Supercritical biharmonic equations with power-type nonlinearity

The biharmonic supercritical equation $\Delta^2u=|u|^{p-1}u$, where $n>4$ and $p>(n+4)/(n-4)$, is studied in the whole space $\mathbb{R}^n$ as well as in a modified form with $\lambda(1+u)^p$ as right-hand-side with an additional eigenvalue parameter $\lambda>0$ in the unit ball, in the latter case together with Dirichlet boundary conditions. As for entire regular radial solutions we prove oscillatory behaviour around the explicitly known radial {\it singular} solution, provided $p\in((n+4)/(n-4),p_c)$, where $p_c\in ((n+4)/(n-4),\infty]$ is a further critical exponent, which was introduced in a recent work by Gazzola and the second author. The third author proved already that these oscillations do not occur in the complementing case, where $p\ge p_c$. Concerning the Dirichlet problem we prove existence of at least one singular solution with corresponding eigenvalue parameter. Moreover, for the extremal solution in the bifurcation diagram for this nonlinear biharmonic eigenvalue problem, we prove smoothness as long as $p\in((n+4)/(n-4),p_c)$

High-performance analog front-end (AFE) for EOG systems

Electrooculography is a technique for measuring the corneo-retinal standing potential of the human eye. The resulting signal is called the electrooculogram (EOG). The primary applications are in ophthalmological diagnosis and in recording eye movements to develop simple human–machine interfaces (HCI). The electronic circuits for EOG signal conditioning are well known in the field of electronic instrumentation; however, the specific characteristics of the EOG signal make a careful electronic design necessary. This work is devoted to presenting the most important issues related to the design of an EOG analog front-end (AFE). In this respect, it is essential to analyze the possible sources of noise, interference, and motion artifacts and how to minimize their effects. Considering these issues, the complete design of an AFE for EOG systems is reported in this work.info:eu-repo/semantics/publishedVersio

A Model for Zebrafish Ventricular Action Potential

From the '90s, the interest in the use of zebrafish has exponentially grown thanks to the numerous characteristics, very close to the human ones, that make this little fish very attractive in different fields. Thus, zebrafish has been increasingly proposed as a pharmacological and genetic screening model. The growing interest and the relevance of this animal model motivate the development of a mathematical model of the action potential of the zebrafish to facilitate the understanding of the mechanisms associated with its electrophysiological behavior and how they correlated with those observed in humans. This work presents the first attempt to develop a mathematical model of the adult zebrafish action potential. The model is based on the Ten Tusscher formulation of the action potential of human cardiomyocyte in which the main currents have been reparametrized to be adapted to those of the zebrafish, while extending the model to account for the T-type calcium current present in the zebrafish. Preliminary results of the proposed model show an action potential morphology in good agreement with experimental data

Study of impact on helicopter blade

This article presents a study of damage in structures that are similar to helicopter blade sections, subjected to an impact. These complex composite structures were impacted by a steel ball of 125 g at impact speed ranging from 30 to 130 m/s. This led to properly highlight the kinematics of the impact and to define the sequence of the damage’s mechanisms. An explicit FE model is also presented. The damage modelling of the roving is performed through a scale change. It allows a good representation of observed experimental behaviour. As the mesh density is low, it can be used for the modelling of a real structure

Eurocode 7 and rock engineering design: The case of rockfall protection barriers

The Eurocode 7 or EC7 is the Reference Design Code (RDC) for geotechnical design including rock engineering design within the European Union (EU). Moreover, its principles have also been adopted by several other countries, becoming a key design standard for geotechnical engineering worldwide. It is founded on limit state design (LSD) concepts, and the reliability of design is provided mainly by a semi-probabilistic method based on partial factors. The use of partial factors is currently an advantage, mainly for the simplicity in its applicability, and a limitation, especially concerning geotechnical designs. In fact, the application of partial factors to geotechnical design has proven to be difficult. In this paper, the authors focus on the way to apply EC7 principles to rock engineering design by analyzing the design of rockfall protection structures as an example. A real case of slope subjected to rockfall is reported to outline the peculiarity connected to rock engineering. The main findings are related to the complementarity of the reliability-based design (RBD) approach within EC7 principles and the possibility of overcoming the limitations of a partial factor approach to this type of engineering problem

Eurocode 7 and rock engineering design: The case of rockfall protection barriers

The Eurocode 7 or EC7 is the Reference Design Code (RDC) for geotechnical design including rock engineering design within the European Union (EU). Moreover, its principles have also been adopted by several other countries, becoming a key design standard for geotechnical engineering worldwide. It is founded on limit state design (LSD) concepts, and the reliability of design is provided mainly by a semi-probabilistic method based on partial factors. The use of partial factors is currently an advantage, mainly for the simplicity in its applicability, and a limitation, especially concerning geotechnical designs. In fact, the application of partial factors to geotechnical design has proven to be difficult. In this paper, the authors focus on the way to apply EC7 principles to rock engineering design by analyzing the design of rockfall protection structures as an example. A real case of slope subjected to rockfall is reported to outline the peculiarity connected to rock engineering. The main findings are related to the complementarity of the reliability-based design (RBD) approach within EC7 principles and the possibility of overcoming the limitations of a partial factor approach to this type of engineering problem

Time-Dependent Gutzwiller Theory for Multiband Hubbard Models

Based on the variational Gutzwiller theory, we present a method for the computation of response functions for multiband Hubbard models with general local Coulomb interactions. The improvement over the conventional random-phase approximation is exemplified for an infinite-dimensional two-band Hubbard model where the incorporation of the local multiplet-structure leads to a much larger sensitivity of ferromagnetism on the Hund coupling. Our method can be implemented into LDA+Gutzwiller schemes and will therefore be an important tool for the computation of response functions for strongly correlated materials.Comment: 4 pages, 3 figure