A numerical comparison between degenerate parabolic and quasilinear hyperbolic models of cell movements under chemotaxis

We consider two models which were both designed to describe the movement of eukaryotic cells responding to chemical signals. Besides a common standard parabolic equation for the diffusion of a chemoattractant, like chemokines or growth factors, the two models differ for the equations describing the movement of cells. The first model is based on a quasilinear hyperbolic system with damping, the other one on a degenerate parabolic equation. The two models have the same stationary solutions, which may contain some regions with vacuum. We first explain in details how to discretize the quasilinear hyperbolic system through an upwinding technique, which uses an adapted reconstruction, which is able to deal with the transitions to vacuum. Then we concentrate on the analysis of asymptotic preserving properties of the scheme towards a discretization of the parabolic equation, obtained in the large time and large damping limit, in order to present a numerical comparison between the asymptotic behavior of these two models. Finally we perform an accurate numerical comparison of the two models in the time asymptotic regime, which shows that the respective solutions have a quite different behavior for large times.Comment: One sentence modified at the end of Section 4, p. 1

Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy

We study the asymptotic time behavior of global smooth solutions to general entropy dissipative hyperbolic systems of balance law in m space dimensions, under the Shizuta-Kawashima condition. We show that these solutions approach constant equilibrium state in the Lp-norm at a rate O(t^(-m/2(1-1/p))), as t tends to $\infty$, for p in [min (m,2),+ \infty]. Moreover, we can show that we can approximate, with a faster order of convergence, theconservative part of the solution in terms of the linearized hyperbolic operator for m >= 2, and by a parabolic equation in the spirit of Chapman-Enskog expansion. The main tool is given by a detailed analysis of the Green function for the linearized problem

A hyperbolic model of chemotaxis on a network: a numerical study

In this paper we deal with a semilinear hyperbolic chemotaxis model in one space dimension evolving on a network, with suitable transmission conditions at nodes. This framework is motivated by tissue-engineering scaffolds used for improving wound healing. We introduce a numerical scheme, which guarantees global mass densities conservation. Moreover our scheme is able to yield a correct approximation of the effects of the source term at equilibrium. Several numerical tests are presented to show the behavior of solutions and to discuss the stability and the accuracy of our approximation

Review of extreme wind speeds in three sites of southern Argentina

La valoración de la acción del viento sobre un edificio en la etapa de diseño requiere conocer la magnitud de las máximas velocidades de viento a las que estará expuesta la estructura durante su vida útil. En la práctica profesional, esta información se extrae del llamado mapa de vientos, que es parte de los reglamentos nacionales de acción del viento sobre estructuras civiles. En Argentina, el reglamento pertinente es el CIRSOC 102. Si bien fue editado en 2005, el mapa de vientos que trae este reglamento se basa principalmente en información meteorológica del período entre 1970 y 1990. En este trabajo se discute la metodología usada para construir este mapa, a la luz de procedimientos más actualizados desarrollados en los últimos 20 años. Se ilustra la discusión aplicando algunos de estos nuevos procedimientos a registros de tres estaciones meteorológicas de zonas donde el clima está dominado por depresiones y se muestra la conveniencia de actualizar el mapa.The assessment of wind loads on a building during design requires knowing the maximum wind speed to which the structure will be exposed during its lifetime. Practitioners obtain this information from the so-called wind map, which is part of the national codes of practice of wind actions on civil structures. In Argentina, the relevant code is the CIRSOC 102. Although it was edited in 2005, the wind map of this code is based on meteorological data collected between 1970 and 1990. In this paper, the methodology used to build this map is discussed in view of more up-to-date procedures developed in the last 20 years. The discussion is illustrated by applying some of these newer procedures to records of three meteorological stations located in areas where the climate is dominated by depressions, and the convenience of updating the map is shown.Fil: Natalini, Bruno. Universidad Nacional del Nordeste; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Natalini, Mario Bruno. Universidad Nacional del Nordeste; Argentin

Extreme wind speeds in north-eastern Argentina

The extreme wind map of the Argentinean code of practice CIRSOC 102 was updated in 1997 from records of the period 1967-1990. The information contained in this map is represented by the Basic Wind Speed, V. The contribution of the uncertainty of V to the whole uncertainty of the design wind load, of either a building or structure, is dominant with regard to the other variables that make up the wind load. Some authors asses this contribution to be above 70%, which underlines the importance of having good quality estimations of V. For this reason the extreme wind maps are updated periodically.In this work, results of V calculated from updated records of seven meteorological stations in north-eastern Argentina (NEA region) are presented. The values turn out to be noticeably lower than those of the CIRSOC 102; a reduction that is magnified when evaluated in terms of resulting wind loads. The records have been previously depurated after a combined assessment of both the quality of the instrumentation and the completeness of every yearly record. 95% confidence limits are presented, being the first time confidence limits are published for Argentina. Further values of V obtained after consolidating data of some stations in superstations are presented. Reductions of the confidence limits ranging 30% to 50% were observed.El mapa de vientos extremos del reglamento CIRSOC 102 fue actualizado en 1997 a partir de registros que comprenden el período 1967-1990. La información contenida en este mapa está representada por la Velocidad Básica de Viento, V. La contribución de la incertidumbre de V a la incertidumbre total de la carga de viento de diseño de un edificio o estructura, es dominante respecto a todas las otras variables que conforman la carga de viento. Algunos autores colocan esta contribución por arriba del 70%, lo que da una idea de la importancia de contar con estimaciones de V de buena calidad. Por esta razón, los mapas de vientos extremos son actualizados periódicamente. En este trabajo se presentan resultados de V calculados a partir de datos actualizados de siete estaciones meteorológicas en el nordeste de argentina (región NEA). Los valores son sensiblemente más bajos que los del CIRSOC 102; una diferencia que se magnifica cuando se la evalúa a nivel de cargas de viento resultante. Los registros fueron depurados previamente de registros anuales incompletos o medidos con instrumentación inadecuada. Se presentan por primera vez para Argentina los intervalos de confianza del 95%. Se presentaron también valores de V consolidando algunas estaciones en superestaciones, observándose reducciones del intervalo de confianza de 30 a 50%.Fil: Natalini, Bruno. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Investigación Para El Desarrollo Territorial y del Habitat Humano. Universidad Nacional del Nordeste. Facultad de Arquitectura y Urbanismo. Instituto de Investigación Para El Desarrollo Territorial y del Habitat Humano.; Argentina. Universidad Nacional del Nordeste. Facultad de Ingeniería; ArgentinaFil: Natalini, Mario Bruno. Universidad Nacional del Nordeste. Facultad de Ingeniería; Argentin