Examinando por Materia "Partial differential equations"
Mostrando 1 - 7 de 7
Resultados por página
Opciones de ordenación
Ítem Analytical solution for transient flow of a generalized bingham fluid with memory in a movable tube using computer algebra(SPRINGER, 2007-01-01) Ospina, Juan; Velez, Mario; Ospina, Juan; Velez, Mario; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónA rheological linear model for a certain generalized Bingham fluid with rheological memory, which flows in a movable tube is proposed and analytically solved. The model is a system of two linear and coupled partial differential equations with integral memory. We apply the Laplace transform method making the inverse transform by means of the Bromwich integral and the theorem of residues and the analytical solution are obtained using computer algebra. We deduce the explicit forms of the velocity and stress profiles for the generalized Bingham fluid in terms of Bessel and Struve functions. Various limit cases are obtained and the standard Hagen-Poiseuille and Buckingham-Reiner equations are recovered from more general equations. This works shows the powerful of Maple to solve complex rheological problems in an analytical form as it is presented here by the first time. © Springer-Verlag Berlin Heidelberg 2007.Ítem Biomedical computer vision using computer algebra: Analysis of a case of rhinocerebral mucormycosis in a diabetic boy(Springer Science + Business Media, 2010-01-01) Vélez, M.; Ospina, J.; Vélez, M.; Ospina, J.; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónComputer algebra is applied to biomedical computer vision. Specifically certain biomedical images resulting from a case of rhinocerebral mucormysocis in a diabetic boy are analyzed using techniques in computational geometry and in algebraic-geometric topology. We apply convolution and deblurring via diffusion equation from the side of computational geometry and knot theory, graph theory and singular homology form the side of algebraic-geometric topology. Our strategy consists in to represent the biomedical images using algebraic structures in such way that the peculiarities of the images are represented using algebraic complexities. With our strategy we obtain an automatic procedure for the analysis and the diagnostic based on biomedical images. © 2010 Springer-Verlag Berlin Heidelberg.Ítem Construcción de soluciones numéricas de problemas de difusión fuertemente acoplados singulares(Universidad EAFIT, 2007) Guerra Mazo, Miryam Lucía; Guerra Tamayo, Rubén Darío; Sánchez Cano, José Albeiro86 p.Ítem Problemas de frontera para la Ecuación de Helmholtz(Universidad EAFIT, 2007) Torres García, Luis Eduardo; Triviño Macías, Jorge Enrique; Villegas Gutiérrez, Jairo Albertov, 73 p.Ítem Solución viscosa a un sistema de elasticidad generalizado(Universidad EAFIT, 2011) Gómez Plata, Adrián Ricardo; Cerón Gómez, MillerÍtem Solution of the Navier Stokes model in 1D using finite differences schemes(Universidad EAFIT, 2021-05-26) Gutiérrez, Ana Sofía; Salazar Arango, Alejandro; Universidad EAFIT, School of Sciences, Department of Mathematical SciencesThe Navier Stokes equations are ones that describe the behavior of fluids. The computational solution of these allows for a way of understanding and predicting them while being cost-effective. The fundamental equations arise from the principles of conservation of energy, momentum, and mass described in New ton’s second law, the first law of thermodynamics, and the continuity equation respectively. The obtained system of equations can be used for different fluid simulations under different circumstances such as Newtonian, compressible, or isothermal flow fluids. The objectives of this project are to describe the problem and the origin of the equations; to approximate the solution to the Navier Stokes system in one dimension through a finite differences discretization scheme used in numerical analysis to solve PDE; to mathematically analyse the selected approach in terms of error and convergence; to present examples using different boundaries conditions.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.