arXiv subjects

Bernard Lacaze

Publications and source records attributed to Bernard Lacaze.

8 recordsLinked to original sources

arXiv2020

Modelling attenuation and velocity of ultrasonics in reconstituted milk powder

In the context of food quality control, ultrasonics provide proven methods which are able to replace manual controls. The latter are subject to the lack of objectivity of human judgement. Automatic control increases reliability and reduces costs. This paper revisits data coming from ultrasonics through reconstituted milk powder. Two characteristics are studied using five productions of a well known manufacturer. Measured attenuation and dispersion of ultrasonics are explained through stable probability laws and random propagation times. We have proved elsewhere that this model is available in many propagation problems,in acoustics, ultrasonics and in the electromagnetic world.

physics.data-an↗

arXiv2019

From periodic sampling to irregular sampling through PNS (Periodic Nonuniform Sampling)

Resampling is an operation costly in calculation time and accuracy. It regularizes irregular sampling, replacing N data by N periodic estimations. This stage can be suppressed, using formulas built with incoming data and completed by sequences of elements which influence decreases when the number of data increases. Obviously, some spectral properties (for processes) and some asymptotic properties (for the sampling sequence) have to be fulfilled. In this paper, we explain that it is possible to elaborate a logical theory, starting from the ordinary periodic sampling, and generalized by the PNS (Periodic Nonuniform Sampling), to treat more general irregular samplings. The "baseband spectrum" hypothesis linked to the "Nyquist bound" (or Shannon bound) is generalized to spectra in a finite number of intervals, suited to the "Landau condition".

physics.data-an↗

arXiv2017

A Blade Tip-Timing method based on Periodic Nonuniform Sampling of order 2

Vibrations are among main causes of fatigue and damages leading to destruction of rotating blades. Consequently, motions of blades have to be carefully studied, and in particular, periodic components. Blade Tip-Timing (BTT) methods achieve non-intrusive measurements which is a great advantage with respect to classical methods. They can be modelled by a Periodic Nonuniform Sampling of order L equal to the number of probes (PNSL). In this paper, we develop the case L=2, and we prove that this model is sufficient for finding the places of asynchronous frequency lines, with their amplitudes and their phases. To increase L will increase the redundance and then the accuracy of the method.

physics.data-an↗

arXiv2016

New indices of coherence for one or two-dimensional fields

The modern definition of optical coherence highlights a frequency dependent function based on a matrix of spectra and cross-spectra. Due to general properties of matrices, such a function is invariant in changes of basis. In this article, we attempt to measure the proximity of two stationary fields by a real and positive number between 0 and 1. The extremal values will correspond to uncorrelation and linear dependence, similar to a correlation coefficient which measures linear links between random variables. We show that these "indices of coherence" are generally not symmetric, and not unique. We study and we illustrate this problem together for one-dimensional and two-dimensional fields in the framework of stationary processes.

physics.optics↗

arXiv2014

Stable probability laws modeling random propagation times of waves crossing different media

In a communication scheme, there exist points at the transmitter and at the receiver where the wave is reduced to a finite set of functions of time which describe amplitudes and phases. For instance, the information is summarized in electrical cables which preceed or follow antennas. In many cases, a random propagation time is sufficient to explain changes induced by the medium. In this paper we study models based on stable probability laws which explain power spectra due to propagation of different kinds of waves in different media, for instance, acoustics in quiet or turbulent atmosphere, ultrasonics in liquids or tissues, or electromagnetic waves in free space or in cables. Physical examples show that a sub-class of probability laws appears in accordance with the causality property of linear filters.

physics.data-an↗

arXiv2012

Equivalent random propagation time for coaxial cables

Propagation of monochromatic electromagnetic waves in free space results in a widening of the spectral line. On the contrary, propagation preserves monochromaticity in the case of acoustic waves. In this case, the propagation can be modelled by a linear invariant filter leading to attenuations and phases changes. Due to the Beer-Lambert law, the associated transfer function is an exponential of power functions with frequency-dependent parameters. In recent papers, we have proved that the acoustic propagation time can be modelled as a random variable following a stable probability distribution. In this paper, we show that the same model can be applied to the propagation in coaxial cables.

physics.ins-det↗

arXiv2012

About the Bidimensional Beer-Lambert Law

In acoustics, ultrasonics and in electromagnetic wave propagation, the crossed medium can be often modelled by a linear invariant filter (LIF) which acts on a wide-sense stationary process. Its complex gain follows the Beer-Lambert law i.e is in the form exp [-\alphaz] where z is the thickness of the medium and αdepends on the frequency and on the medium properties. This paper addresses a generalization for electromagnetic waves when the beam polarization has to be taken into account. In this case, we have to study the evolution of both components of the electric field (assumed orthogonal to the trajectory). We assume that each component at z is a linear function of both components at 0. New results are obtained modelling each piece of medium by four LIF. They lead to a great choice of possibilities in the medium modelling. Particular cases can be deduced from works of R. C. Jones on deterministic monochromatic light. keywords: linear filtering, polarization, Beer-Lambert law, random processes.

physics.optics↗

arXiv2010

Beams Propagation Modelled by Bi-filters

In acoustic, ultrasonic or electromagnetic propagation, crossed media are often modelled by linear filters with complex gains in accordance with the Beer-Lambert law. This paper addresses the problem of propagation in media where polarization has to be taken into account. Because waves are now bi-dimensional, an unique filter is not sufficient to represent the effects of the medium. We propose a model which uses four linear invariant filters, which allows to take into account exchanges between components of the field. We call it bi-filter because it has two inputs and two outputs. Such a circuit can be fitted to light devices like polarizers, rotators and compensators and to propagation in free space. We give a generalization of the Beer-Lambert law which can be reduced to the usual one in some cases and which justifies the proposed model for propagation of electromagnic beams in continuous media.

physics.optics↗