Anomalous thresholds and edge singularities in Electrical Impedance Tomography

Studies of models of current flow behaviour in Electrical Impedance Tomography (EIT) have shown that the current density distribution varies extremely rapidly near the edge of the electrodes used in the technique. This behaviour imposes severe restrictions on the numerical techniques used in image reconstruction algorithms. In this paper we have considered a simple two dimensional case and we have shown how the theory of end point/pinch singularities which was developed for studying the anomalous thresholds encountered in elementary particle physics can be used to give a complete description of the analytic structure of the current density near to the edge of the electrodes. As a byproduct of this study it was possible to give a complete description of the Riemann sheet manifold of the eigenfunctions of the logarithmic kernel. These methods can be readily extended to other weakly singular kernels.Comment: Correction of a misprint which occurred in the unnumbered formula preceding Eq. (14), LaTeX file as an uuencoded file, 40 pages with 12 figures, uses epsf.st

First-principles molecular-dynamics simulations of a hydrous silica melt: Structural properties and hydrogen diffusion mechanism

We use {\it ab initio} molecular dynamics simulations to study a sample of liquid silica containing 3.84 wt.% H$_2$O.We find that, for temperatures of 3000 K and 3500 K,water is almost exclusively dissolved as hydroxyl groups, the silica network is partially broken and static and dynamical properties of the silica network change considerably upon the addition of water.Water molecules or free O-H groups occur only at the highest temperature but are not stable and disintegrate rapidly.Structural properties of this system are compared to those of pure silica and sodium tetrasilicate melts at equivalent temperatures. These comparisons confirm the picture of a partially broken tetrahedral network in the hydrous liquid and suggest that the structure of the matrix is as much changed by the addition of water than it is by the addition of the same amount (in mole %) of sodium oxide. On larger length scales, correlations are qualitatively similar but seem to be more pronounced in the hydrous silica liquid. Finally, we study the diffusion mechanisms of the hydrogen atoms in the melt. It turns out that HOSi$_2$ triclusters and SiO dangling bonds play a decisive role as intermediate states for the hydrogen diffusion.Comment: 25 pages, 18 figures. submitte

New fitting scheme to obtain effective potential from Car-Parrinello molecular dynamics simulations: Application to silica

A fitting scheme is proposed to obtain effective potentials from Car-Parrinello molecular dynamics (CPMD) simulations. It is used to parameterize a new pair potential for silica. MD simulations with this new potential are done to determine structural and dynamic properties and to compare these properties to those obtained from CPMD and a MD simulation using the so-called BKS potential. The new potential reproduces accurately the liquid structure generated by the CPMD trajectories, the experimental activation energies for the self-diffusion constants and the experimental density of amorphous silica. Also lattice parameters and elastic constants of alpha-quartz are well-reproduced, showing the transferability of the new potential.Comment: 6 pages, 5 figure

New method to characterize a machining system: application in turning

Many studies simulates the machining process by using a single degree of freedom spring-mass sytem to model the tool stiffness, or the workpiece stiffness, or the unit tool-workpiece stiffness in modelings 2D. Others impose the tool action, or use more or less complex modelings of the efforts applied by the tool taking account the tool geometry. Thus, all these models remain two-dimensional or sometimes partially three-dimensional. This paper aims at developing an experimental method allowing to determine accurately the real three-dimensional behaviour of a machining system (machine tool, cutting tool, tool-holder and associated system of force metrology six-component dynamometer). In the work-space model of machining, a new experimental procedure is implemented to determine the machining system elastic behaviour. An experimental study of machining system is presented. We propose a machining system static characterization. A decomposition in two distinct blocks of the system "Workpiece-Tool-Machine" is realized. The block Tool and the block Workpiece are studied and characterized separately by matrix stiffness and displacement (three translations and three rotations). The Castigliano's theory allows us to calculate the total stiffness matrix and the total displacement matrix. A stiffness center point and a plan of tool tip static displacement are presented in agreement with the turning machining dynamic model and especially during the self induced vibration. These results are necessary to have a good three-dimensional machining system dynamic characterization

Comparative classical and ab initio Molecular Dynamics study of molten and glassy germanium dioxide

A Molecular Dynamics (MD) study of static and dynamic properties of molten and glassy germanium dioxide is presented. The interactions between the atoms are modelled by the classical pair potential proposed by Oeffner and Elliott (OE) [Oeffner R D and Elliott S R 1998, Phys. Rev. B, 58, 14791]. We compare our results to experiments and previous simulations. In addition, an ab initio method, the so-called Car-Parrinello Molecular Dynamics (CPMD), is applied to check the accuracy of the structural properties, as obtained by the classical MD simulations with the OE potential. As in a similar study for SiO2, the structure predicted by CPMD is only slightly softer than that resulting from the classical MD. In contrast to earlier simulations, both the static structure and dynamic properties are in very good agreement with pertinent experimental data. MD simulations with the OE potential are also used to study the relaxation dynamics. As previously found for SiO2, for high temperatures the dynamics of molten GeO2 is compatible with a description in terms of mode coupling theory.Comment: 27 pages, 16 figure

Computational Modeling of Silicate Glasses: A Quantitative Structure-Property Relationship Perspective

This article reviews the present state of Quantitative Structure-Property Relationships (QSPR) in glass design and gives an outlook into future developments. First an overview is given of the statistical methodology, with particular emphasis to the integration of QSPR with molecular dynamics simulations to derive informative structural descriptors. Then, the potentiality of this approach as a tool for interpretative and predictive purposes is highlighted by a number of recent inspiring applications