Polynomials Associated with Equilibria of Affine Toda-Sutherland Systems

An affine Toda-Sutherland system is a quasi-exactly solvable multi-particle dynamics based on an affine simple root system. It is a `cross' between two well-known integrable multi-particle dynamics, an affine Toda molecule and a Sutherland system. Polynomials describing the equilibrium positions of affine Toda-Sutherland systems are determined for all affine simple root systems.Comment: 9 page

The q-harmonic oscillator and an analog of the Charlier polynomials

A model of a q-harmonic oscillator based on q-Charlier polynomials of Al-Salam and Carlitz is discussed. Simple explicit realization of q-creation and q-annihilation operators, q-coherent states and an analog of the Fourier transformation are found. A connection of the kernel of this transform with biorthogonal rational functions is observed

Continued fraction solution of Krein's inverse problem

The spectral data of a vibrating string are encoded in its so-called characteristic function. We consider the problem of recovering the distribution of mass along the string from its characteristic function. It is well-known that Stieltjes' continued fraction provides a solution of this inverse problem in the particular case where the distribution of mass is purely discrete. We show how to adapt Stieltjes' method to solve the inverse problem for a related class of strings. An application to the excursion theory of diffusion processes is presented.Comment: 18 pages, 2 figure

Finite-Size Corrections to Anomalous Dimensions in N=4 SYM Theory

The scaling dimensions of large operators in N=4 supersymmetric Yang-Mills theory are dual to energies of semiclassical strings in AdS(5)xS(5). At one loop, the dimensions of large operators can be computed with the help of Bethe ansatz and can be directly compared to the string energies. We study finite-size corrections for Bethe states which should describe quantum corrections to energies of extended semiclassical strings.Comment: 10 page

The Bivariate Normal Copula

We collect well known and less known facts about the bivariate normal distribution and translate them into copula language. In addition, we prove a very general formula for the bivariate normal copula, we compute Gini's gamma, and we provide improved bounds and approximations on the diagonal.Comment: 24 page

The inverse spectral problem for the discrete cubic string

Given a measure $m$ on the real line or a finite interval, the "cubic string" is the third order ODE $-\phi'''=zm\phi$ where $z$ is a spectral parameter. If equipped with Dirichlet-like boundary conditions this is a nonselfadjoint boundary value problem which has recently been shown to have a connection to the Degasperis-Procesi nonlinear water wave equation. In this paper we study the spectral and inverse spectral problem for the case of Neumann-like boundary conditions which appear in a high-frequency limit of the Degasperis--Procesi equation. We solve the spectral and inverse spectral problem for the case of $m$ being a finite positive discrete measure. In particular, explicit determinantal formulas for the measure $m$ are given. These formulas generalize Stieltjes' formulas used by Krein in his study of the corresponding second order ODE $-\phi''=zm\phi$.Comment: 24 pages. LaTeX + iopart, xypic, amsthm. To appear in Inverse Problems (http://www.iop.org/EJ/journal/IP

Toward Forecasting Volcanic Eruptions using Seismic Noise

During inter-eruption periods, magma pressurization yields subtle changes of the elastic properties of volcanic edifices. We use the reproducibility properties of the ambient seismic noise recorded on the Piton de la Fournaise volcano to measure relative seismic velocity variations of less than 0.1 % with a temporal resolution of one day. Our results show that five studied volcanic eruptions were preceded by clearly detectable seismic velocity decreases within the zone of magma injection. These precursors reflect the edifice dilatation induced by magma pressurization and can be useful indicators to improve the forecasting of volcanic eruptions.Comment: Supplementary information: http://www-lgit.obs.ujf-grenoble.fr/~fbrengui/brenguier_SI.pdf Supplementary video: http://www-lgit.obs.ujf-grenoble.fr/~fbrengui/brenguierMovieVolcano.av

Field induced stationary state for an accelerated tracer in a bath

Our interest goes to the behavior of a tracer particle, accelerated by a constant and uniform external field, when the energy injected by the field is redistributed through collision to a bath of unaccelerated particles. A non equilibrium steady state is thereby reached. Solutions of a generalized Boltzmann-Lorentz equation are analyzed analytically, in a versatile framework that embeds the majority of tracer-bath interactions discussed in the literature. These results --mostly derived for a one dimensional system-- are successfully confronted to those of three independent numerical simulation methods: a direct iterative solution, Gillespie algorithm, and the Direct Simulation Monte Carlo technique. We work out the diffusion properties as well as the velocity tails: large v, and either large -v, or v in the vicinity of its lower cutoff whenever the velocity distribution is bounded from below. Particular emphasis is put on the cold bath limit, with scatterers at rest, which plays a special role in our model.Comment: 20 pages, 6 figures v3:minor corrections in sec.III and added reference