Papers by germain rousseaux
XIVèmes Journées, Toulon, 2016
We present an interdisciplinary review of the generalized Cerenkov emission of radiation from uni... more We present an interdisciplinary review of the generalized Cerenkov emission of radiation from uniformly moving sources in the different contexts of classical electromagnetism, superfluid hydrodynamics, and classical hydrodynamics. The details of each specific physical systems enter our theory via the dispersion law of the excitations. A geometrical recipe to obtain the emission patterns in both real and wavevector space from the geometrical shape of the dispersion law is discussed and applied to a number of cases of current experimental interest. Some consequences of these emission processes onto the stability of condensed-matter analogs of gravitational systems are finally illustrated.
Fluke oscillations of cetaceans (whales, dolphins and porpoises) imprint the ocean surface with a... more Fluke oscillations of cetaceans (whales, dolphins and porpoises) imprint the ocean surface with an oval patch that surface waves cannot enter. Scientists have hypothesized that modification of surface tension by surfactants creates flukeprints. Here, we show, on the contrary, that the formation of flukeprint is primarily due to a wave-current interaction problem. We provide Particle Image Velocimetry measurements of anisotropy and vorticity in the flow generated by a mock whale fluke in a laboratory experiment. We explain for the first time why long gravity waves enter the flukeprint, whereas short gravity waves are blocked.
ESAIM: Control, Optimisation and Calculus of Variations, 2015
ABSTRACT We determine the parametric hull of a given volume which minimizes the total water resis... more ABSTRACT We determine the parametric hull of a given volume which minimizes the total water resistance for a given speed of the ship. The total resistance is the sum of Michell's wave resistance and of the viscous resistance, approximated by assuming a constant viscous drag coefficient. We prove that the optimized hull exists, is unique, symmetric, smooth and that it depends continuously on the speed. Numerical simulations show the efficiency of the approach, and complete the theoretical results.
We present the theory, the design and the discussion of an experiment which allows to choose betw... more We present the theory, the design and the discussion of an experiment which allows to choose between the local formulation of Riemann-Lorenz and the non-local formulation of Heaviside-Hertz in order to describe Classical Electromagnetism.
Physics of Fluids, 2014
ABSTRACT
Lecture Notes in Physics, 2013
The European Physical Journal Plus, 2013
A flat particle bed under an oscillatory viscous flow is generally unstable and leads to the form... more A flat particle bed under an oscillatory viscous flow is generally unstable and leads to the formation of ripples. Such patterns are encountered in coastal regions where sea waves in shallow waters induce a back and forth fluid motion on sandy sea beds. Using a cylindrical oscillating tank, we have studied in laboratory, at very high resolution, the wavelength selection, the morphology and the temporal evolution of theses ripples . Three dynamical stages can be observed. Initially, the rolling of individual grains on the flat sand bed induces small rolling grain ripples. At this stage the wavelength selection depends only on the grain diameter, the viscous boundary layer and the viscous length. In a second stage, the ripples follow a coarsening process which increase both the height and the wavelength of the patterns. For few cases, especially close to the onset of ripple formation, a logarithmic growth of the wavelength is observed. Then, if we wait long enough the system always evolves to a final vortex ripple state which is mainly controlled by the amplitude of the fluid excursion.
Nonlinear Dynamics, 2009
Here, we make the theoretical and numerical analysis of the non-linear equation describing the ev... more Here, we make the theoretical and numerical analysis of the non-linear equation describing the evolution of the "bead, hoop and spring" (BHS) dynamical system derived by Ochoa and Clavijo in (Eur. J. Phys. 27:1277Phys. 27: -1288Phys. 27: , 2006. In particular, we solve by standard techniques of non-linear physics an approximation of their equation neglecting the centrifugal effect before giving a more mathematical and exact treatment. The analogy with phase transitions is underlined. We point out the existence of finite-time singularities in the phase-space and we derive a criterion for possible oscillations.
Eprint Arxiv Physics 0503108, Mar 13, 2005
Several mathematical formulae are used nowadays in order to compute a magnetic torque. We demonst... more Several mathematical formulae are used nowadays in order to compute a magnetic torque. We demonstrate that its more general expression is the vectorial product of the current density with the vector potential. We associate this Larmor's torque with Amp\`{e}re's force and more specifically with Helmholtz mechanical tension, which is at the origin of the longitudinal stresses in "open" circuits carrying current. We show that Amp\`{e}re's force enters into the realm of Newtonian Electrodynamics and we explain the absence of contradiction with special relativity. Hence, we provide for the first time a theoretical basis for the numerous experiments, which claimed to have demonstrated the existence of the longitudinal mechanical tension starting with the historical Amp\`{e}re's hairpin demonstration and the more modern ones of the Graneaus and of Saumont.
The compatibility "demonstrated" by Rovelli & al. between various "gauge conditions" both in Clas... more The compatibility "demonstrated" by Rovelli & al. between various "gauge conditions" both in Classical Electromagnetism and General Relativity can be better understood if one distinguishes "gauge conditions" of the solution type and "gauge conditions" of the constraint type.
European Journal of Physics, Mar 1, 2007
Here, we solve a simplified version (corresponding to oscillations with small amplitudes) of the ... more Here, we solve a simplified version (corresponding to oscillations with small amplitudes) of the nonlinear equation describing the evolution of the bead, hoop and spring problem derived by Ochoa and Clavijo (2006 Eur. J. Phys. 27 1277 88) with the so-called amplitude equation method. We point out the analogy with the equation derived by us previously in Rousseaux et al (2005 Eur. J. Phys. 26 1065 78) and which describes the nonlinear dynamics of a conical pendulum. Our comment illustrates the usefulness of nonlinear techniques for teachers, such as the amplitude equation formalism, since these can be applied to all nonlinear oscillators.
Eprint Arxiv Physics 0511047, Nov 5, 2005
Based on an analogy between Fluid Mechanics and Electromagnetism, we claim that the gauge conditi... more Based on an analogy between Fluid Mechanics and Electromagnetism, we claim that the gauge conditions of Classical Electromagnetism are not equivalent contrary to the common belief. These "gauges" are usually considered as mathematical conditions that one must specify in order to solve any electromagnetic problem. Here, the author shows that these conditions are physical constraints which can be interpreted as electromagnetic continuity equations. As a consequence, light cannot be considered as a pure transverse wave in vacuum from the point of view of the potentials. We discuss the (lack of) meaning of gauge transformations.
One of us (Y.P.) has shown the existence of a longitudinal component in the propagation of light ... more One of us (Y.P.) has shown the existence of a longitudinal component in the propagation of light waves on the basis of the kinematics underlying Poincar\'{e}'s ellipse. We show how this statement agrees with the electromagnetic theory. We recall that the second of us supports the existence of a "fine structure" of Electromagnetism that is, the co-existence of two theories, one based on the fields (Heaviside-Hertz) and the other on the potentials (Riemann-Lorenz). The existence of two different kinematics (the "fine structure" of Special Relativity : Einstein or Poincar\'{e}) corresponds to these two formulations of Classical Electromagnetism. With this goal in mind, we prove the relativistic covariance of the Helmholtz decomposition of the vector potential. This one translates into a generalized compensation for all directions of propagation, on the basis of the tangent to Poincar\'{e}'s ellipse, between the scalar potential and the longitudinal component of the vector potential. The adoption by Poincar\'{e} of the Lorenz gauge condition (with longitudinal and temporal components) is in contrast with the Einsteinian photon and the Einsteinian kinematics with only transversal components compatible with the choice of the "completed" Coulomb gauge condition (transverse gauge).
Eur J Phys, 2006
We discuss an article by Le Bellac and Lévy-Leblond in which they have identified two Galilean li... more We discuss an article by Le Bellac and Lévy-Leblond in which they have identified two Galilean limits of electromagnetism (1973 Nuovo Cimento B 14 217-33). We use their results to point out some confusion in the literature, and in the teaching of special relativity and electromagnetism. For instance, it is not widely recognized that there exist two well-defined non-relativistic limits, so that researchers and teachers are likely to utilize an incoherent mixture of both. Recent works have shed new light on the choice of gauge conditions in classical electromagnetism. We retrieve the results of Le Bellac and Lévy-Leblond first by examining orders of magnitudes and then with a Lorentz-like manifestly covariant approach to Galilean covariance based on a five-dimensional Minkowski manifold. We emphasize the Riemann-Lorenz approach based on the vector and scalar potentials as opposed to the Heaviside-Hertz formulation in terms of electromagnetic fields.
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Papers by germain rousseaux