A physical memristor based Muthuswamy-Chua-Ginoux system.

In 1976, Leon Chua showed that a thermistor can be modeled as a memristive device. Starting from this statement we designed a circuit that has four circuit elements: a linear passive inductor, a linear passive capacitor, a nonlinear resistor and a thermistor, that is, a nonlinear "locally active" memristor. Thus, the purpose of this work was to use a physical memristor, the thermistor, in a Muthuswamy-Chua chaotic system (circuit) instead of memristor emulators. Such circuit has been modeled by a new three-dimensional autonomous dynamical system exhibiting very particular properties such as the transition from torus breakdown to chaos. Then, mathematical analysis and detailed numerical investigations have enabled to establish that such a transition corresponds to the so-called route to Shilnikov spiral chaos but gives rise to a "double spiral attractor".

Delayed dynamics in an electronic relaxation oscillator.

We present an experimental investigation of the complex dynamics of a modulated relaxation oscillator implemented by using a unipolar junction transistor (UJT) showing the transition to chaos through torus breakdown. In a previous paper a continuous model was introduced for the same system, explaining chaos based on analogy with a memristor. We propose here a new approach based on a piecewise linear model with delay considering a measured parasitic delay effect. The inclusion of this delay, accounting for memory effects, increases the dimensionality of the model, allowing the transition to chaos as observed in the experiment. The piecewise delayed model shows analogies with a two-dimensional leaky integrate-and-fire model used in neurodynamics.

An ultrasonic contactless sensor for breathing monitoring.

The monitoring of human breathing activity during a long period has multiple fundamental applications in medicine. In breathing sleep disorders such as apnea, the diagnosis is based on events during which the person stops breathing for several periods during sleep. In polysomnography, the standard for sleep disordered breathing analysis, chest movement and airflow are used to monitor the respiratory activity. However, this method has serious drawbacks. Indeed, as the subject should sleep overnight in a laboratory and because of sensors being in direct contact with him, artifacts modifying sleep quality are often observed. This work investigates an analysis of the viability of an ultrasonic device to quantify the breathing activity, without contact and without any perception by the subject. Based on a low power ultrasonic active source and transducer, the device measures the frequency shift produced by the velocity difference between the exhaled air flow and the ambient environment, i.e., the Doppler effect. After acquisition and digitization, a specific signal processing is applied to separate the effects of breath from those due to subject movements from the Doppler signal. The distance between the source and the sensor, about 50 cm, and the use of ultrasound frequency well above audible frequencies, 40 kHz, allow monitoring the breathing activity without any perception by the subject, and therefore without any modification of the sleep quality which is very important for sleep disorders diagnostic applications. This work is patented (patent pending 2013-7-31 number FR.13/57569).

Van der Pol and the history of relaxation oscillations: toward the emergence of a concept.

Relaxation oscillations are commonly associated with the name of Balthazar van der Pol via his paper (Philosophical Magazine, 1926) in which he apparently introduced this terminology to describe the nonlinear oscillations produced by self-sustained oscillating systems such as a triode circuit. Our aim is to investigate how relaxation oscillations were actually discovered. Browsing the literature from the late 19th century, we identified four self-oscillating systems in which relaxation oscillations have been observed: (i) the series dynamo machine conducted by Gérard-Lescuyer (1880), (ii) the musical arc discovered by Duddell (1901) and investigated by Blondel (1905), (iii) the triode invented by de Forest (1907), and (iv) the multivibrator elaborated by Abraham and Bloch (1917). The differential equation describing such a self-oscillating system was proposed by Poincaré for the musical arc (1908), by Janet for the series dynamo machine (1919), and by Blondel for the triode (1919). Once Janet (1919) established that these three self-oscillating systems can be described by the same equation, van der Pol proposed (1926) a generic dimensionless equation which captures the relevant dynamical properties shared by these systems. Van der Pol's contributions during the period of 1926-1930 were investigated to show how, with Le Corbeiller's help, he popularized the "relaxation oscillations" using the previous experiments as examples and, turned them into a concept.

Prediction of the vibro-acoustic behavior of a submerged shell non periodically stiffened by internal frames.

This paper describes the development of a numerical model to predict the vibro-acoustic behavior of an externally fluid loaded shell with non-uniformly space stiffeners and transversal bulkheads. This model constitutes an extension of the existing semi-analytic capability in predicting the acoustics of axisymmetric structures. It is based on the circumferential admittance approach (CAA) which consists in substructuring the problem so that the fluid loaded shell constitutes one subsystem and the frames constitute other independent subsystems. These subsystems are coupled together by assembling the circumferential admittances that characterize each uncoupled subsystem. Different numerical approaches can be used to estimate these admittances. The standard finite element code is well adapted for evaluating the admittances of the internal frames whatever their cross-section geometries and material properties. Classical discretization methods such as finite elements and boundary elements are too time-consuming for the fluid loaded shell. To avoid this obstacle, three different approaches with different degrees of approximation are proposed to estimate the shell admittances. Comparisons with a reference case are proposed to evaluate the accuracy and the efficiency of each of these three approaches. With the optimal approach, CAA gives very good results in satisfactory computing time. It is well-adapted for analyzing the behavior of a submarine pressure hull in a wide frequency range of interest.