10,817 research outputs found
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
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