Bayesian estimate of the degree of a polynomial given a noisy data sample

A widely used method to create a continuous representation of a discrete data-set is regression analysis. When the regression model is not based on a mathematical description of the physics underlying the data, heuristic techniques play a crucial role and the model choice can have a significant impact on the result. In this paper, the problem of identifying the most appropriate model is formulated and solved in terms of Bayesian selection. Besides, probability calculus is the best way to choose among different alternatives. The results obtained are applied to the case of both univariate and bivariate polynomials used as trial solutions of systems of thermodynamic partial differential equations.Comment: 10 pages, 5 figures, submitted to Metrologi

Application of acoustic methods for a non-destructive evaluation of the elastic properties of several typologies of materials

In solid phase materials, differently from what happens in the fluid phase, elastic waves propagate both through longitudinal and transverse waves. From the speed of propagation of longitudinal and transverse waves, it is possible to evaluate important elastic properties of the solids under study, namely the Young's modulus, the Poisson's coefficient, the bulk modulus and the shear modulus. This work suggests an accurate method for measuring wave propagation speeds in homogeneous and non-homogeneous materials with the purpose to evaluate their mechanical properties and the associated uncertainty. First of all, to assess the performance of the proposed methodology, based on the "pulse-echo" technique, in terms of accuracy and precision, measurements of wave propagation speeds have been carried out, in atmospheric conditions, in well-known homogeneous and isotropic materials, such as copper, aluminum, stainless steel and also polymethyl methacrylate (Plexiglas (R)), Teflon (R) and optical glass BK7. These results were compared with the values reported in literature (if present), showing how published speed of sound data are very disperse and not so reliable owing to the lack of a precise uncertainty evaluation and of the temperature value associated to the measurement. Then, the same experimental apparatus was used for measuring speed of sound as a function of temperature (from 274.15 to 313.15 K) for 304 stainless steel and oxygen free copper, showing a good accuracy of the results also for temperature conditions far from ambient. Finally, the same procedure was applied to a non-homogeneous solid, obtaining some very preliminary results in typical mediterranean building material, as Carrara marble

Acoustical characterization of polysaccharide polymers tissue-mimicking materials

Tissue-mimicking phantoms play a crucial role in medical ultrasound research because they can simulate biological soft tissues. In last years, many types of polymeric tissues have been proposed and characterized from an acoustical and a thermal point of view, but, rarely, a deep discussion about the quality of the measurements, in terms of the uncertainty evaluation, has been reported. In this work, considering the necessity to develop laboratory standards for the measurement of ultrasonic exposure and dose quantities, a detailed description of the experimental apparatuses for the sound speed and the attenuation coefficient measurements is given, focusing the attention on the uncertainty evaluation both of the results and analysis algorithms. In particular, this algorithm reveals a novel empirical relation, fixing a limit to the energy content (therefore limits the number of cycles) of the three parts in which the authors have proposed to divide the acoustical signal. Furthermore, the realisation of multi-components phantoms, Agar and Phytagel based tissue-mimicking gels along with others long chain molecules (dextrane or polyvinyl alcohol) and scattering materials (silicon carbide and kieselguhr) are investigated. This paper reports accurate speed of sound and attenuation coefficient measurements. Speed of sound is measured by a pulse-echo technique in far-field condition, using an optical glass buffer rod; while attenuation coefficient is determined by an insertion technique, using demineralized water as reference material. The experimental sound speed results are subjected to an overall estimated relative uncertainty of about 1.5% and the attenuation coefficient uncertainty is less than 2.5%. For the development of laboratory standards, a detailed analysis of the measurement uncertainty is fundamental to make sample properties comparable. The authors believe this study could represent the right direction to make phantoms characterizations referable and traceable.Tissue-mimicking phantoms play a crucial role in medical ultrasound research because they can simulate biological soft tissues. In last years, many types of polymeric tissues have been proposed and characterized from an acoustical and a thermal point of view, but, rarely, a deep discussion about the quality of the measurements, in terms of the uncertainty evaluation, has been reported. In this work, considering the necessity to develop laboratory standards for the measurement of ultrasonic exposure and dose quantities, a detailed description of the experimental apparatuses for the sound speed and the attenuation coefficient measurements is given, focusing the attention on the uncertainty evaluation both of the results and analysis algorithms. In particular, this algorithm reveals a novel empirical relation, fixing a limit to the energy content (therefore limits the number of cycles) of the three parts in which the authors have proposed to divide the acoustical signal.Furthermore, the realisation of multi-components phantoms, Agar and Phytagel based tissue-mimicking gels along with others long chain molecules (dextrane or polyvinyl alcohol) and scattering materials (silicon carbide and kieselguhr) are investigated.This paper reports accurate speed of sound and attenuation coefficient measurements. Speed of sound is measured by a pulse-echo technique in far-field condition, using an optical glass buffer rod; while attenuation coefficient is determined by an insertion technique, using demineralized water as reference material.The experimental sound speed results are subjected to an overall estimated relative uncertainty of about 1.5% and the attenuation coefficient uncertainty is less than 2.5%. For the development of laboratory standards, a detailed analysis of the measurement uncertainty is fundamental to make sample properties comparable. The authors believe this study could represent the right direction to make phantoms characterizations referable and traceable. (C) 2014 Elsevier B.V. All rights reserved

Pro-Pro: progress and problems of the experiment for the acoustic determination of the Boltzmann constant at INRIM

none6http://forum.bipm.orgR.M.GAVIOSO; G. BENEDETTO; P. A. GIULIANO ALBO; MERLONE A; A. BALSAMO; R. SPAGNOLOGavioso, ROBERTO MARIA; G., Benedetto; GIULIANO ALBO, PAOLO ALBERTO; Merlone, Andrea; Balsamo, Alessandro; R., Spagnol