Examinando por Materia "Diffusion"

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    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 Computación
    An 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.
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    The development of a peak-time criterion for designing controlled-release devices
    (ELSEVIER SCIENCE BV, 2016-08-25) Simon, L.; Ospina, J.; Simon, L.; Ospina, J.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
    This work consists of estimating dynamic characteristics for topically-applied drugs when the magnitude of the flux increases to a maximum value, called peak flux, before declining to zero. This situation is typical of controlled- released systems with a finite donor or vehicle volume. Laplace transforms were applied to the governing equations and resulted in an expression for the flux in terms of the physical characteristics of the system. After approximating this function by a second-order model, three parameters of this reduced structure captured the essential features of the original process. Closed-form relationships were then developed for the peak flux and time-to-peak based on the empirical representation. Three case studies that involve mechanisms, such as diffusion, partitioning, dissolution and elimination, were selected to illustrate the procedure. The technique performed successfully as shown by the ability of the second-order flux to match the prediction of the original transport equations. A main advantage of the proposed method is that it does not require a solution of the original partial differential equations. Less accurate results were noted for longer lag times. (C) 2016 Elsevier B.V. All rights reserved.
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    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 Computación
    Solution 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.
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    A FIRST-ORDER TIME CONSTANT ESTIMATION FOR NONLINEAR DIFFUSION PROBLEMS
    (TAYLOR & FRANCIS INC, 2014-06-03) Simon, Laurent; Ospina, Juan; Simon, Laurent; Ospina, Juan; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
    A Laplace transform-based procedure was proposed to calculate the effective time constant for a class of nonlinear diffusion problems. The governing mathematical representation was first estimated with a linear model by omitting the nonlinear term. The solution to this problem was later introduced into the original equation, which was solved with Laplace transforms, resulting in a first-order approximation of the real system's behavior. A time constant was calculated using frequency-domain expressions. Two case studies were considered to illustrate the methodology. As the rate of heat supplied to a rod is raised, the speed at which the temperature reached an equilibrium value decreased. Increasing the maximum velocity in reaction-diffusion transport by a factor of three lowered the time constant by only 1.7%. The applications of this method range from biosensor dynamics to process control. © 2014 Copyright Taylor and Francis Group, LLC.
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    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 Computación
    A 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.
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    Using computer algebra for Yang-Baxterization applied to quantum computing
    (SPIE-INT SOC OPTICAL ENGINEERING, 2006-05-12) Velez, Mario; Ospina, Juan; Velez, Mario; Ospina, Juan; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
    Using Computer Algebra Software (Mathematica and Maple), the recently introduced topic of Yang-Baxterization applied to quantum computing, is explored from the mathematical and computational views. Some algorithms of computer algebra were elaborated with the aim to make the calculations to obtain some of results that were originally presented in the paper by Shang-Kauffman-Ge. Also certain new results about computational Yang-baxterization are presented. We obtain some Hamiltonians for hypothetical physical systems which can be realized within the domain of spin chains and certain diffusion process. We conclude that it is possible to have real physical systems on which implement, via Yang-baxterization, the standard quantum gates with topological protection. Finally some lines for future research are deligned.