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The story of wave-particle duality in quantum mechanics has been told a thousand times. This modest contribution is to get back to a few points, including memories of a discussion we had on a possible experimental evidence of quantum effects at macroscopic scale, but in a way totally unrelated to the experiments he and his group made quite later to exhibit a model of wave-particle duality. The more general question of interpreting/understanding quantum mechanics will be also scrutinized once more.

Among theories of the physical world, quantum mechanics remains a topic of lively discussions on its so-called interpretation. For some it remains an open question to understand how deterministic equations of this theory, as established long ago, may combine with a fundamental uncertainty. We consider the process of spontaneous emission by an atom interacting with infinite number of degrees of freedom of the electromagnetic field. There is uncertainty in the evolution of the photo-emission process which was characterized as Markovian by using the equations of quantum mechanics when the decay of the atom is due to the coupling with the vacuum field. The Markovian property leads us naturally to describe spontaneous emission by using the classical Kolmogorov equation for the probability evolution of a parameter defining the state of the atom. We explain that Everett’s many-worlds interpretation weld together our description, and appears therefore as a consequence of the equations of quantum mechanics, that solves in this case the riddle of deterministic equations describing random events.

A common observation is the one of reflection of the Sun or the Moon by the slightly perturbed surface of water. In ”Impression, soleil levant”, now in Marmottant museum in Paris, Monet painted the luminous stripe resulting of this reflection when the source is low on the horizon. As we explain this stripe originates from the fluctuations of the angle of the reflecting surface when they are big enough to spread the multiple images to make them overlap, which requires that the fluctuations of the surface angle are of the same order as the angle of the Sun (or Moon) above the horizon. At higher angle the stripe become a set of non overlapping points representing each the reflected image of the source. This makes an interesting percolation transition by a continuous change of a parameter.

Following the idea that dissipation in turbulence at high Reynolds number is dominated by singular events in space–time and described by solutions of the inviscid Euler equations, we draw the conclusion that in such flows, scaling laws should depend only on quantities appearing in the Euler equations. This excludes viscosity or a turbulent length as scaling parameters and constrains drastically possible analytical pictures of this limit. We focus on the drag law deduced by Newton for a projectile moving quickly in a fluid at rest. Inspired by this Newton's drag force law (proportional to the square of the speed of the moving object in the limit of large Reynolds numbers), which is well verified in experiments when the location of the detachment of the boundary layer is defined, we propose an explicit relationship between the Reynolds stress in the turbulent wake and quantities depending on the velocity field (averaged in time but depending on space). This model takes the form of an integrodifferential equation for the velocity which is eventually solved for a Poiseuille flow in a circular pipe. [ABSTRACT FROM AUTHOR]

Capillarity's modern applications are found in fields ranging from biology and oceanography to propulsion, material science, and novel devices, two centuries after seminal work on capillary phenomenon by Pierre-Simon Laplace and Thomas Young. Various applications and the future research in capillary phenomena are discussed.

The present understanding of supernova explosion of massive stars as a two-step process, with an initial gravitational collapse toward the center of the star followed by an expansion of matter after a bouncing on the core, meets several difficulties. We show that it is not the only possible one: a simple model based on fluid mechanics, catastrophe theory, and stability properties of the equilibrium state shows that one can have also a simultaneous inward/outward motion in the early stage of the instability of the supernova described by a dynamical saddle-center bifurcation. The existence of this simultaneous inward/outward motion is sensitive to the model in such systems with long-range interactions. If a constant temperature is assumed (canonical ensemble), an overall inward motion occurs, but if one imposes with the same equation of state the constraint of energy conservation (microcanonical ensemble) there is an inward velocity field near the center of the star together with an outward velocity field in the rest of the star. We discuss the expansion stage of the remnants away from the collapsed core, and propose a new explanation for the formation of shock waves in the ejecta which differs from the usual Sedov–Taylor self-similar description. [ABSTRACT FROM AUTHOR]