Extension of Murray's law using a non-Newtonian model of blood flow.

BACKGROUND: So far, none of the existing methods on Murray's law deal with the non-Newtonian behavior of blood flow although the non-Newtonian approach for blood flow modelling looks more accurate. MODELING: In the present paper, Murray's law which is applicable to an arterial bifurcation, is generalized to a non-Newtonian blood flow model (power-law model). When the vessel size reaches the capillary limitation, blood can be modeled using a non-Newtonian constitutive equation. It is assumed two different constraints in addition to the pumping power: the volume constraint or the surface constraint (related to the internal surface of the vessel). For a seek of generality, the relationships are given for an arbitrary number of daughter vessels. It is shown that for a cost function including the volume constraint, classical Murray's law remains valid (i.e. SigmaR(c) = cste with c = 3 is verified and is independent of n, the dimensionless index in the viscosity equation; R being the radius of the vessel). On the contrary, for a cost function including the surface constraint, different values of c may be calculated depending on the value of n. RESULTS: We find that c varies for blood from 2.42 to 3 depending on the constraint and the fluid properties. For the Newtonian model, the surface constraint leads to c = 2.5. The cost function (based on the surface constraint) can be related to entropy generation, by dividing it by the temperature. CONCLUSION: It is demonstrated that the entropy generated in all the daughter vessels is greater than the entropy generated in the parent vessel. Furthermore, it is shown that the difference of entropy generation between the parent and daughter vessels is smaller for a non-Newtonian fluid than for a Newtonian fluid.

The late roman pottery imports in the East of Hispania Tarraconensis

Recent studies provided new data about late Roman imports (ARS, amphorae, lamps) in the coast of Hispania Tarraconensis. Concerning urban contexts (the ancient towns of Barcino, Tarraco and others) and rural settlements, the data allow us to identify the imports and the economic trends of the region from the 4th to the late 6th /early 7th centuries. We hope this paper to be an interpretative work of synthesis about the economic relationship between town and country in Catalonia and Northern Comunidad Valenciana in the Late Antiquity.

An experience beyond continuous assessment activities: virtual tour to the medieval medicinal plant garden of the Pedralbes monastery

[eng] The group of teaching innovation in the area of Botany (GIBAF), University of Barcelona (UB), is raised each year to design new accreditation activities under continuous evaluation framework. We present the experience carried out during the academic year 2008-09 in the course of Pharmaceutical Botany. The aim has been to involve students for a semester in the authorship of a tutored project immediately useful and of easy permanence, beyond its assessment proving usefulness. The Medicinal Plants Garden of the Monastery of Pedralbes has been used as a resource and a collaboration agreement has been signed between the UB faculty and the Institute of Culture of Barcelona. The students have developed the work using the Moodle platform CampusvirtualUB into five stages which included preparation of files by students that have been modified in some steps following the various feedbacks from teachers. At the beginning of the activity, students were provided with a complete schedule of activities, the schedule for its implementation, and a total of 18 forced-use library resources. Finally, through Google sites, a website has been implemented, allowing for a virtual tour of the garden, documenting by referenced literature 50 medicinal plants for their nomenclature, botanical description, distribution, uses historical, current and future) and toxicity. The result of the activity was presented at a public ceremony in the Monastery of Pedralbes and is available at: http://sites.google.com/site/jardimedievalpedralbes/ [spa] El grupo de innovación docente integrado por profesores del área de Botánica (GIBAF) de la Universidad de Barcelona (UB) se plantea cada curso el diseño de nuevas actividades acreditativas en el marco de la evaluación continuada. Se presenta la experiencia llevada a cabo durante el curso 2008-09 en la asignatura Botánica Farmacéutica. El objetivo ha sido implicar durante un semestre a los estudiantes en la autoría de un proyecto tutorizado de inmediata utilidad y clara perdurabilidad, más allá de su utilidad acreditativa. Como recurso se ha utilizado el Jardín de Plantas Medicinales del Monasterio de Pedralbes y se ha firmado un convenio de colaboración docente entre la UB y el Instituto de Cultura de Barcelona. Los estudiantes han realizado el trabajo utilizando la plataforma Moodle del Campus virtual de la UB en cinco etapas que han incluido la confección de unas fichas que se han ido modificando en función de las diversas retroacciones de los profesores. Al inicio de la actividad, se facilitó a los estudiantes el cronograma completo de la actividad, la pauta para su realización, así como un total de 18 recursos bibliográficos de uso obligado. Finalmente, a través de GoogleSites, se ha realizado una web que permite realizar un paseo virtual por el jardín, documentando de forma referenciada para las 50 plantas medicinales su nomenclatura, descripción botánica, distribución, usos (históricos, actuales y futuros) y toxicidad. El resultado de la actividad fue presentado en un acto público en el Monasterio de Pedralbes y puede consultarse en: http://sites.google.com/site/jardimedievalpedralbes/