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

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

EFFECTS OF STRAIN RATE AND TEMPERATURE ON THE MECHANICAL PROPERTIES OF GFRP COMPOSITES

In this work, the mechanical response of a composite material based on glass fibers embedded in an epoxy resin was experimentally studied as a function of strain rate and temperature. It was shown that for the temperature range from 23 to 100 °C the elastic properties of the composite are significant affected and the strain rate influences only the ultimate strength. The experimental research data and the approaches presented in this work should significantly extend our knowledge of the effect of elevated temperatures on the mechanical behavior of high temperature polymer matrix composites

Estimativa de área foliar e de modelos de crescimento em plantas de lima ácida ?Tahiti? por métodos diretos e indiretos.

O trabalho visou estimar a área foliar total (AFT em m 2) de plantas de lima ácida ?Tahiti? (Centros latifólia Tan) no tempo, desenvolver modelos de estimativa de AFT com base em variáveis biométricas das plantas e avaliar o desempenho do método IAF-LUX nas estimativas de AFT. O estudo foi conduzido na Fazenda Boa Vista, pertencente à Iaçu Agropastoril Ltda., localizada no município de Iaçu, semiárido baiano, sob as coordenadas geográficas 12°46?00? de latitude sul e 40°13?00? de longitude oeste, e altitude de 280 m.PDF. 101_11