Examinando por Materia "Legendre polynomials"
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Ítem Controlled drug release from a spheroidal matrix(ELSEVIER SCIENCE BV, 2019-01-01) Simon L.; Ospina J.; Simon L.; Ospina J.; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónDrug transport through a spheroidal matrix was studied using Fick's second law of diffusion in spherical coordinates. The prolate spheroid-shaped geometry was described by a small angular deformation applied at the surface of the body. An infinite series of Legendre polynomials of order two was first used to develop an expression for the solute concentration in the Laplace domain. This method resulted in closed-form expressions for the effective time constant and the cumulative percentage of drug released in terms of critical model parameters. The procedure predicted published solutions very well. More moisture was observed at the center of the body when compared to the focal point. As the aspect ratio increased, the effective time constant decreased. At 0.38 unit time, 98.6% of the loaded drug was released from the device. © 2018 Elsevier B.V.Ítem Electronic and Topological Analysis for New Phases of Chromium Nitride(WILEY-V C H VERLAG GMBH, 2018-01-01) Marin-Suarez, Marco; Alzate-Vargas, Leidy L.; David, Jorge; Arroyave-Franco, Mauricio; Velez, Mario E.; Marin-Suarez, Marco; Alzate-Vargas, Leidy L.; David, Jorge; Arroyave-Franco, Mauricio; Velez, Mario E.; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónChromium nitride (CrN) in its NaCl-type phase has been widely studied through density functional theory (DFT) in order to analyze its electronic properties. By the means of DFT with the Becke's three parameter Lee-Yang-Parr (B3LYP) hybrid functional, the same stoichiometry is studied in two unreported hypothetical phases in addition to the nonsynthesized and previously reported zinc-blende-type phase. The cohesive energy of every structure is calculated, and the analysis of this quantity indicated that all crystals are stable and that there is an unreported phase more stable than the synthesized one. The calculated electronic dispersion relation and density of electronic states allowed for the determination that these three phases have a conducting behavior. The symmetry of some bands is determined as a result of the crystal field splitting for chromium d states. The topology of the electron density was studied in order to determine its properties at bond critical points (BCPs). The form of the Laplacian of the density and its gradient trajectories allowed to locate ring critical points in these structures. From these calculations, it is concluded that all three phases are ionic crystals. The synthesized NaCl-type phase is studied in order to compare and confirm the results. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimÍtem Taylor-petrov-galerkin method for the numerical solution of KdV equation(Hikari Ltd., 2016-01-01) Jairo Villegas, G.; Lida Buitrago, G.; Jorge Castaño, B.; Jairo Villegas, G.; Lida Buitrago, G.; Jorge Castaño, B.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y AplicacionesIn order to find the approximate solution of the KdV equation, we use the finite element method of Taylor-Petrov-Galerkin, in which discretization in the time variable is carried out using Taylor series expansion and for discretization in space are considered as test functions cubic B-splines and Legendre polynomials as weight functions. These functions are adequate in that they satisfy continuity, integrability and orthogonality required to apply the method. © 2015 Jairo Villegas G., Lida Buitrago G. and Jorge Castaño B.