The Experts below are selected from a list of 3342 Experts worldwide ranked by ideXlab platform
Chihyang Wu - One of the best experts on this subject based on the ideXlab platform.
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discrete ordinate solutions associated with the finite Legendre Transform for radiative transfer in a slab with sinusoidal refractive index
International Communications in Heat and Mass Transfer, 2012Co-Authors: Chihyang WuAbstract:Abstract In this work, we develop an alternative discrete ordinate approximation for radiative transfer in a refractive slab. The present method treats the angular derivative term of the radiative transfer equation for a planar medium with varying refractive index (VRI) by using a finite Legendre Transform which gives a simple expression of the angular derivative term. Thus, the solution procedure does not march along direction, and so is not restricted to a monotonic variation of refractive index. We apply this method to study radiative heat transfer in a cold slab with anisotropic scattering, diffuse boundaries and sinusoidal VRI. We also solve the problems by the discrete curved ray tracing (DCRT). The hemispherical reflectance and transmittance of slabs with irradiation from the upper surroundings obtained by the present method and those obtained by the DCRT are in excellent agreement. For a slab of a sinusoidal refractive index with the minimum at the center plane, the gradient of refractive index causes the internal reflection of a part of irradiation, which reduces the transmittance of the slab. Other effects of the VRI, the optical thickness, the scattering albedo, the anisotropically scattering coefficient and the boundary reflection are also investigated.
Mohamed Gantri - One of the best experts on this subject based on the ideXlab platform.
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corrigendum to solution of radiative transfer equation with a continuous and stochastic varying refractive index by Legendre Transform method
Computational and Mathematical Methods in Medicine, 2016Co-Authors: Riadh Baazaoui, Mohamed GantriAbstract:Through this corrigendum the authors declare that a version of this article entitled “Solution of Radiative Transfer Equation with a Continuous and Stochastic Varying Refractive Index by Legendre Transform Method” [1] that was published elsewhere has been retracted [2]. One of the authors of that article was missing from this article. The correct list of the authors and their affiliations are as shown above.
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solution of radiative transfer equation with a continuous and stochastic varying refractive index by Legendre Transform method
Computational and Mathematical Methods in Medicine, 2014Co-Authors: Mohamed GantriAbstract:The present paper gives a new computational framework within which radiative transfer in a varying refractive index biological tissue can be studied. In our previous works, Legendre Transform was used as an innovative view to handle the angular derivative terms in the case of uniform refractive index spherical medium. In biomedical optics, our analysis can be considered as a forward problem solution in a diffuse optical tomography imaging scheme. We consider a rectangular biological tissue-like domain with spatially varying refractive index submitted to a near infrared continuous light source. Interaction of radiation with the biological material into the medium is handled by a radiative transfer model. In the studied situation, the model displays two angular redistribution terms that are treated with Legendre integral Transform. The model is used to study a possible detection of abnormalities in a general biological tissue. The effect of the embedded nonhomogeneous objects on the transmitted signal is studied. Particularly, detection of targets of localized heterogeneous inclusions within the tissue is discussed. Results show that models accounting for variation of refractive index can yield useful predictions about the target and the location of abnormal inclusions within the tissue.
A Plastino - One of the best experts on this subject based on the ideXlab platform.
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fisher based thermodynamics its Legendre Transform and concavity properties
Physical Review E, 1999Co-Authors: B R Frieden, A Plastino, Bernard H SofferAbstract:: It is shown that the Legendre-Transform structure of thermodynamics can be replicated without any change if one replaces the entropy S by Fisher's information measure I. Also, the important thermodynamic property of concavity is shown to be obeyed by I. By this use of the Fisher information measure we develop a thermodynamics that seems to be able to treat equilibrium and nonequilibrium situations in a manner entirely similar to the conventional one.
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on the universality of thermodynamics Legendre Transform structure
Physics Letters A, 1997Co-Authors: A PlastinoAbstract:Abstract It is shown that the Legendre Transform structure of thermodynamics does not depend upon the functional form of the entropy. It is a just a necessary consequence of Jaynes' maximum entropy principle. Moreover, in the important special case of the canonical ensemble, the Legendre Transform structure of thermodynamics is shown to be independent of the functional form of the mean energy constraint as well.
Paul W. Ayers - One of the best experts on this subject based on the ideXlab platform.
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density functional theory with additional basic variables extended Legendre Transform
Physical Review A, 2009Co-Authors: Paul W. Ayers, Patricio FuentealbaAbstract:In a recent series of papers, Higuchi and Higuchi defined an extended constrained-search procedure by extending the Levy constrained search by adding additional constraints. As shown here, this procedure can be equivalently formulated in terms of Lieb's Legendre Transformation functional. The Legendre Transform approach has advantages in cases where the additional constraints are restrictive enough to cause problems with $N$-representability.
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coordinate scaling of the kinetic energy in pair density functional theory a Legendre Transform approach
International Journal of Quantum Chemistry, 2009Co-Authors: Rogelio Cuevassaavedra, Paul W. AyersAbstract:We show that the kinetic energy functional in pair density functional theory is homogeneous of degree 2 with respect to coordinate scaling. Although this result was already derived by Levy and Ziesche using the constrained search method (Levy and Ziesche, J Chem Phys 2001, 115, 9110), we derive our result using the Legendre Transform formulation (Ayers et al., J Chem Phys 2006, 124, 054101). The advantage of this approach is that in the Legendre Transform functional, the N-representability problem is solved by the functional. By contrast, in the Levy–Ziesche approach, the computationally impracticable N-representability constraints have to be imposed separately. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009
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Legendre-Transform functionals for spin-density-functional theory.
Journal of Chemical Physics, 2006Co-Authors: Paul W. Ayers, Weitao YangAbstract:We provide a rigorous proof that the Hohenberg-Kohn theorem holds for spin densities by extending Lieb’s Legendre-Transform formulation to spin densities. The resulting spin-density-functional theory resolves several troublesome issues. Most importantly, the present paper provides an explicit construction for the spin potentials at any point along the adiabatic connection curve, thus providing a formal basis for the use of exchange-correlation functionals of the spin density in the Kohn-Sham density-functional theory (DFT). The practical implications of this result for unrestricted Kohn-Sham DFT calculations is considered, and the existence of holes below the Fermi level is discussed. We argue that an orbital’s energy tends to increase as its occupation number increases, which provides the basis for a computational algorithm for determining the occupation numbers in Kohn-Sham DFT and helps explain the origin of Hund’s rules and holes below the Fermi level.
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generalizations of the hohenberg kohn theorem i Legendre Transform constructions of variational principles for density matrices and electron distribution functions
Journal of Chemical Physics, 2006Co-Authors: Paul W. Ayers, Sidney Golden, Mel LevyAbstract:Given a general, N-particle Hamiltonian operator, analogs of the Hohenberg-Kohn theorem are derived for functions that are more general than the particle density, including density matrices and the diagonal elements thereof. The generalization of Lieb’s Legendre Transform ansatz to the generalized Hohenberg-Kohn functional not only solves the υ-representability problem for these entities, but, more importantly, also solves the N-representability problem. Restricting the range of operators explored by the Legendre Transform leads to a lower bound on the true functional. If all the operators of interest are incorporated in the restricted maximization, however, the variational principle dictates that exact results are obtained for the systems of interest. This might have important implications for practical work not only for density matrices but also for density functionals. A follow-up paper will present a useful alternative approach to the v- and N-representability problems based on the constrained search ...
Mel Levy - One of the best experts on this subject based on the ideXlab platform.
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generalizations of the hohenberg kohn theorem i Legendre Transform constructions of variational principles for density matrices and electron distribution functions
Journal of Chemical Physics, 2006Co-Authors: Paul W. Ayers, Sidney Golden, Mel LevyAbstract:Given a general, N-particle Hamiltonian operator, analogs of the Hohenberg-Kohn theorem are derived for functions that are more general than the particle density, including density matrices and the diagonal elements thereof. The generalization of Lieb’s Legendre Transform ansatz to the generalized Hohenberg-Kohn functional not only solves the υ-representability problem for these entities, but, more importantly, also solves the N-representability problem. Restricting the range of operators explored by the Legendre Transform leads to a lower bound on the true functional. If all the operators of interest are incorporated in the restricted maximization, however, the variational principle dictates that exact results are obtained for the systems of interest. This might have important implications for practical work not only for density matrices but also for density functionals. A follow-up paper will present a useful alternative approach to the v- and N-representability problems based on the constrained search ...