Uniqueness for the electrostatic inverse boundary value problem with piecewise constant anisotropic conductivities

We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body $\Omega\subset\mathbb{R}^{n}$ when the so-called Neumann-to-Dirichlet map is locally given on a non empty curved portion $\Sigma$ of the boundary $\partial\Omega$. We prove that anisotropic conductivities that are \textit{a-priori} known to be piecewise constant matrices on a given partition of $\Omega$ with curved interfaces can be uniquely determined in the interior from the knowledge of the local Neumann-to-Dirichlet map

Opposite effects of NO2_2 on electrical injection in porous silicon gas sensors

The electrical conductance of porous silicon fabricated with heavily doped p-type silicon is very sensitive to NO$_2$. A concentration of 10 ppb can be detected by monitoring the current injection at fixed voltage. However, we show that the sign of the injection variations depends on the porous layer thickness. If the thickness is sufficiently low -- of the order of few \micro\meter{} -- the injection decreases instead of increasing. We discuss the effect in terms of an already proposed twofold action of NO$_2$, according to which the free carrier density increases, and simultaneously the energy bands are bent at the porous silicon surface.Comment: 3 pages, 3 figures, requires SIunits packag

Lipschitz stability for the electrostatic inverse boundary value problem with piecewise linear conductivities

We consider the electrostatic inverse boundary value problem also known as electrical impedance tomography (EIT) for the case where the conductivity is a piecewise linear function on a domain $\Omega\subset\mathbb{R}^n$ and we show that a Lipschitz stability estimate for the conductivity in terms of the local Dirichlet-to-Neumann map holds true.Comment: 28 pages. arXiv admin note: text overlap with arXiv:1405.047

Photon energy lifter

We propose a time-dependent photonic structure, in which the carrier frequency of an optical pulse is shifted without changing its shape. The efficiency of the device takes advantage of slow group velocities of light attainable in periodic photonic structures. The frequency shifting effect is quantitatively studied by means of Finite Difference Time Domain simulations for realistic systems with optical parameters of conventional silicon technology.Comment: 4 pages 5 figure

High order direct Arbitrary-Lagrangian-Eulerian schemes on moving Voronoi meshes with topology changes

We present a new family of very high order accurate direct Arbitrary-Lagrangian-Eulerian (ALE) Finite Volume (FV) and Discontinuous Galerkin (DG) schemes for the solution of nonlinear hyperbolic PDE systems on moving 2D Voronoi meshes that are regenerated at each time step and which explicitly allow topology changes in time. The Voronoi tessellations are obtained from a set of generator points that move with the local fluid velocity. We employ an AREPO-type approach, which rapidly rebuilds a new high quality mesh rearranging the element shapes and neighbors in order to guarantee a robust mesh evolution even for vortex flows and very long simulation times. The old and new Voronoi elements associated to the same generator are connected to construct closed space--time control volumes, whose bottom and top faces may be polygons with a different number of sides. We also incorporate degenerate space--time sliver elements, needed to fill the space--time holes that arise because of topology changes. The final ALE FV-DG scheme is obtained by a redesign of the fully discrete direct ALE schemes of Boscheri and Dumbser, extended here to moving Voronoi meshes and space--time sliver elements. Our new numerical scheme is based on the integration over arbitrary shaped closed space--time control volumes combined with a fully-discrete space--time conservation formulation of the governing PDE system. In this way the discrete solution is conservative and satisfies the GCL by construction. Numerical convergence studies as well as a large set of benchmarks for hydrodynamics and magnetohydrodynamics (MHD) demonstrate the accuracy and robustness of the proposed method. Our numerical results clearly show that the new combination of very high order schemes with regenerated meshes with topology changes lead to substantial improvements compared to direct ALE methods on conforming meshes

Three Pillars of Automated Home-Cage Phenotyping of Mice: Novel Findings, Refinement, and Reproducibility Based on Literature and Experience

Animal models of neurodegenerative and neuropsychiatric disorders require extensive behavioral phenotyping. Currently, this presents several caveats and the most important are: (i) rodents are nocturnal animals, but mostly tested during the light period; (ii) the conventional behavioral experiments take into consideration only a snapshot of a rich behavioral repertoire; and (iii) environmental factors, as well as experimenter influence, are often underestimated. Consequently, serious concerns have been expressed regarding the reproducibility of research findings on the one hand, and appropriate welfare of the animals (based on the principle of 3Rs—reduce, refine and replace) on the other hand. To address these problems and improve behavioral phenotyping in general, several solutions have been proposed and developed. Undisturbed, 24/7 home-cage monitoring (HCM) is gaining increased attention and popularity as demonstrating the potential to substitute or complement the conventional phenotyping methods by providing valuable data for identifying the behavioral patterns that may have been missed otherwise. In this review, we will briefly describe the different technologies used for HCM systems. Thereafter, based on our experience, we will focus on two systems, IntelliCage (NewBehavior AG and TSE-systems) and Digital Ventilated Cage (DVC®, Tecniplast)—how they have been developed and applied during recent years. Additionally, we will touch upon the importance of the environmental/experimenter artifacts and propose alternative suggestions for performing phenotyping experiments based on the published evidence. We will discuss how the integration of telemetry systems for deriving certain physiological parameters can help to complement the description of the animal model to offer better translation to human studies. Ultimately, we will discuss how such HCM data can be statistically interpreted and analyzed.Peer reviewe

Solar Reector Design

The design of solar panels is investigated. Different aspects of this problem are presented. A formula averaging the solar energy received on a given location is derived rst. The energy received by the collecting solar panel is then calculated using a specially designed algorithm. The geometry of the device collecting the energy may then be optimised using different algorithms. The results show that for a given depth, devices of smaller width are more energy efficient than those of wider dimensions. This leads to a more economically efficient design

Lipschitz stability for the inverse conductivity problem for a conformal class of anisotropic conductivities

We consider the stability issue of the inverse conductivity problem for a conformal class of anisotropic conductivities in terms of the local Dirichlet\u2013 Neumann map. We extend here the stability result obtained by Alessandrini and Vessella (Alessandrini G and Vessella S 2005 Lipschitz stability for the inverse conductivity problem Adv. Appl. Math. 35 207\u2013241), where the authors considered the piecewise constant isotropic case