Global Attractor and Omega-Limit Sets Structure for a Phase-Field Model of Thermal Alloys

In this paper, the existence of weak solutions is established for a phase-field model of thermal alloys supplemented with Dirichlet boundary conditions. After that, the existence of global attractors for the associated multi-valued dynamical systems is proved, and the relationship among these sets is established. Finally, we provide a more detailed description of the asymptotic behaviour of solutions via the omega-limit sets. Namely, we obtain a characterization–through the natural stationary system associated to the model–of the elements belonging to the omega-limit sets under suitable assumptions

Gradient-like nonlinear semigroups with infinitely many equilibria and applications to cascade systems

We consider an autonomous dynamical system coming from a coupled system in cascade where the uncoupled part of the system satisfies that the solutions comes from −∞ and goes to ∞ to equilibrium points, and where the coupled part generates asymptotically a gradient-like nonlinear semigroup. Then, the complete model is proved to be also gradient-like. The interest of this extension comes, for instance, in models where a continuum of equilibrium points holds, and for example a Lojasiewicz-Simon condition is satisfied. Indeed, we illustrate the usefulness of the theory with several examples.Fundação de Amparo à Pesquisa do Estado de São PauloConselho Nacional de Desenvolvimento Científico e TecnológicoCoordenação de aperfeiçoamento de pessoal de nivel superiorMinisterio de Ciencia e InnovaciónJunta de AndalucíaMinisterio de Educació

Asymptotic Behaviour of a Phase-Field Model with Three Coupled Equations Without Uniqueness

AbstractWe prove the existence of weak solutions for a phase-field model with three coupled equations with unknown uniqueness, and state several dynamical systems depending on the regularity of the initial data. Then, the existence of families of global attractors (level-set depending) for the corresponding multi-valued semiflows is established, applying an energy method. Finally, using the regularizing effect of the problem, we prove that these attractors are in fact the same

Al final del camí

Tractament de connexió i renaturalització del final del corredor verd i activació de la zona, mitjançant la recuperació d'una antiga argilera convertida en cementiri, i la instal·lació del nou complex fúnebre municipal a les naus industrials en desús

Attractors for a Double Time-Delayed 2D-Navier-Stokes Model

In this paper, a double time-delayed 2D-Navier-Stokes model is considered. It includes delays in the convective and the forcing terms. Existence and uniqueness results and suitable dynamical systems are established. We also analyze the existence of pullback attractors for the model in several phase-spaces and the relationship among them

Summary of workshop large outdoor fires and the built environment

Large outdoorfires present a risk to the built environment. Wildfires that spread into communities, referred to as Wildland-Urban Interface (WUI)fires, havedestroyed communities throughout the world, and are an emerging problem infire safety science. Other examples are large urbanfires including those that haveoccurred after earthquakes. Research into large outdoorfires, and how to potentially mitigate the loss of structures in suchfires, lags other areas offire safety scienceresearch. At the same time, common characteristics betweenfire spread in WUIfires and urbanfires have not been fully exploited. In this paper, an overview of thelarge outdoorfire risk to the built environment from each region is presented. Critical research needs for this problem in the context offire safety scienceare provided.The present paper seeks to develop the foundation for an international research needs roadmap to reduce the risk of large outdoorfires to the built environment.Peer ReviewedPreprin

Evolutionary system for prediction and optimization of hardware architecture performance

The design of computer architectures is a very complex problem. The multiple parameters make the number of possible combinations extremely high. Many researchers have used simulation, although it is a slow solution since evaluating a single point of the search space can take hours. In this work we propose using evolutionary multilayer perceptron (MLP) to compute the performance of an architecture parameter settings. Instead of exploring the search space, simulating many configurations, our method randomly selects some architecture configurations; those are simulated to obtain their performance, and then an artificial neural network is trained to predict the remaining configurations performance. Results obtained show a high accuracy of the estimations using a simple method to select the configurations we have to simulate to optimize the MLP. In order to explore the search space, we have designed a genetic algorithm that uses the MLP as fitness function to find the niche where the best architecture configurations (those with higher performance) are located. Our models need only a small fraction of the design space, obtaining small errors and reducing required simulation by two orders of magnitude.Peer ReviewedPostprint (published version