Examinando por Materia "Laplace transforms"
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Ítem Approximated analytical solution to an Ebola optimal control problem(Board Members, 2016-01-01) Hincapié-Palacio, D.; Ospina, J.; Torres, D.F.M.; Hincapié-Palacio, D.; Ospina, J.; Torres, D.F.M.; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónAn analytical expression for the optimal control of an Ebola problem is obtained. The analytical solution is found as a first-order approximation to the Pontryagin Maximum Principle via the Euler-Lagrange equation. An implementation of the method is given using the computer algebra system Maple. Our analytical solutions confirm the results recently reported in the literature using numerical methods.Ítem Basic reproductive rate of a spatial epidemic model using computer algebra software(2005-01-01) Doracelly Hincapié, P.; Juan Ospina, G.; Doracelly Hincapié, P.; Juan Ospina, G.; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónUsing computer algebra software we obtain the basic reproductive rate corresponding to the propagation of a directly transmitted disease in a circular habitat when the disease is endemic at the boundary. The method used is the Laplace Transform Technique and calculus of residues. The results that were obtained include both the explicit form of the R0 for the boundary condition that was considered, as the explicit symbolic solution of the model equation. The method that was used can be extended to other more complex problems such as indirectly transmitted diseases with one or more intermediary hosts or effects of genetic, immunological, geographical or social heterogeneity in the human population. This application indicates that the computer algebra software for symbolic computation has a very promissory future in mathematical epidemiology.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 Dynamic analysis and performance evaluation of the BIAcore surface plasmon resonance biosensor(SPIE-INT SOC OPTICAL ENGINEERING, 2015-01-01) Simon, Laurent; Ospina, Juan; Simon, Laurent; Ospina, Juan; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónSolution procedures were proposed to analyze nonlinear mass transport through an optical biosensor. A generalized collocation technique was applied to predict the dynamic behavior of an analyte along the flow chamber as a result of convection, diffusion and chemical reaction. The method estimated the effective time constants for reaching average steady-state concentrations of the free and bound analytes in the cell. When diffusion in the direction of flow was neglected, a closed-form solution, based on double Laplace transforms, was obtained after linearizing the original system. In both models, an increase in the sample diffusion coefficient lowered the effective time constant. This approach may help researchers evaluate the performance of biosensors and meet specific design criteria. © 2015 SPIE.Ítem Dynamic analysis of heat transfer through a fin of constant cross-sectional area: Specified fin tip temperature(2009-01-01) Carranza, R.G.; Ospina Giraldo, J.F.; Carranza, R.G.; Ospina Giraldo, J.F.; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónA dynamic analysis is performed for heat transfer through a fin with constant cross-sectional area and with a specified fin tip temperature. The process starts with a dynamic energy balance around the fin. Laplace transforms and the Bromwich Integral are used to solve analytically the resulting partial differential equation. The final purely analytical solution is compared to the well known steady state solution. The two match exactly as time approaches infinity. Furthermore it is shown that the steady-state and dynamic characteristics of the fin are directly tied to the Biot number. Copyright © 2009 by ASME.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 Two-dimensional description of absorption in humans after dermal exposure to volatile organic compounds(TAYLOR & FRANCIS INC, 2017-06-03) Simon, Laurent; Ospina, Juan; Simon, Laurent; Ospina, Juan; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónA two-dimensional diffusion model was developed to predict the absorption of chemicals in humans following dermal contact. A firstorder evaporation rate equation was applied to the skin surface while a perfect-sink boundary condition was imposed at the stratum corneum/viable epidermis interface. Initially, there was a certain amount of the substance present within the stratum corneum at the end of the exposure period. Laplace transform techniques were implemented to solve the governing equations and to derive an expression for the time elapsed before reaching 90% of the final amount of chemical absorbed by the body. This index was 0.43, 2.67, 6.91, and 36.9 h for ethanol, diphenylamine, p-nitroaniline, and benzyl butyl-phthalate, respectively. Simulations show that surface evaporation is important for highly volatile compounds. A large fraction of the amount of poorly volatile compounds, available in the skin after exposure, was absorbed into the bloodstream. © Taylor & Francis Group, LLC.Ítem Two-dimensional transport analysis of transdermal drug absorption with a non-perfect sink boundary condition at the skin-capillary interface(ELSEVIER SCIENCE INC, 2013-07-01) Simon, Laurent; Ospina, Juan; Simon, Laurent; Ospina, Juan; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónA transient percutaneous drug absorption model was solved in two dimensions. Clearance of the topically-applied pharmaceutical occured at the skin-capillary boundary. Timolol penetration profiles in the dermal tissue were produced revealing concentration gradients in the directions normal and parallel to the skin surface. Ninety-eight percent of the steady-state flux was reached after 85. h or four time constants. The analytical solution procedure agreed with published results. As the clearance rate increased relative to diffusion, the delivery rate and amount of drug absorbed into the bloodstream increased while the time to reach the equilibrium flux decreased. Researchers can apply the closed-form expressions to simulate the process, estimate key parameters and design devices that meet specific performance requirements. © 2013 Elsevier Inc.