In this paper, we are going to investigate an overdetermined problem for a general class of anisotropic equations on a cylindrical domain Ω ⊂ R N , N ≥ 2. Our aim is to show that if the overdetermined problem admits a solution in a suitable weak sense, then the underlying domain Ω and the corresponding solution u satisfy some symmetry properties. This result represents the anisotropic extension to one of the main results obtained by LE Payne and GA Philippin in their previous paper. KEYWORDS anisotropic equation, maximum principles, overdetermined problems, symmetry MSC CLASSIFICATION 35N25; 35B50

In classical mechanics, determining the governing equations of motion using finite element analysis (FEA) of an elastic multibody system (MBS) leads to a system of second order differential equations. To integrate this, it must be transformed into a system of first-order equations. However, this can also be achieved directly and naturally if Hamilton’s equations are used. The paper presents this useful alternative formalism used in conjunction with the finite element method for MBSs. The motion equations in the very general case of a three-dimensional motion of an elastic solid are obtained. To illustrate the method, two examples are presented. A comparison between the integration times in the two cases presents another possible advantage of applying this method.

No abstract

In this paper we are going to investigate a free boundary value problem for the anisotropic N-Laplace operator on a ring domain \Omega : = {\Omega _0}\backslash {\bar \Omega _1} \subset {\mathbb{R}^N}, N ≥ 2. Our aim is to show that if the problem admits a solution in a suitable weak sense, then the underlying domain Ω is a Wulff shaped ring. The proof makes use of a maximum principle for an appropriate P-function, in the sense of L.E. Payne and some geometric arguments involving the anisotropic mean curvature of the free boundary.

This article is proposing a mathematical model as a basis for radon detection by measurement alpha particle concentration with a carbon nanotubes-based sensor. The working principle at the basis of the mathematical model of the presented sensor is based on the fact that, the concentration of alpha particle in the air is a linear function of radon concentration. The collision between each alpha particle and the attachment of alpha particle to the carbon nanotube, changes the nanotube's own oscillation frequency. After activation, the carbon nanotubes oscillations in frequency depends on their own geometrical dimensions and their mechano-electrical properties. The initial oscillation frequencies spectra of the matrix of carbon nanotube with the same geometrical dimension is compared with the oscillation frequency spectra collected after the sensor is exposed to air sample. Based on their relative frequency variations of the recorded spectra, the radon concentration is evaluated. Radon concentration is determined on the bases of the linear relationship between its concentration and the alpha particles one. According to these theoretical assumptions, the use of carbon nanotubes sensor appears to be suitable for radon concentration measurement with the advantages to be a reusable and a low cost solution.