In this paper, we look at the influence of the choice of the Reynolds tensor on the derivation of some multiphasic incompressible fluid models, called Kazhikhov-Smagulov type models. We show that a compatibility condition between the viscous tensor and the diffusive term allows us to obtain similar models without assuming a small diffusive term as it was done for instance by A. Kazhikhov and Sh. Smagulov. We begin with two examples: The first one concerning pollution and the last one concerning a model of combustion at low Mach number. We give the compatibility condition that provides a class of models of the Kazhikhov-Smagulov type. We prove that these models are globally well posed without assumptions between the density and the diffusion terms.
Autism Spectrum Disorder (ASD) is a neurodevelopmental disorder characterized by persistent difficulties including repetitive patterns of behavior known as stereotypical motor movements (SMM). So far, several techniques have been implemented to track and identify SMMs. In this context, we propose a deep learning approach for SMM recognition, namely, convolutional neural networks (CNN) in time and frequency-domains. To solve the intrasubject SMM variability, we propose a robust CNN model for SMM detection within subjects, whose parameters are set according to a proper analysis of SMM signals, thereby outperforming state-of-the-art SMM classification works. And, to solve the intersubject variability, we propose a global, fast, and light-weight framework for SMM detection across subjects which combines a knowledge transfer technique with an SVM classifier, therefore resolving the “real-life” medical issue associated with the lack of supervised SMMs per testing subject in particular. We further show that applying transfer learning across domains instead of transfer learning within the same domain also generalizes to the SMM target domain, thus alleviating the problem of the lack of supervised SMMs in general.
This work studies a mathematical model describing the static process of contact between a piezoelectric body and a thermally-electrically conductive foundation. The behavior of the material is modeled with a thermo-electro-elastic constitutive law. The contact is described by Signorini's conditions and Tresca's friction law including the electrical and thermal conductivity conditions. A variational formulation of the model in the form of a coupled system for displacements, electric potential, and temperature is derived. Existence and uniqueness of the solution are proved using the results of variational inequalities and a fixed point theorem.
We study an evolution problem which describes the quasistatic contact of a viscoelastic body with a foundation. We model the contact with normal damped response and a local friction law. We derive a variational formulation of the model and we establish the existence of a unique weak solution to the problem. The proof is based on monotone operators and fixed point arguments. We also establish the continuous dependence of the solution on the contact boundary conditions.
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