Lyapunov Exponent and Criticality in the Hamiltonian Mean Field Model

We investigate the dependence of the largest Lyapunov exponent of a $N$-particle self-gravitating ring model at equilibrium with respect to the number of particles and its dependence on energy. This model has a continuous phase-transition from a ferromagnetic to homogeneous phase, and we numerically confirm with large scale simulations the existence of a critical exponent associated to the largest Lyapunov exponent, although at variance with the theoretical estimate. The existence of chaos in the magnetized state evidenced by a positive Lyapunov exponent, even in the thermodynamic limit, is explained by the resonant coupling of individual particle oscillations to the diffusive motion of the center of mass of the system due to the thermal excitation of a classical Goldstone mode. The transition from "weak" to "strong" chaos occurs at the onset of the diffusive motion of the center of mass of the non-homogeneous equilibrium state, as expected. We also discuss thoroughly for the model the validity and limits of a geometrical approach for their analytical estimate.Comment: 21 pages, 14 figure

Asymptotic behavior of Boussinesq system of KdV-KdV type

This work deals with the local rapid exponential stabilization for a Boussinesq system of KdV-KdV type introduced by J. Bona, M. Chen and J.-C. Saut. This is a model for the motion of small amplitude long waves on the surface of an ideal fluid. Here, we will consider the Boussinesq system of KdV-KdV type posed on a finite domain, with homogeneous Dirichlet--Neumann boundary controls acting at the right end point of the interval. Our goal is to build suitable integral transformations to get a feedback control law that leads to the stabilization of the system. More precisely, we will prove that the solution of the closed-loop system decays exponentially to zero in the $L^2(0,L)$--norm and the decay rate can be tuned to be as large as desired if the initial data is small enough.Comment: 21 page

Enhancement of digital images through band ratio techniques for geological applications

The fundamentals in the use of band ratio techniques to enhance spectral signatures of geologic interest are discussed. The path radiance, additive term of the measured radiance at any given wavelength, is almost completely eliminated from LANDSAT images by subtracting the smallest value of the radiance measured in each channel, at shadows caused by topographic relief and clouds, and deep clear water bodies. By ratioing successive spectral channels the effect of solar angle of elevation is minimized and the product expresses, to a first approximation, a relationship between reflectances, which are intrinsic characteristics of the targets. Ratios between noncorrelated channels, such as R 7/4, R 7/5, and R 6/4 are useful to show variations in the vegetation cover, probably related to geobotanical associations

The improved nuclear parton distributions

In this paper we propose an improvement of the EKS nuclear parton distributions for the small x region of high energy processes, where the perturbative high parton density effects cannot be disregarded. We analyze the behavior of the ratios $xG_A/xG_N$ and $F_2^A/F_2^D$ and verify that at small x they are strongly modified when compared to the EKS predictions. The implications of our results for the heavy ion collisions in RHIC and LHC are discussed.Comment: 16 pages, 2 figure

Secalonic acid A from Pseudoparmelia sphaerospora (Nyl.) Hale and P. hypomilta (Fée) Hale (Parmeliaceae)

Secalonic acid A, a yellow pigment from fungal metabolism, was isolated from the lichens Pseudoparmelia sphaerospora and P. hypomilta. From P. sphaerospora was also isolated the depsidone hypostictic acid. The structure of these compounds was determined by spectroscopic methods and comparison with literature data