Universality of Einstein Equations for the Ricci Squared Lagrangians

It has been recently shown that, in the first order (Palatini) formalism, there is universality of Einstein equations and Komar energy-momentum complex, in the sense that for a generic nonlinear Lagrangian depending only on the scalar curvature of a metric and a torsionless connection one always gets Einstein equations and Komar's expression for the energy-momentum complex. In this paper a similar analysis (also in the framework of the first order formalism) is performed for all nonlinear Lagrangians depending on the (symmetrized) Ricci square invariant. The main result is that the universality of Einstein equations and Komar energy-momentum complex also extends to this case (modulo a conformal transformation of the metric).Comment: 21 pages, Late

Remarks on Conserved Quantities and Entropy of BTZ Black Hole Solutions. Part II: BCEA Theory

The BTZ black hole solution for (2+1)-spacetime is considered as a solution of a triad-affine theory (BCEA) in which topological matter is introduced to replace the cosmological constant in the model. Conserved quantities and entropy are calculated via Noether theorem, reproducing in a geometrical and global framework earlier results found in the literature using local formalisms. Ambiguities in global definitions of conserved quantities are considered in detail. A dual and covariant Legendre transformation is performed to re-formulate BCEA theory as a purely metric (natural) theory (BCG) coupled to topological matter. No ambiguities in the definition of mass and angular momentum arise in BCG theory. Moreover, gravitational and matter contributions to conserved quantities and entropy are isolated. Finally, a comparison of BCEA and BCG theories is carried out by relying on the results obtained in both theories.Comment: PlainTEX, 20 page

Remarks on Conserved Quantities and Entropy of BTZ Black Hole Solutions. Part I: the General Setting

The BTZ stationary black hole solution is considered and its mass and angular momentum are calculated by means of Noether theorem. In particular, relative conserved quantities with respect to a suitably fixed background are discussed. Entropy is then computed in a geometric and macroscopic framework, so that it satisfies the first principle of thermodynamics. In order to compare this more general framework to the prescription by Wald et al. we construct the maximal extension of the BTZ horizon by means of Kruskal-like coordinates. A discussion about the different features of the two methods for computing entropy is finally developed.Comment: PlainTEX, 16 pages. Revised version 1.

The Role of Probe Attenuation in the Time-Domain Reflectometry Characterization of Dielectrics

The influence of the measurement setup on the estimation of dielectric permittivity spectra from time-domain reflectometry (TDR) responses is investigated. The analysis is based on a simplified model of the TDR measurement setup, where an ideal voltage step is applied to an ideal transmission line that models the probe. The main result of this analysis is that the propagation in the probe has an inherent band limiting effect, and the estimation of the high-frequency permittivity parameters is well conditioned only if the wave attenuation for a round trip propagation in the dielectric sample is small. This is a general result, holding for most permittivity model and estimation scheme. It has been verified on real estimation problems by estimating the permittivity of liquid dielectrics and soil samples via an high-order model of the TDR setup and a parametric inversion approac

Lagrangian Symmetries of Chern-Simons Theories

This paper analyses the Noether symmetries and the corresponding conservation laws for Chern-Simons Lagrangians in dimension $d=3$. In particular, we find an expression for the superpotential of Chern-Simons gravity. As a by-product the general discussion of superpotentials for 3rd order natural and quasi-natural theories is also given.Comment: 16 pages in LaTeX, some comments and references added. to appear in Journal of Physics A: Mathematical and Genera

Special issue: Surface engineering of light alloys

Light alloys (mainly aluminum, magnesium and titanium alloys) are of great interest in applications where lightweight has an high impact, such as automotive, aerospace and biomedical fields [...

Ultrasonic distance sensor improvement using a two-level neural network

This paper discusses the performance improvement that a neural network can provide to a contactless distance sensor based on the measurement of the time of flight (TOF) of an ultrasonic (US) pulse. The sensor, which embeds a correction system for the temperature effect, achieves a distance uncertainty (rms) of less than 0.5 mm over 0.5 m by using a two-level neural network to process the US echo and determine the TOF in the presence of environmental acoustic noise. The network embeds a "guard" neuron that guards against gross measurement errors, which would be possible in the presence of high environmental noise

Hamiltonian, Energy and Entropy in General Relativity with Non-Orthogonal Boundaries

A general recipe to define, via Noether theorem, the Hamiltonian in any natural field theory is suggested. It is based on a Regge-Teitelboim-like approach applied to the variation of Noether conserved quantities. The Hamiltonian for General Relativity in presence of non-orthogonal boundaries is analysed and the energy is defined as the on-shell value of the Hamiltonian. The role played by boundary conditions in the formalism is outlined and the quasilocal internal energy is defined by imposing metric Dirichlet boundary conditions. A (conditioned) agreement with previous definitions is proved. A correspondence with Brown-York original formulation of the first principle of black hole thermodynamics is finally established.Comment: 29 pages with 1 figur

Permittivity measurement of sand and clay soil with a capacitive sensor

The determination of permittivity of sand and clay soil over a wide frequency band can be useful in several applications. Fringing Capacitive sensors can be used to measure the real and imaginary part of the permittivity of materials in the RF and microwave frequency bands. In this paper the use of a commercial capacitive sensor has been exploited in order to characterize sand and clay soils with different water content. Liquid and granular materials are particular suited for this kind of sensor because the sensor can be dipped into the sample thus avoiding contact problems between the surface of the sensor and the material as for solid one. The measurement setup is composed by an Agilent Coaxial Probe kit 85070D, an HP 8720B Network analyzer and PC for data acquisition. This sensor works in the frequency range 200MHz-20GHz. The calibration procedure is based on three reference measurements (air, short circuit and deionized water). The setup and the calibration procedure has been tested by measuring the permittivity of several reference liquids (methanol, ethanol, acetone, water with different salt concentration). The comparison with the Cole-Cole model was also performed. Then, several samples of sand and clay soil with different water content have been considered. This measurement technique has also been compared with a frequency domain approach for the permittivity determination based on the double-delay method