A time discretization scheme for a nonlocal degenerate problem modelling resistance spot welding

This is the author's PDF version of an article published in Mathematical Modelling of Natural Phenomena© 2015. The definitive version is available at http://www.mmnp-journal.org/articles/mmnp/abs/2015/06/mmnp2015106p90/mmnp2015106p90.htmlIn the current work we construct a nonlocal mathematical model describing the phase transition occurs during the resistance spot welding process in the industry of metallurgy. We then consider a time discretization scheme for solving the resulting nonlocal moving boundary problem. The scheme consists of solving at each time step a linear elliptic partial differential equation and then making a correction to account for the nonlinearity. The stability and error estimates of the developed scheme are investigated. Finally some numerical results are presented confirming the efficiency of the developed numerical algorithm

Functional behaviour of TiO2films doped with noble metals

To evaluate the effects of different concentrations of noble metal in a TiO2 matrix, different films of both Ag:TiO2 and Au:TiO2 systems were prepared. Mechanical and tribological characterization was carried out to evaluate the coatings response as a function of the noble metals composition and (micro)structure of the films. The overall set of results indicates that the amorphous films reveal better results than the crystalline ones. For the amorphous samples, the reduced Young’s modulus and the adhesion critical loads followed similar tendencies in both sets of films. Wear rates were similar for all samples except for the one with the highest silver content. To improve brittleness of TiO2 films, the results seem to indicate that a slight metal doping is preferred, and Au showed to be a better choice than Ag. In fact, the sample with the lowest Au content revealed a better mechanical behaviour than the pure TiO2 film.This research was sponsored by FEDER funds through the COMPETE program (Programa Operacional Factores de Competitividade) and by FCT (Fundação para a Ciência e a Tecnologia), under the projects PEST-C/FIS/UI607/2013 and PEst-C/EME/UI0285/2013. The authors also acknowledge the financial support by the project Nano4color – Design and develop a new generation of color PVD coatings for decorative applications (FP7 EC R4SME Project No. 315286)

Thin films composed of Ag nanoclusters dispersed in TiO2: Influence of composition and thermal annealing on the microstructure and physical responses

Noble metal powders containing gold and silver have been used for many centuries, providing different colours in the windows of the medieval cathedrals and in ancient Roman glasses. Nowadays, the interest in nanocomposite materials containing noble nanoparticles embedded in dielectric matrices is related with their potential use for a wide range of advanced technological applications. They have been proposed for environmental and biological sensing, tailoring colour of functional coatings, or for surface enhanced Raman spectroscopy. Most of these applications rely on the so-called localised surface plasmon resonance absorption, which is governed by the type of the noble metal nanoparticles, their distribution, size and shape and as well as of the dielectric characteristics of the host matrix. The aim of this work is to study the influence of the composition and thermal annealing on the morphological and structural changes of thin films composed of Ag metal clusters embedded in a dielectric TiO2 matrix. Since changes in size, shape and distribution of the clusters are fundamental parameters for tailoring the properties of plasmonic materials, a set of films with different Ag concentrations was prepared. The optical properties and the thermal behaviour of the films were correlated with the structural and morphological changes promoted by annealing. The films were deposited by DC magnetron sputtering and in order to promote the clustering of the Ag nanoparticles the as-deposited samples were subjected to an in-air annealing protocol. It was demonstrated that the clustering of metallic Ag affects the optical response spectrum and the thermal behaviour of the films.This research was sponsored by FEDER funds through the COMPETE program (Programa Operacional Factores de Competitividade) and by FCT (Fundação para a Ciência e a Tecnologia), under the projects PEST-C/FIS/UI607/2013 and PEst-C/EME/UI0285/2013. The authors also acknowledge the financial support by the project Nano4color – Design and develop a new generation of color PVD coatings for decorative applications (FP7 EC R4SME Project No. 315286). J. Borges also acknowledges the support by the European social fund within the framework of realising the project “Support of inter-sectoral mobility and quality enhancement of research teams at Czech Technical University in Prague”, CZ.1.07/2.3.00/30.0034. C. Lopes acknowledges FCT for the PhD grant SFRH/BD/103373/2014. F.M. Couto acknowledges CAPES – Foundation, Ministry of Education of Brazil, Brasília – DF 70040-20, Brazil, funding by stage sandwich doctorate, through PDSE – Doctoral Program Sandwich

Continuous dependence on data for quasiautonomous nonlinear boundary value problems

We devote this paper to quasiautonomous second-order differential equations in Hilbert spaces governed by maximal monotone operators. Some bilocal boundary conditions are associated. We discuss the continuous dependence of the solution both on the operator and on the boundary values. One uses the methods of nonlinear analysis. Some applications to internal approximate schemes are given

Finite difference schemes with monotone operators

Several existence theorems are given for some second-order difference equations associated with maximal monotone operators in Hilbert spaces. Boundary conditions of monotone type are attached. The main tool used here is the theory of maximal monotone operators

An Optimal Control Problem for a Predator-Prey Reaction-Diffusion System

An optimal control problem is studied for a predator-prey system of PDE, with a logistic growth rate of the prey and a general functional response of the predator. The control function has two components. The purpose is to maximize a mean density of the two species in their habitat. The existence of the optimal solution is analyzed and some necessary optimality conditions are established. The form of the optimal control is found in some particular cases

Necessary Optimality Conditions for a Lotka-Volterra Three Species System

An optimal control problem is studied for a Lotka-Volterra system of three differential equations. It models an ecosystem of three species which coexist. The species are supposed to be separated from each others. Mathematically, this is modeled with the aid of two control variables. Some necessary conditions of optimality are found in order to maximize the total number of individuals at the end of a given time interval

Existence of Reaction-Diffusion Waves with Nonlinear Boundary Conditions

The paper is devoted to a reaction-diffusion equation in an infinite two-dimensional strip with nonlinear boundary conditions. The existence of travelling waves is proved in the bistable case by the Leray-Schauder method. It is based on a topological degree for elliptic problems in unbounded domains and on a priori estimates of solutions

Preface to the Issue Nonlocal Reaction-Diffusion Equations

1. Nonlocal reaction-diffusion equations in population dynamics Nonlocal reaction-diffusion equations are intensively studied during the last decade in relation with prob-lems in population dynamics and other applications. In comparison with traditional reaction-diffusion equations they possess new mathematical properties and richer nonlinear dynamics. Many studies are devoted to the nonlocal reaction-diffusion equation ∂u ∂