Homogenization of the p-Laplacian with nonlinear boundary condition on critical size particles: identifying the strange term for the some non smooth and multivalued operators

We extend previous papers in the literature concerning the homogenization of Robin type boundary conditions for quasilinear equations, in the case of microscopic obstacles of critical size: here we consider nonlinear boundary conditions involving some maximal monotone graphs which may correspond to discontinuous or non-Lipschitz functions arising in some catalysis problems.The research of the first two authors was partially supported as members of the Research Group MOMAT (Ref. 910480) of the UCM. The research of J.I. Diaz was partially supported by the project ref. MTM 2014-57113 of the DGISPI (Spain). The research of D. Gómez-Castro was supported by a FPU Grant from the Ministerio de Educación, Cultura y Deporte (Spain)

Characterizing the strange term in critical size homogenization: Quasilinear equations with a general microscopic boundary condition

The aim of this paper is to consider the asymptotic behavior of boundary value problems in n-dimensional domains with periodically placed particles, with a general microscopic boundary condition on the particles and a p-Laplace diffusion operator on the interior, in the case in which the particles are of critical size. We consider the cases in which 1<p<n{1<p<n}, n≥3{n\geq 3}. In fact, in contrast to previous results in the literature, we formulate the microscopic boundary condition in terms of a Robin type condition, involving a general maximal monotone graph, which also includes the case of microscopic Dirichlet boundary conditions. In this way we unify the treatment of apparently different formulations, which before were considered separately. We characterize the so called “strange term” in the homogenized problem for the case in which the particles are balls of critical size. Moreover, by studying an application in Chemical Engineering, we show that the critically sized particles lead to a more effective homogeneous reaction than noncritically sized particles

Homogenization of the p-Laplacian with nonlinear boundary condition on critical size particles: Identifying the strange term for the some non smooth and multivalued operators

We extend previous papers in the literature concerning the homogenization of Robin type boundary conditions for quasilinear equations, in the case of microscopic obstacles of critical size: here we consider nonlinear boundary conditions involving some maximal monotone graphs which may correspond to discontinuous or non-Lipschitz functions arising in some catalysis problems

utomated real-time classification of functional states: the significance of individual tuning stage

Automated classification of a human functional state is an important problem, with applications including stress resistance evaluation, supervision over operators of critical infrastructure, teaching and phobia therapy. Such classification is particularly efficient in systems for teaching and phobia therapy that include a virtual reality module, and provide the capability for dynamic adjustment of task complexity. In this paper, a method for automated real-time binary classification of human functional states (calm wakefulness vs. stress) based on discrete wavelet transform of EEG data is considered. It is shown that an individual tuning stage of the classification algorithm — a stage that allows the involvement of certain information on individual peculiarities in the classification, using very short individual learning samples, significantly increases classification reliability. The experimental study that proved this assertion was based on a specialized scenario in which individuals solved the task of detecting objects with given properties in a dynamic set of flying objects