Modeling of an aircraft fre extinguishing process with a porous medium equation.

The aim of this work is to provide a formulation of a non-linear difusion model in the form of a Porous Medium Equation (PME) with application to a fre extinguishing process in an aircraft engine nacelle. The work starts by describing some relevant publications currently related to fre suppression modelling methods with emphasis in the aerospace sector. The PME is then introduced highlighting some key relevant features (particularly the fnite speed of propagation) compared to the classical Heat Equation (HE). We will refer as u to the extinguisher or suppressor concentration in the media, which is postulated to be governed by a PME equation of the form: where Without losing generality and in virtue of the mass transfer application, we will consider that any solution is u ≥ 0. The set of equation and conditions expressed from (1) to (4) will be referred as problem P. From a mathematical perspective, the main areas of analysis are related to the existence of solutions, the obtaining of particular solutions as asymptotic approach and the application or particularization to a representative aircraft engine nacelle domain where a fre may happen.post-print3,45 M

1 V CMOS subthreshold log domain PDM

A new CMOS circuit strategy for very low-voltage Pulse-Duration Modulators (PDM) is proposed. Optimization of voltage supply scaling below the sum of threshold voltages is based on Instantaneous Log Companding processing through the MOSFET operating in weak inversion. A 1 V VLSI PDM circuit for very low-voltage audio applications such as Hearing Aids is presented, showing good agreement between simulated and experimental data.Comisión Interministerial de Ciencia y Tecnología TIC97-1159, TIC99-1084European Union 2306

Dret i polítiques ambientals en la Comunitat Valenciana

El autor analiza principalmente la legislación de la Comunidad Valenciana relativa a espacios naturales y zonas de protección, y vedas y reservas de caza y pesca.L’autor analitza principalment la legislació de la Comunitat Valenciana relativa a espais naturals i zones de protección, i vedes i reserves de caça i pescaThe author focuses mainly on analysing the Valencian Community legislation on natural spaces and protection zones, as well as hunting and fishing closed seasons and reserves

Travelling waves and instability in a Fisher-KPP problem with a non-linear advection and a high order diffusion.

pre-print594 K

La distribución competencial en materia de costas

Sobre la zona litoral hi ha una concurrència de competències que determina la necessitat d’integrar a la seva ordenació i gestió els interessos presents. Amb aquesta finalitat, la doctrina constitucional ha utilitzat els paràmetres de la cooperació i, si no n’hi havia, la determinació de la competència prevalent. En aquest context, l’ordenació del territori i del litoral per les comunitats autònomes, per les seves funcions de distribució d’usos i d’articulació de les visions sectorials i locals concurrents, es configura com l’instrument idoni per aconseguir-ne la gestió integral, que atengui tant la finalitats de la Llei de costes com els interessos autonòmics i municipals sobre aquesta. En aquest sentit, són diversos els títols estatals que condicionen aquesta competència autonòmica i que justifiquen el repartiment de funcions i les formes de col•laboració que preveu la Llei, entre els quals es poden considerar les facultats que deriven de la seva titularitat del domini, de la protecció del medi ambient litoral, la regulació de les condicions bàsiques per a l’exercici de drets i el compliment de deures constitucionals, i altres títols amb incidència sobre aquest espai.On the coastline, there is a conflict of powers which determines the need to coordinate existing interests in the planning and management of the coastal zone. For this reason, constitutional principles have employed cooperation parameters, and failing these, the prevailing competence has been determined. In this context, territorial and coastline planning by Spanish Autonomous Communities (AC) has been adopted as the ideal instrument to accomplish the coastline’s all-round management since AC decide on land use and coordinate sectorial and local competences. This instrument considers not only the objectives of the Coastal Law, but also the local and regional interests in it. In this sense, there are several state regulations that condition this regional competence and justify the assignment of tasks and the forms of collaboration as set out in the Law. Among them, it is necessary to consider the powers which are a result of the ownership of the domain, the protection of the coastal environment, the regulation of the basic conditions for the exercise of rights, the fulfilment of constitutional duties, and any other regulations which may affect this area.Sobre la zona litoral se da una concurrencia de competencias que determina la necesidad de integrar en su ordenación y gestión los intereses presentes. Para ello, la doctrina constitucional ha utilizado los parámetros de la cooperación y, en su defecto, la determinación de la competencia prevalente. En este contexto, la ordenación del territorio y del litoral por las Comunidades Autónomas, por sus funciones de distribución de usos y de articulación de las visiones sectoriales y locales concurrentes, se configura como el instrumento idóneo para lograr su gestión integral, que atienda tanto a la finalidades de la Ley de Costas como a los intereses autonómicos y municipales sobre la misma. En este sentido, son diversos los títulos estatales que condicionan esa competencia autonómica y que justifican el reparto de funciones y las formas de colaboración que prevé la Ley, entre los que cabe considerar las facultades que derivan de su titularidad del dominio, de la protección del medio ambiente litoral, la regulación de las condiciones básicas para el ejercicio de derechos y el cumplimiento de deberes constitucionales, y otros títulos con incidencia sobre este espacio

Travelling Waves Approach in a Parabolic Coupled System for Modelling the Behaviour of Substances in a Fuel Tank.

The aim of this work was to provide a formulation of a non-linear diffusion model with forced convection in the form of a reaction–absorption system. The model was studied with analytical and numerical approaches in the frame of the parabolic operators theory. In addition, the solutions are applied to a gas interaction phenomenon with the intention of producing an inerted ullage in an Airbus A320 aircraft centre fuel tank. We made use of the travelling wave (TW) solutions approach to study the existence of solutions, stability and the precise evolution of profiles. The application exercise sought to answer a key question for aerospace sciences which can be formulated as the time required to ensure an aircraft fuel tank is safe (inerted) to prevent explosion due to the presence of oxygen in the tank ullage.post-print721 K

Characterization of Traveling Waves Solutions to an Heterogeneous Diffusion Coupled System with Weak Advection.

The aim of this work is to characterize Traveling Waves (TW) solutions for a coupled system with KPP-Fisher nonlinearity and weak advection. The heterogeneous diffusion introduces certain instabilities in the TW heteroclinic connections that are explored. In addition, a weak advection reflects the existence of a critical combined TW speed for which solutions are purely monotone. This study follows purely analytical techniques together with numerical exercises used to validate or extent the contents of the analytical principles. The main concepts treated are related to positivity conditions, TW propagation speed and homotopy representations to characterize the TW asymptotic behaviour.post-print637 K

A mathematical analysis of an extended MHD Darcy–Forchheimer type fluid.

The presented analysis has the aim of introducing general properties of solutions to an Extended Darcy–Forchheimer flow. The Extended Darcy–Forchheimer set of equations are introduced based on mathematical principles. Firstly, the diffusion is formulated with a non-homogeneous operator, and is supported by the addition of a non-linear advection together with a non-uniform reaction term. The involved analysis is given in generalized Hilbert–Sobolev spaces to account for regularity, existence and uniqueness of solutions supported by the semi-group theory. Afterwards, oscillating patterns of Travelling wave solutions are analyzed inspired by a set of Lemmas focused on solutions instability. Based on this, the Geometric Perturbation Theory provides linearized flows for which the eigenvalues are provided in an homotopy representation, and hence, any exponential bundles of solutions by direct linear combination. In addition, a numerical exploration is developed to find exact Travelling waves profiles and to study zones where solutions are positive. It is shown that, in general, solutions are oscillating in the proximity of the null critical state. In addition, an inner region (inner as a contrast to an outer region where solutions oscillate) of positive solutions is shown to hold locally in time.post-print2749 K

Invasive-invaded system of non-Lipschitz porous medium equations with advection.

This work provides analytical results towards applications in the field of invasive-invaded systems modelled with non-linear diffusion and with advection. The results focus on showing regularity, existence and uniqueness of weak solutions using the condition of a non-linear slightly positive parabolic operator and the reaction-absorption monotone properties. The coupling in the reaction-absorption terms, that characterizes the species interaction, impedes the formulation of a global comparison principle that is shown to exist locally. Additionally, the present work provides analytical solutions obtained as selfsimilar minimal and maximal profiles. A propagating diffusive front is shown to exist until the invaded specie notes the existence of the invasive. When the desertion of the invaded starts, the diffusive front vanishes globally and the non-linear diffusion concentrates only on the propagating tail which exhibits finite speed. Finally, the invaded specie is shown to exhibit an exponential decay along a characteristic curve. Such exponential decay is not trivial in the non-linear diffusion case and confirms that the invasive continues to feed on the invaded during the desertion.post-print379 K

Existence, uniqueness and travelling waves to model an invasive specie interaction with heterogeneous reaction and non-linear diffusion.

It is the objective to provide a mathematical treatment of a model to predict the behaviour of an invasive specie proliferating in a domain, but with a certain hostile zone. The behaviour of the invasive is modelled in the frame of a non-linear diffusion (of Porous Medium type) equation with non-Lipschitz and heterogeneous reaction. First of all, the paper examines the existence and uniqueness of solutions together with a comparison principle. Once the regularity principles are shown, the solutions are studied within the Travelling Waves (TW) domain together with stability analysis in the frame of the Geometric Perturbation Theory (GPT). As a remarkable finding, the obtained TW profile follows a potential law in the stable connection that converges to the stationary solution. Such potential law suggests that the pressure induced by the invasive over the hostile area increases over time. Nonetheless, the finite speed, induced by the non-linear diffusion, slows down a possible violent invasion.post-print287 K