Valérie Messager

Near-critical-angle scattering for the characterization of clouds of bubbles: particular effects

We report experimental investigations on the influence of various optical effects on the far-field scattering pattern produced by a cloud of optical bubbles near the critical scattering angle. Among the effects considered, there is the change of the relative refractive index of the bubbles (gas bubbles or some liquid-liquid droplets), the influence of intensity gradients induced by the laser beam intensity profile and by the spatial filtering of the collection optics, the coherent and multiple scattering effects occurring for densely packed bubbles, and the tilt angle of spheroidal optical bubbles. The results obtained herein are thought to be fundamental for the development of future works to model these effects and for the extension of the range of applicability of an inverse technique (referenced herein as the critical angle refractometry and sizing technique), which is used to determine the size distribution and composition of bubbly flows.

Henri Poincaré and the principle of relativity

Often considered as the last ‘encyclopedist’, Henri Poincaré died one hundred years ago. If he was a prominent man in 1900 French Society, his heritage is not so clearly recognised, particularly in France. Among his too often misunderstood works is his contribution to the theory of relativity, mainly because it is almost never presented within Poincarés general approach to science, including his philosophical writings. Our aim is therefore to provide an historical account of the main steps (experimental as well as theoretical) which led Poincaré to contribute to the theory of relativity. Starting from the optical experiments which led to the inconsistency of the classical (Galilean) composition law for velocities to explain light propagation, we introduce the FitzGerald and Lorentz contraction which was viewed as the ‘sole hypothesis’ to explain the Michelson and Morley experiment. We then show that Poincarés contribution starts with a discussion of the principles governing the mechanics and was built step by step up to express in all its generality the principle of relativity. Poincaré thus showed the invariance of the Maxwell equations under the Lorentz transformation. In doing so, he also discovered the right composition law for velocities. Poincarés approach to philosophy is detailed to help the reader to understand what a theory meant to him.

Automatic Sleep Scoring from a Single Electrode Using Delay Differential Equations

Sleep scoring is commonly performed from electroencephalogram (EEG), electrooculogram (EOG), and electromyogram (EMG) to produce a so-called hypnogram. A neurologist thus visually encodes each epoch of 30 s into one of the sleep stages (wake, REM sleep, S1, S2, S3, S4). To avoid such a long process (about 3–4 hours) a technique for automatic sleep scoring from the signal of a single EEG electrode located in the C3/A2 area using nonlinear delay differential equations (DDEs) is presented here. Our approach considers brain activity as resulting from a dynamical system whose parameters should vary according to the sleep stages. It is thus shown that there is at least one coefficient that depends on sleep stages and which can be used to construct a hypnogram. The correlation between manual hypnograms and the coefficient evolution is around 80%, that is, about the inter-rater variability. In order to rank sleep quality from the best to the worst, we introduced a global sleep quality index which is used to compare manual and automatic sleep scorings, thus using our ability to state about sleep quality that is the final goal for physicians.

A genesis of special relativity

The genesis of special relativity is intimately related to the development of the theory of light propagation. When optical phenomena were described, there are typically two kinds of theories: (i) One based on light rays and light particles and (ii) one considering the light as waves. When diffraction and refraction were experimentally discovered, light propagation became more often described in terms of waves. Nevertheless, when attempts were made to explain how light was propagated, it was nearly always in terms of a corpuscular theory combined with an ether, a subtle medium supporting the waves. Consequently, most of the theories from Newtons to those developed in the 19th century were dual and required the existence of an ether. We therefore used the ether as our Ariadne thread for explaining how the principle of relativity became generalized to the so-called Maxwell equations around the 1900s. Our aim is more to describe how the successive ideas were developed and interconnected than framing the context in which these ideas arose.