Chebyshev, Legendre, Hermite and other orthonormal polynomials in D-dimensions

We propose a general method to construct symmetric tensor polynomials in the D-dimensional Euclidean space which are orthonormal under a general weight. The D-dimensional Hermite polynomials are a particular case of the present ones for the case of a gaussian weight. Hence we obtain generalizations of the Legendre and of the Chebyshev polynomials in D dimensions that reduce to the respective well-known orthonormal polynomials in D=1 dimensions. We also obtain new D-dimensional polynomials orthonormal under other weights, such as the Fermi-Dirac, Bose-Einstein, Graphene equilibrium distribution functions and the Yukawa potential. We calculate the series expansion of an arbitrary function in terms of the new polynomials up to the fourth order and define orthonormal multipoles. The explicit orthonormalization of the polynomials up to the fifth order (N from 0 to 4) reveals an increasing number of orthonormalization equations that matches exactly the number of polynomial coefficients indication the correctness of the present procedure.Comment: 20 page

Energy dependence of a vortex line length near a zigzag of pinning centers

A vortex line, shaped by a zigzag of pinning centers, is described here through a three-dimensional unit cell containing two pinning centers positioned symmetrically with respect to its center. The unit cell is a cube of side $L=12\xi$, the pinning centers are insulating spheres of radius $R$, taken within the range $0.2\xi$ to $3.0\xi$, $\xi$ being the coherence length. We calculate the free energy density of these systems in the framework of the Ginzburg-Landau theory.Comment: Submitted to Braz. Jour. Phys. (http://www.sbfisica.org.br/bjp) 11 pages, 6 figures, 1 table, LaTex 2

Bright spots in the darkness of cancer: A review of starfishes-derived compounds and their anti-tumor action

The fight against cancer represents a great challenge for researchers and, for this reason, the search for new promising drugs to improve cancer treatments has become inevitable. Oceans, due to their wide diversity of marine species and environmental conditions have proven to be precious sources of potential natural drugs with active properties. As an example, in this context several studies performed on sponges, tunicates, mollusks, and soft corals have brought evidence of the interesting biological activities of the molecules derived from these species. Also, echinoderms constitute an important phylum, whose members produce a huge number of compounds with diverse biological activities. In particular, this review is the first attempt to summarize the knowledge about starfishes and their secondary metabolites that exhibited a significant anticancer effect against different human tumor cell lines. For each species of starfish, the extracted molecules, their effects, and mechanisms of action are described

Study of the beam-cavity interaction in the PS 10 MHz RF system

The eleven main accelerating cavities of the Proton Synchrotron (PS) at CERN consist of two ferrite-loaded coaxial lambda/4 resonators each. Both resonators oscillate in phase, as their gaps are electrically connected by short bars. They are in addition magnetically coupled via the bias loop used for cavity tuning. The cavities are equipped with a wide-band feedback system, limiting the beam loading, and a further reduction of the beam induced voltage is achieved by relays which short-circuit each half-resonator gap when the cavity is not in use. Asymmetries of the beam induced voltage observed in the two half-cavities indicate that the coupling between the two resonators is not as tight as expected. The total cavity impedance coupling to the beam may be affected differently by the contributions of both resonators. A dedicated measurement campaign with high-intensity proton beam and numerical simulation have been performed to investigate the beam-cavity interaction. This paper reports the result of the study and the work aiming at the development of a model of the system, including the wide-band feedback, which reproduces this interaction

Quantum information becomes classical when distributed to many users

Any physical transformation that equally distributes quantum information over a large number M of users can be approximated by a classical broadcasting of measurement outcomes. The accuracy of the approximation is at least of the order 1/M. In particular, quantum cloning of pure and mixed states can be approximated via quantum state estimation. As an example, for optimal qubit cloning with 10 output copies, a single user has error probability p > 0.45 in distinguishing classical from quantum output--a value close to the error probability of the random guess.Comment: 4 pages, no figures, published versio

Paramagnetic excited vortex states in superconductors

We consider excited vortex states, which are vortex states left inside a superconductor once the external applied magnetic field is switched off and whose energy is lower than of the normal state. We show that this state is paramagnetic and develop here a general method to obtain its Gibbs free energy through conformal mapping. The solution for any number of vortices in any cross section geometry can be read off from the Schwarz - Christoffel mapping. The method is based on the first order equations used by A. Abrikosov to discover vortices.Comment: 14 pages, 7 figure

Fully dissipative relativistic lattice Boltzmann method in two dimensions

In this paper, we develop and characterize the fully dissipative Lattice Boltzmann method for ultra-relativistic fluids in two dimensions using three equilibrium distribution functions: Maxwell-J\"uttner, Fermi-Dirac and Bose-Einstein. Our results stem from the expansion of these distribution functions up to fifth order in relativistic polynomials. We also obtain new Gaussian quadratures for square lattices that preserve the spatial resolution. Our models are validated with the Riemann problem and the limitations of lower order expansions to calculate higher order moments are shown. The kinematic viscosity and the thermal conductivity are numerically obtained using the Taylor-Green vortex and the Fourier flow respectively and these transport coefficients are compared with the theoretical prediction from Grad's theory. In order to compare different expansion orders, we analyze the temperature and heat flux fields on the time evolution of a hot spot

Massive photons and Lorentz violation

All quadratic translation- and gauge-invariant photon operators for Lorentz breakdown are included into the Stueckelberg Lagrangian for massive photons in a generalized \xi-gauge. The corresponding dispersion relation and tree-level propagator are determined exactly, and some leading-order results are derived. The question of how to include such Lorentz-violating effects into a perturbative quantum-field expansion is addressed. Applications of these results within Lorentz-breaking quantum field theories include the regularization of infrared divergences as well as the free propagation of massive vector bosons.Comment: 12 pages, 1 figur

Effect of the boundary condition on the vortex patterns in mesoscopic three-dimensional superconductors - disk and sphere

The vortex state of mesoscopic three-dimensional superconductors is determined using a minimization procedure of the Ginzburg-Landau free energy. We obtain the vortex pattern for a mesoscopic superconducting sphere and find that vortex lines are naturally bent and are closest to each other at the equatorial plane. For a superconducting disk with finite height, and under an applied magnetic field perpendicular to its major surface, we find that our method gives results consistent with previous calculations. The matching fields, the magnetization and $H_{c3}$, are obtained for models that differ according to their boundary properties. A change of the Ginzburg-Landau parameters near the surface can substantially enhance $H_{c3}$ as shown here.Comment: 7 pages, 4 figures (low resolution