Analysis of segregated boundary-domain integral equations for mixed variable-coefficient BVPs in exterior domains

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2011 Birkhäuser Boston.Some direct segregated systems of boundary–domain integral equations (LBDIEs) associated with the mixed boundary value problems for scalar PDEs with variable coefficients in exterior domains are formulated and analyzed in the paper. The LBDIE equivalence to the original boundary value problems and the invertibility of the corresponding boundary–domain integral operators are proved in weighted Sobolev spaces suitable for exterior domains. This extends the results obtained by the authors for interior domains in non-weighted Sobolev spaces.The work was supported by the grant EP/H020497/1 ”Mathematical analysis of localised boundary-domain integral equations for BVPs with variable coefficients” of the EPSRC, UK

Analyticity and criticality results for the eigenvalues of the biharmonic operator

We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov). We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove that balls are always critical domains under volume constraint.Comment: To appear on the proceedings of the conference "Geometric Properties for Parabolic and Elliptic PDE's - 4th Italian-Japanese Workshop" held in Palinuro (Italy), May 25-29, 201

Understanding bottom-up continuous hydrothermal synthesis of nanoparticles using empirical measurement and computational simulation

Continuous hydrothermal synthesis was highlighted in a recent review as an enabling technology for the production of nanoparticles. In recent years, it has been shown to be a suitable reaction medium for the synthesis of a wide range of nanomaterials. Many single and complex nanomaterials such as metals, metal oxides, doped oxides, carbonates, sulfides, hydroxides, phosphates, and metal organic frameworks can be formed using continuous hydrothermal synthesis techniques. This work presents a methodology to characterize continuous hydrothermal flow systems both experimentally and numerically, and to determine the scalability of a counter current supercritical water reactor for the large scale production (>1,000 T·year–1) of nanomaterials. Experiments were performed using a purpose-built continuous flow rig, featuring an injection loop on a metal salt feed line, which allowed the injection of a chromophoric tracer. At the system outlet, the tracer was detected using UV/Vis absorption, which could be used to measure the residence time distribution within the reactor volume. Computational fluid dynamics (CFD) calculations were also conducted using a modeled geometry to represent the experimental apparatus. The performance of the CFD model was tested against experimental data, verifying that the CFD model accurately predicted the nucleation and growth of the nanomaterials inside the reactor

Dirichlet and neumann exterior problems for the n-dimensional laplace operator an approach in weighted sobolev spaces

AbstractThis paper solves Dirichlet and Neumann problems for the Laplace operator in exterior domains of Rn. The behaviours at infinity of the data and the solution are determined by setting each problem in weighted Sobolev spaces, that extend the classical Wm,p spaces and are very well adapted to the theoretical and numerical solution of problems involving the Laplace operator

Author manuscript, published in "AlgoTel (2009)" Analyse des Corrélations entre Pannes dans les Systèmes de Stockage Pair-à-Pair †

Dans cet article, nous présentons et étudions des modèles analytiques de systèmes de stockage pair-à-pair fiables à long terme. Les pairs sont sujets à des pannes définitives (défaillance du disque, départ du pair) induisant la perte de toutes les données stockées par le pair. Ces pannes ont lieu en continu. Afin de pérenniser les données il est indispensable d’user de redondance et de maintenir celle-ci au moyen d’un processus permanent de reconstruction. Dans un premier temps nous considérons une approche classiquement utilisée dans la littérature, consistant à modéliser chaque bloc par une chaîne de Markov et à négliger les interdépendances entre blocs. Si celle-ci permet le calcul du comportement moyen du système (par exemple la demande moyenne en bande passante), elle est insuffisante pour en évaluer les fluctuations. Nos simulations démontrent que ces fluctuations sont très importantes même pour des grands systèmes comportant des milliers de pairs. Nous proposons alors un nouveau modèle stochastique prenant en compte l’interdépendance des pannes de blocs, et nous en donnons une approximation fluide. Ceci nous permet de caractériser le comportement du système (calcul de tous les moments) mais aussi de le simuler efficacement, car il est indépendant de la taille du système. La pertinence de notre modèle est validée en comparant les résultats obtenus par des simulations utilisant d’un côté notre modèle fluide et de l’autre un modèle à événements discrets reproduisant fidèlement le comportement du système

Good Edge-Labelling of Graphs

apport de recherch

Energy-Aware Routing in Software-Defined Network using Compression

Software-defined Network (SDN) is a new networking paradigm enabling innovation through network programmability. Over past few years, many applications have been built using SDN such as server load balancing, virtual-machine migration, traffic engineering and access control. In this paper, we focus on using SDN for energy-aware routing (EAR). Since traffic load has a small influence on the power consumption of routers, EAR allows putting unused links into sleep mode to save energy. SDN can collect traffic matrix and then computes routing solutions satisfying QoS while being minimal in energy consumption. However, prior works on EAR have assumed that the SDN forwarding table switch can hold an infinite number of rules. In practice, this assumption does not hold since such flow tables are implemented in Ternary Content Addressable Memory (TCAM) which is expensive and power hungry. We consider the use of wildcard rules to compress the forwarding tables. In this paper, we propose optimization methods to minimize energy consumption for a backbone network while respecting capacity constraints on links and rule space constraints on routers. In details, we present two exact formulations using Integer Linear Program (ILP) and introduce efficient heuristic algorithms. Based on simulations on realistic network topologies, we show that using this smart rule space allocation, it is possible to save almost as much power consumption as the classical EAR approach