaxy

Fractional-Spin Integrals of Motion for the Boundary Sine-Gordon Model at the Free Fermion Point

We construct integrals of motion (IM) for the sine-Gordon model with boundary at the free Fermion point which correctly determine the boundary S matrix. The algebra of these IM (``boundary quantum group'' at q=1) is a one-parameter family of infinite-dimensional subalgebras of twisted affine sl(2). We also propose the structure of the fractional-spin IM away from the free Fermion point.Comment: 19 pages, LaTeX, no figure

Kerr black hole lensing for generic observers in the strong deflection limit

We generalize our previous work on gravitational lensing by a Kerr black hole in the strong deflection limit, removing the restriction to observers on the equatorial plane. Starting from the Schwarzschild solution and adding corrections up to the second order in the black hole spin, we perform a complete analytical study of the lens equation for relativistic images created by photons passing very close to a Kerr black hole. We find out that, to the lowest order, all observables (including shape and shift of the black hole shadow, caustic drift and size, images position and magnification) depend on the projection of the spin on a plane orthogonal to the line of sight. In order to break the degeneracy between the black hole spin and its inclination relative to the observer, it is necessary to push the expansion to higher orders. In terms of future VLBI observations, this implies that very accurate measures are needed to determine these two parameters separately.Comment: 17 pages, 4 figures, one section added, to appear on Physical Review

Long Range Magnetic Order and the Darwin Lagrangian

We simulate a finite system of $N$ confined electrons with inclusion of the Darwin magnetic interaction in two- and three-dimensions. The lowest energy states are located using the steepest descent quenching adapted for velocity dependent potentials. Below a critical density the ground state is a static Wigner lattice. For supercritical density the ground state has a non-zero kinetic energy. The critical density decreases with $N$ for exponential confinement but not for harmonic confinement. The lowest energy state also depends on the confinement and dimension: an antiferromagnetic cluster forms for harmonic confinement in two dimensions.Comment: 5 figure

Dimensional crossover and incipient quantum size effects in superconducting niobium nanofilms

Superconducting and normal state properties of sputtered Niobium nanofilms have been systematically investigated, as a function of film thickness in a d=9-90 nm range, on different substrates. The width of the superconducting-to-normal transition for all films remained in few tens of mK, thus remarkably narrow, confirming their high quality. We found that the superconducting critical current density exhibits a pronounced maximum, three times larger than its bulk value, for film thickness around 25 nm, marking the 3D-to-2D crossover. The extracted magnetic penetration depth shows a sizeable enhancement for the thinnest films, aside the usual demagnetization effects. Additional amplification effects of the superconducting properties have been obtained in the case of sapphire substrates or squeezing the lateral size of the nanofilms. For thickness close to 20 nm we also measured a doubled perpendicular critical magnetic field compared to its saturation value for d>33 nm, indicating shortening of the correlation length and the formation of small Cooper pairs in the condensate. Our data analysis evidences an exciting interplay between quantum-size and proximity effects together with strong-coupling effects and importance of disorder in the thinnest films, locating the ones with optimally enhanced critical properties close to the BCS-BEC crossover regime

A Characterization of Bispecial Sturmian Words

A finite Sturmian word w over the alphabet {a,b} is left special (resp. right special) if aw and bw (resp. wa and wb) are both Sturmian words. A bispecial Sturmian word is a Sturmian word that is both left and right special. We show as a main result that bispecial Sturmian words are exactly the maximal internal factors of Christoffel words, that are words coding the digital approximations of segments in the Euclidean plane. This result is an extension of the known relation between central words and primitive Christoffel words. Our characterization allows us to give an enumerative formula for bispecial Sturmian words. We also investigate the minimal forbidden words for the set of Sturmian words.Comment: Accepted to MFCS 201

Maximal Closed Substrings

A string is closed if it has length 1 or has a nonempty border without internal occurrences. In this paper we introduce the definition of a maximal closed substring (MCS), which is an occurrence of a closed substring that cannot be extended to the left nor to the right into a longer closed substring. MCSs with exponent at least 2 are commonly called runs; those with exponent smaller than 2, instead, are particular cases of maximal gapped repeats. We show that a string of length n contains O(n1.5) MCSs. We also provide an output-sensitive algorithm that, given a string of length n over a constant-size alphabet, locates all m MCSs the string contains in O(nlog n+ m) time

Thermodynamic Properties and Phase Transitions in a Mean-Field Ising Spin Glass on Lattice Gas: the Random Blume-Emery-Griffiths-Capel Model

The study of the mean-field static solution of the Random Blume-Emery-Griffiths-Capel model, an Ising-spin lattice gas with quenched random magnetic interaction, is performed. The model exhibits a paramagnetic phase, described by a stable Replica Symmetric solution. When the temperature is decreased or the density increases, the system undergoes a phase transition to a Full Replica Symmetry Breaking spin-glass phase. The nature of the transition can be either of the second order (like in the Sherrington-Kirkpatrick model) or, at temperature below a given critical value, of the first order in the Ehrenfest sense, with a discontinuous jump of the order parameter and accompanied by a latent heat. In this last case coexistence of phases takes place. The thermodynamics is worked out in the Full Replica Symmetry Breaking scheme, and the relative Parisi equations are solved using a pseudo-spectral method down to zero temperature.Comment: 24 pages, 12 figure