Conservation laws for invariant functionals containing compositions

The study of problems of the calculus of variations with compositions is a quite recent subject with origin in dynamical systems governed by chaotic maps. Available results are reduced to a generalized Euler-Lagrange equation that contains a new term involving inverse images of the minimizing trajectories. In this work we prove a generalization of the necessary optimality condition of DuBois-Reymond for variational problems with compositions. With the help of the new obtained condition, a Noether-type theorem is proved. An application of our main result is given to a problem appearing in the chaotic setting when one consider maps that are ergodic.Comment: Accepted for an oral presentation at the 7th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2007), to be held in Pretoria, South Africa, 22-24 August, 200

Evidence of defect-induced ferromagnetism in ZnFe2_{2}O4_{4} thin films

X-ray absorption near-edge and grazing incidence X-ray fluorescence spectroscopy are employed to investigate the electronic structure of ZnFe$_{2}$O$_{4}$ thin films. The spectroscopy techniques are used to determine the non-equilibrium cation site occupancy as a function of depth and oxygen pressure during deposition and its effects on the magnetic properties. It is found that low deposition pressures below 10$^{-3}$ mbar cause iron superoccupation of tetrahedral sites without Zn$^{2+}$ inversion, resulting in an ordered magnetic phase with high room temperature magnetic moment.Comment: Accepted for publication in Phys. Rev.

Production of optical phase space vortices with non-locally distributed mode converters

Optical vortices have been observed in a wide variety of optical systems. They can be observed directly in the wavefront of optical beams, or in the correlations between pairs of entangled photons. We present a novel optical vortex which appears in a non-local plane of the two-photon phase space, composed of a single degree of freedom of each photon of an entangled pair. The preparation of this vortex can be viewed as a "non-local" or distributed mode converter. We show how these novel optical vortices of arbitrary order can be prepared in the spatial degrees of freedom of entangled photons.Comment: To appear in upcoming special issue "Orbital Angular Momentum" of the Journal of Optic

GHASP: an H{\alpha} kinematic survey of spiral and irregular galaxies -- IX. The NIR, stellar and baryonic Tully-Fisher relations

We studied, for the first time, the near infrared, stellar and baryonic Tully-Fisher relations for a sample of field galaxies taken from an homogeneous Fabry-Perot sample of galaxies (the GHASP survey). The main advantage of GHASP over other samples is that maximum rotational velocities were estimated from 2D velocity fields, avoiding assumptions about the inclination and position angle of the galaxies. By combining these data with 2MASS photometry, optical colors, HI masses and different mass-to-light ratio estimators, we found a slope of 4.48\pm0.38 and 3.64\pm0.28 for the stellar and baryonic Tully-Fisher relation, respectively. We found that these values do not change significantly when different mass-to-light ratios recipes were used. We also point out, for the first time, that rising rotation curves as well as asymmetric rotation curves show a larger dispersion in the Tully-Fisher relation than flat ones or than symmetric ones. Using the baryonic mass and the optical radius of galaxies, we found that the surface baryonic mass density is almost constant for all the galaxies of this sample. In this study we also emphasize the presence of a break in the NIR Tully-Fisher relation at M(H,K)\sim-20 and we confirm that late-type galaxies present higher total-to-baryonic mass ratios than early-type spirals, suggesting that supernova feedback is actually an important issue in late-type spirals. Due to the well defined sample selection criteria and the homogeneity of the data analysis, the Tully-Fisher relation for GHASP galaxies can be used as a reference for the study of this relation in other environments and at higher redshifts.Comment: 16 pages, 6 figures. Accepted for publication in MNRA