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Register a new userSoluciones Discretas para Sistemas Matriciales en Derivadas Parciales Hiperbolicos y Singulares
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In this paper we study the construction of a discrete solution for a hyperbolic system of partial differentials of the strongly coupled type. In its construction, the discrete separation of matricial variable method was followed. Two separate equations in differences were obtained: a singular matricial and the other one a Sturm Liouville vectorial problem, which by the superposition principle yield a stable discrete solution.
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This paper presents a finite-volume method, together with fully adaptive multi-resolution scheme to obtain spatial adaptation, and a Runge-Kutta-Fehlberg scheme with a local time-varying step to obtain temporal adaptation, to solve numerically the known bidominio equations that model the electrical activity of the tissue in the myocardium. Two simple models are considered for membrane flows and ionic currents. First we define an approximate solution and we verify its convergence to the corresponding weak solution of the continuum problem, obtaining in this way an alternative demonstration that the continuum problem is well-posed. Next we introduce the multiresolution technique and derive an optimal noise reduction threshold. The efficiency and precision of our method is seen in the reduction of machine time, memory usage, and errors in comparison to other methods. ----- En este trabajo se presenta un metodo de volumenes finitos enriquecido con un esquema de multiresolucion completamente adaptativo para obtener adaptatividad espacial, y un esquema Runge-Kutta-Fehlberg con paso temporal de variacion local para obtener adaptatividad temporal, para resolver numericamente las conocidas ecuaciones bidominio que modelan la actividad electrica del tejido en el miocardio. Se consideran dos modelos simples para las corrientes de membrana y corrientes ionicas. En primer lugar definimos una solucion aproximada y nos referimos a su convergencia a la correspondiente solucion debil del problema continuo, obteniendo de este modo una demostracion alternativa de que el problema continuo es bien puesto. Luego de introducir la tecnica de multiresolucion, se deriva un umbral optimo para descartar la informacion no significativa, y tanto la eficiencia como la precision de nuestro metodo es vista en terminos de la aceleracion de tiempo de maquina, compresion de memoria computacional y errores en diferentes normas.
Institutional repositories are deposits of different types of digital files for access, disseminate and preserve them. This paper aims to explain the importance of repositories in the academic field of engineering as a way to democratize knowledge by teachers, researchers and students to contribute to social and human development. These repositories, usually framed in the Open Access Initiative, allow to ensure access free and open (unrestricted legal and economic) to different sectors of society and, thus, can make use of the services they offer. Finally, that repositories are evolving in the academic and scientific, and different disciplines of engineering should be prepared to provide a range of services through these systems to society of today and tomorrow.
Being aware of the motivation problems observed in many scientific oriented careers, we present two experiences to expose to college students to environments, methodologies and discovery techniques addressing contemporary problems. This experiences are developed in two complementary contexts: an Introductory Physics course, where we motivated to physics students to participate in research activities, and a multidisciplinary hotbed of research oriented to advanced undergraduate students of Science and Engineering (that even produced three poster presentations in international conferences). Although these are preliminary results and require additional editions to get statistical significance, we consider they are encouraging results. On both contexts we observe an increase in the students motivation to orient their careers with emphasizing on research. In this work, besides the contextualization support for these experiences, we describe six specific activities to link our students to research areas, which we believe can be replicated on similar environments in other educational institutions.
We analyze the asymptotic behavior of a partial differential equation (PDE) model for hematopoiesis. This PDE model is derived from the original agent-based model formulated by (Roeder et al., Nat. Med., 2006), and it describes the progression of blood cell development from the stem cell to the terminally differentiated state. To conduct our analysis, we start with the PDE model of (Kim et al, JTB, 2007), which coincides very well with the simulation results obtained by Roeder et al. We simplify the PDE model to make it amenable to analysis and justify our approximations using numerical simulations. An analysis of the simplified PDE model proves to exhibit very similar properties to those of the original agent-based model, even if for slightly different parameters. Hence, the simplified model is of value in understanding the dynamics of hematopoiesis and of chronic myelogenous leukemia, and it presents the advantage of having fewer parameters, which makes comparison with both experimental data and alternative models much easier.
We discuss a novel strategy for computing the eigenvalues and eigenfunctions of the relativistic Dirac operator with a radially symmetric potential. The virtues of this strategy lie on the fact that it avoids completely the phenomenon of spectral pollution and it always provides two-side estimates for the eigenvalues with explicit error bounds on both eigenvalues and eigenfunctions. We also discuss convergence rates of the method as well as illustrate our results with various numerical experiments.
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