One-Phase Stefan-Like Problems with Latent Heat Depending on the Position and Velocity of the Free Boundary and with Neumann or Robin Boundary Conditions at the Fixed Face

A one-phase Stefan-type problem for a semi-infinite material which has as its main feature a variable latent heat that depends on the power of the position and the velocity of the moving boundary is studied. Exact solutions of similarity type are obtained for the cases when Neumann or Robin boundary conditions are imposed at the fixed face. Required relationships between data are presented in order that these problems become equivalent to the problem where a Dirichlet condition at the fixed face is considered. Moreover, in the case where a Robin condition is prescribed, the limit behaviour is studied when the heat transfer coefficient at the fixed face goes to infinity.Fil: Bollati, Julieta. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaFil: Tarzia, Domingo Alberto. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentin

A new mathematical formulation for a phase change problem with a memory flux

A mathematical formulation for a one-phase change problem in a form of Stefan problem with a memory flux is obtained. The hypothesis that the integral of weighted backward fluxes is proportional to the gradient of the temperature is considered. The model that arises involves fractional derivatives with respect to time both in the sense of Caputo and of Riemann–Liouville. An integral relation for the free boundary, which is equivalent to the “fractional Stefan condition”, is also obtained.Fil: Roscani, Sabrina Dina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; ArgentinaFil: Bollati, Julieta. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; ArgentinaFil: Tarzia, Domingo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentin

Heat waves and human well-being in Madrid (Spain)

Heat waves pose additional risks to urban spaces because of the additional heat provided by urban heat islands (UHIs) as well as poorer air quality. Our study focuses on the analysis of UHIs, human thermal comfort, and air quality for the city of Madrid, Spain during heat waves. Heat wave periods are defined using the long-term records from the urban station Madrid-Retiro. Two types of UHI were studied: the canopy layer UHI (CLUHI) was evaluated using air temperature time-series from five meteorological stations; the surface UHI (SUHI) was derived from land surface temperature (LST) images from MODIS (Moderate Resolution Imaging Spectroradiometer) products. To assess human thermal comfort, the Physiological Equivalent Temperature (PET) index was applied. Air quality was analyzed from the records of two air quality networks. More frequent and longer heat waves have been observed since 1980; the nocturnal CLUHI and both the diurnal and nocturnal SUHI experience an intensification, which have led to an increasing number of tropical nights. Conversely, thermal stress is extreme by day in the city due to the lack of cooling by winds. Finally, air quality during heat waves deteriorates because of the higher than normal amount of particles arriving from Northern AfricaThis research was funded by the research project number CGL2016-80154-R “Análisis y modelización de eventos climáticos extremos en Madrid: olas de calor e inversiones térmicas” funded by Convocatoria 2016 de Proyectos de I+D+I, correspondientes al programa estatal de Investigación, Desarrollo e Innovación Orientada a los Retos de la Sociedad, from the Spanish Ministry of Educatio

La PNL como base en el desarrollo del speaking en lengua extranjera

Durante estos últimos años la Programación Neurolingüística (PNL) ha ido apareciendo en numerosas fuentes de información como libros, internet… Gracias a ella, podemos conocer el funcionamiento (programación) de nuestro cerebro (neuro) y la expresión de nuestros pensamientos (lingüística). El propósito de este trabajo es mostrar como la PNL gestiona los diferentes recursos que tiene para utilizarlos como herramienta de mejora en el proceso de enseñanzaaprendizaje de una lengua extranjera. La PNL es un recurso que nos permite y facilita la mejora de la competencia comunicativa en aquellos alumnos que presentan problemas a la hora de comunicarse en situaciones que tienen lugar en el aula.Grado en Educación Primari

Convergencia de una familia de problemas discretos de control óptimo elíptico frontera respecto de un parámetro

Se considera un dominio acotado D de Rn con una frontera regular compuesta de dos porciones de frontera F1 y F2. En Gariboldi – Tarzia, Adv. Diff. Eq. Control Processes, 1 (2008), 113-132, se considera la convergencia de una familia de problemas de controles óptimos frontera de tipo Neumann gobernados por ecuaciones variacionales elípticas cuando el parámetro alpha de la familia (el coeficiente de transferencia de calor sobre la porción de frontera F1) tiende a infinito. Se demuestra la convergencia del control óptimo, del estado del sistema y del estado adjunto de la familia de problemas de controles óptimos fronteras de tipo Neumann a los correspondientes de un problema de control óptimo frontera de tipo Neumann también gobernado por una ecuación variacional elíptica con condiciones de contorno de tipo Dirichlet sobre F1. Se consideran, tanto para la familia de problemas de controles óptimos frontera de tipo Neumann como para el problema de control óptimo frontera límite, las aproximaciones numéricas por el método de los elementos finitos con triángulos de Lagrange de tipo 1. Se discretizan las ecuaciones variacionales elípticas que definen el estado del sistema y de su estado adjunto y además las funciones de costo respectivas. El objetivo del presente trabajo es el de estudiar la convergencia de la familia de problemas de controles óptimos fronteras de tipo Neumann discretos cuando el parámetro alpha tiende a infinito. Se demuestra la convergencia del control óptimo discreto, del estado del sistema discreto y del estado adjunto discreto de la familia a los correspondientes del problema de control óptimo frontera de tipo Neumann límite discreto.Fil: Tarzia, Domingo Alberto. Universidad Austral. Facultad de Ciencias Empresariales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Explicit solutions for the Solomon-Wilson-Alexiades's mushy zone model with convective or heat flux boundary conditions

We complete the Solomon-Wilson-Alexiades's mushy zone model (Letters Heat Mass Transfer, 9 (1982), 319-324) for the one-phase Lam\'e-Clapeyron-Stefan problem. We obtain explicit solutions when a convective or heat flux boundary condition is imposed on the fixed face for a semi-infinite material. We also obtain the necessary and sufficient condition on data in order to get these explicit solutions. Moreover, when these conditions are satisfied the two problems are equivalents to the same problem with a temperature boundary condition on the fixed face and therefore an inequality for the coefficient which characterized one of the two free interfaces is also obtained.Comment: 13 page

Determination of one unknown thermal coefficient through the one-phase fractional Lam\'e-Clapeyron-Stefan problem

We obtain explicit expressions for one unknown thermal coefficient (among the conductivity, mass density, specific heat and latent heat of fusion) of a semi-infinite material through the one-phase fractional Lam\'e-Clapeyron-Stefan problem with an over-specified boundary condition on the fixed face $x=0$. The partial differential equation and one of the conditions on the free boundary include a time Caputo's fractional derivative of order $\alpha \in (0,1)$. Moreover, we obtain the necessary and sufficient conditions on data in order to have a unique solution by using recent results obtained for the fractional diffusion equation exploiting the properties of the Wright and Mainardi functions, given in Roscani - Santillan Marcus, Fract. Calc. Appl. Anal., 16 (2013), 802-815, Roscani-Tarzia, Adv. Math. Sci. Appl., 24 (2014), 237-249, and Voller, Int. J. Heat Mass Transfer, 74 (2014), 269-277. This work generalizes the method developed for the determination of unknown thermal coefficients for the classical Lam\'e-Clapeyron-Stefan problem given in Tarzia, Adv. Appl. Math., 3 (1982), 74-82, which are recovered by taking the limit when the order $\alpha\nearrow 1$.Comment: 15 pages, 2 Table

An analytical model for Loc/ID mappings caches

Concerns regarding the scalability of the interdomain routing have encouraged researchers to start elaborating a more robust Internet architecture. While consensus on the exact form of the solution is yet to be found, the need for a semantic decoupling of a node's location and identity is generally accepted as a promising way forward. However, this typically requires the use of caches that store temporal bindings between the two namespaces, to avoid hampering router packet forwarding speeds. In this article, we propose a methodology for an analytical analysis of cache performance that relies on the working-set theory. We first identify the conditions that network traffic must comply with for the theory to be applicable and then develop a model that predicts average cache miss rates relying on easily measurable traffic parameters. We validate the result by emulation, using real packet traces collected at the egress points of a campus and an academic network. To prove its versatility, we extend the model to consider cache polluting user traffic and observe that simple, low intensity attacks drastically reduce performance, whereby manufacturers should either overprovision router memory or implement more complex cache eviction policies.Peer ReviewedPostprint (author's final draft