Computing Volume Bounds of Inclusions by EIT Measurements

The size estimates approach for Electrical Impedance Tomography (EIT) allows for estimating the size (area or volume) of an unknown inclusion in an electrical conductor by means of one pair of boundary measurements of voltage and current. In this paper we show by numerical simulations how to obtain such bounds for practical application of the method. The computations are carried out both in a 2D and a 3D setting.Comment: 20 pages with figure

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

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

Globally diffeomorphic σ -harmonic mappings

Given a two-dimensional mapping U whose components solve a divergence structure elliptic equation,we give necessary and sufficient conditions on the boundary so that U is a global diffeomorphism

Further evidence that the transition of 4D dynamical triangulation is 1st order

We confirm recent claims that, contrary to what was generally believed, the phase transition of the dynamical triangulation model of four-dimensional quantum gravity is of first order. We have looked at this at a volume of 64,000 four-simplices, where the evidence in the form of a double peak histogram of the action is quite clear.Comment: 12 pages, LaTeX2

Demonstration of an electrostatic-shielded cantilever

The fabrication and performances of cantilevered probes with reduced parasitic capacitance starting from a commercial Si3N4 cantilever chip is presented. Nanomachining and metal deposition induced by focused ion beam techniques were employed in order to modify the original insulating pyramidal tip and insert a conducting metallic tip. Two parallel metallic electrodes deposited on the original cantilever arms are employed for tip biasing and as ground plane in order to minimize the electrostatic force due to the capacitive interaction between cantilever and sample surface. Excitation spectra and force-to-distance characterization are shown with different electrode configurations. Applications of this scheme in electrostatic force microscopy, Kelvin probe microscopy and local anodic oxidation is discussed.Comment: 4 pages and 3 figures. Submitted to Applied Physics Letter

An operational approach to real-time dynamic measurement of discharge

Based on the maximization of entropy, microwave sensors are becoming standard approaches for converting point surface velocity measurements into discharge. Unfortunately, this conversion is conditioned by cross-section regularity and by the need to take the surface measures above the vertical where the maximum velocity occurs. Cross-section irregularities and the presence of floodplains, vegetation and/or local bed depressions can change the theoretical applicability conditions of the proposed methods and, due to the wandering of the current, the microwave sensor must be continuously moved to track the maximum velocity. We describe the theoretical development and practical application of a new approach to operationally convert surface velocity and water level, measured using a fixed installation, into discharge. The resulting equation that links the surface point velocity measurement to the discharge is a function of two parameters describing the velocity distribution within the cross-section plus an additional correction factor which describes the non-homogeneity of the different vertical slices into which the cross-section is divided. Interesting results of the approach are shown for the gauging section of Tavagnasco on the Dora Baltea River in Italy with high performances both in terms of calibration and validation

Path integral evaluation of Dbrane amplitudes

We extend Polchinski's evaluation of the measure for the one-loop closed string path integral to open string tree amplitudes with boundaries and crosscaps embedded in Dbranes. We explain how the nonabelian limit of near-coincident Dbranes emerges in the path integral formalism. We give a careful path integral derivation of the cylinder amplitude including the modulus dependence of the volume of the conformal Killing group.Comment: Extended version replacing hep-th/9903184, includes discussion of nonabelian limit, Latex, 10 page

Diffeomorphic approximation of Sobolev homeomorphisms

Every homeomorphism h : X -> Y between planar open sets that belongs to the Sobolev class W^{1,p}(X,Y), 1<p<\infty, can be approximated in the Sobolev norm by diffeomorphisms.Comment: 21 pages, 5 figure

Gravitational binding in 4D dynamical triangulation

In the dynamical triangulation model of four dimensional euclidean quantum gravity we investigate gravitational binding. Two scalar test particles (quenched approximation) have a positive binding energy, thereby showing that the model can represent gravitational attraction.Comment: 19 pages, LaTeX2e, version as accepted by Nucl Phys