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It is well-known, since the works of Miche (1944) and Longuet-Higgins (1950), that, under a standing wave system, second-order pressures at twice the wave frequency penetrate the water column down to the sea-°oor, whatever the waterdepth.... more
It is well-known, since the works of Miche (1944) and Longuet-Higgins (1950), that, under a standing wave system, second-order pressures at twice the wave frequency penetrate the water column down to the sea-°oor, whatever the waterdepth. Recently Gu¶evel proposed that energy could be extracted from the waves with a heaving horizontal plate at the sea bottom, located next to a re°ective cli® or sea-wall, and tuned to oscillate at twice the wave frequency. Encouraging preliminary experiments were conducted in ACRI's wavetank (Lajoie et al. 2007). In this paper we address the theoretical modeling of wave energy extraction with such a device, in the asymptotic case when the waterdepth is very large compared to the wavelength. In section I we assume that the ¯rst-order wave system is little modi¯ed, i.e. the power taken from the waves is a small portion of the power carried by the incoming wave. In section II we relieve this assumption and we show that one hundred percent of the wav...
We demonstrate for the first time and unexpectedly that the Principle of Relativity dictates the choice of the "gauge conditions" in the canonical example of a Gauge Theory namely Classical Electromagnetism. All the known... more
We demonstrate for the first time and unexpectedly that the Principle of Relativity dictates the choice of the "gauge conditions" in the canonical example of a Gauge Theory namely Classical Electromagnetism. All the known "gauge conditions" of the literature are interpreted physically as electromagnetic continuity equations hence the "gauge fields". The existence of a Galilean Electromagnetism with TWO dual limits
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"Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is described by more variables than there are physically independent degree of freedom. The... more
"Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is described by more variables than there are physically independent degree of freedom. The physically meaningful degrees of freedom then reemerge as being those invariant under a transformation connecting the variables (gauge transformation). Thus, one introduces extra variables to make the description more transparent and brings in at the same time a gauge symmetry to extract the physically relevant content. It is a remarkable occurrence that the road to progress has invariably been towards enlarging the number of variables and introducing a more powerful symmetry rather than conversely aiming at reducing the number of variables and eliminating the symmetry" [1]. We claim that the potentials of Classical Electromagnetism are not indetermined with respect to the so-called gauge transformations. Indeed, these transformations raise paradoxes that imply their rejection. Nevertheless, the potentials are still indetermined up to a constant.
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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... 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.
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Research Interests:
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.
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)... 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.
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We study the hydrodynamic phenomenon of waves blocking by a countercurrent with the tools of dynamical systems theory. We show that, for a uniform background velocity and within the small wavelength approximation, the stopping of gravity... more
We study the hydrodynamic phenomenon of waves blocking by a countercurrent with the tools of dynamical systems theory. We show that, for a uniform background velocity and within the small wavelength approximation, the stopping of gravity waves is described by a stationary saddle-node bifurcation due to the spatial resonance of an incident wave with the converted "blueshifted" wave. We explain why the classical regularization effect of interferences avoids the height singularity in complete analogy with the intensity of light close to the principal arc of a rainbow. The application to the behavior of light near a gravitational horizon is discussed.
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We revisit from a modern viewpoint a graphical method of resolution of the Young–Laplace equation proposed by Thomson in 1886 and improved by Boys in 1893. This method, relying on some axisymmetry properties, was applied to the case of... more
We revisit from a modern viewpoint a graphical method of resolution of the Young–Laplace equation proposed by Thomson in 1886 and improved by Boys in 1893. This method, relying on some axisymmetry properties, was applied to the case of pendant drops, drops on a horizontal plane and meniscii. The several initials conditions necessitated a numerical implementation of the Thomson's algorithm,
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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... 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.
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"Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is described by more variables than there are physically independent degree of freedom. The... more
"Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is described by more variables than there are physically independent degree of freedom. The physically meaningful degrees of freedom then reemerge as being those invariant under a transformation connecting the variables (gauge transformation). Thus, one introduces extra variables to make the description more transparent and brings in at the same time a gauge symmetry to extract the physically relevant content. It is a remarkable occurrence that the road to progress has invariably been towards enlarging the number of variables and introducing a more powerful symmetry rather than conversely aiming at reducing the number of variables and eliminating the symmetry" [1]. We claim that the potentials of Classical Electromagnetism are not indetermined with respect to the so-called gauge transformations. Indeed, these transformations raise paradoxes that imply their rejection. Nevertheless, the potentials are still indetermined up to a constant.
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Research Interests:
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We study the propagation of surface waves on a current in the presence of an electromagnetic field. A horizontal (vertical) field strengthens (weakens) the counter-current which blocks the waves. We compute the phase space diagrams... more
We study the propagation of surface waves on a current in the presence of an electromagnetic field. A horizontal (vertical) field strengthens (weakens) the counter-current which blocks the waves. We compute the phase space diagrams (blocking velocities versus period of the waves) with and without surface tension. Three new dimensionless numbers are introduced to compare the relative strengths of gravity, surface tension and field effects. This work shows the importance of an electromagnetic field in order to design wave-breakers or in microfluidics applications.
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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"... 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.
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We have performed an experimental study of the transition of rolling-grain ripples toward vortex ripples. In particular, we have looked for the influence of the grains' diameter, the frequency of... more
We have performed an experimental study of the transition of rolling-grain ripples toward vortex ripples. In particular, we have looked for the influence of the grains' diameter, the frequency of oscillation, and the grains' cohesion. We demonstrate that the rolling-grain ripples are transient patterns which do appear as soon as we are close to the threshold for grain motion, whereas vortex ripples are always the final patterns observed and are the only patterns observed if one is far from the threshold for grain motion. Our results show that the "elasticity" (i.e., the tendency to modify the wavelength by either compression or dilatation) of the vortex ripples explains several discrepancies with respect to the observed evolutions and measurements reported so far in the literature.
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... Université de Nice - Sophia Antipolis, Laboratoire Jean-Alexandre Dieudonné, UMR 6621 CNRS-UNS Parc Valrose, 06108 Nice Cedex 02, France, EU ... However, in 1973, Michel Le Bellac and Jean-Marc Lévy-Leblond postulated the existence of... more
... Université de Nice - Sophia Antipolis, Laboratoire Jean-Alexandre Dieudonné, UMR 6621 CNRS-UNS Parc Valrose, 06108 Nice Cedex 02, France, EU ... However, in 1973, Michel Le Bellac and Jean-Marc Lévy-Leblond postulated the existence of a Galilean limit of Maxwell ...
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Research Interests:
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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)... 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.
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We report an experimental study of a binary sand bed under an oscillating water flow. The formation and evolution of ripples is observed. The appearance of a granular segregation is shown to strongly depend on the sand bed preparation.... more
We report an experimental study of a binary sand bed under an oscillating water flow. The formation and evolution of ripples is observed. The appearance of a granular segregation is shown to strongly depend on the sand bed preparation. The initial wavelength of the mixture is measured. In the final steady state, a segregation in volume is observed instead of a segregation at the surface as reported before. The correlation between this phenomenon and the fluid flow is emphasised. Finally, different ``exotic'' patterns and their geophysical implications are presented.
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We discuss the behaviour of massive modes near a horizon based on a study of the dispersion relation and wave packet simulations of the Klein-Gordon equation. We point out an apparent paradox between two (in principle equivalent) pictures... more
We discuss the behaviour of massive modes near a horizon based on a study of the dispersion relation and wave packet simulations of the Klein-Gordon equation. We point out an apparent paradox between two (in principle equivalent) pictures of black hole evaporation through Hawking radiation. In the picture in which the evaporation is due to the emission of positive-energy modes, one immediately obtains a threshold for the emission of massive particles. In the picture in which the evaporation is due to the absorption of negative-energy modes, such a threshold apparently does not exist. We resolve this paradox by tracing the evolution of the positive-energy massive modes with an energy below the threshold. These are seen to be emitted and move away from the black hole horizon, but they bounce back at a "red horizon" and are re-absorbed by the black hole, thus compensating exactly for the difference between the two pictures. For astrophysical black holes, the consequences are curious but do not affect the terrestrial constraints on observing Hawking radiation. For analogue gravity systems with massive modes, however, the consequences are crucial and rather surprising.
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Experimental studies are conducted to analyze dispersion and miscible viscous fingering of initially circular samples of a given solution displaced linearly at constant speed U by another solution in horizontal Hele-Shaw cells (two glass... more
Experimental studies are conducted to analyze dispersion and miscible viscous fingering of initially circular samples of a given solution displaced linearly at constant speed U by another solution in horizontal Hele-Shaw cells (two glass plates separated by a thin gap). In the stable case of a dyed water sample having the same viscosity as that of displacing nondyed water, we analyze the transition between dispersive and advective transport of the passive scalar displaced linearly. At low displacement speed and after a certain time, the length of the sample increases as a square root of time allowing to compute the value of a dispersion coefficient. At larger injection speed, the displacement remains advective for the duration of the experiment, with a length of the sample increasing linearly in time. A parametric study allows to gain insight into the switch from one regime to another as a function of the gap width of the cell. In the unstable case of viscous glycerol samples displaced by dyed water, the rear interface of the sample where less viscous water pushes more viscous glycerol is unstable with regard to viscous fingering. The interface deforms into fingers, the number and size of which depend on the viscosity ratio between the two solutions and on the displacement speed. We study the influence of these viscous fingering phenomena on the increased spreading of the sample for various mobility ratios and injection speeds.
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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... 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).
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We provide an experimental demonstration that the circular hydraulic jump represents a hydrodynamic white hole or gravitational fountain (the time-reverse of a black hole) by measuring the angle of the Mach cone created by an object in... more
We provide an experimental demonstration that the circular hydraulic jump represents a hydrodynamic white hole or gravitational fountain (the time-reverse of a black hole) by measuring the angle of the Mach cone created by an object in the "supersonic" inner flow region. We emphasise the general character of this gravitational analogy by showing theoretically that the white hole horizon constitutes a stationary and spatial saddle-node bifurcation within dynamical-systems theory. We also demonstrate that the inner region has a "superluminal" dispersion relation, i.e., that the group velocity of the surface waves increases with frequency, and discuss some possible consequences with respect to the robustness of Hawking radiation. Finally, we point out that our experiment shows a concrete example of a possible "transplanckian distortion" of black/white holes.
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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... 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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This work is an attempt to test the concept of hydrodynamic charge (analogous to the electric charge in Electromagnetism) in the simple case of a coherent structure such as the Burgers vortex. We provide experimental measurements of both... more
This work is an attempt to test the concept of hydrodynamic charge (analogous to the electric charge in Electromagnetism) in the simple case of a coherent structure such as the Burgers vortex. We provide experimental measurements of both the so-called Lamb vector and its divergence (the charge) by two-dimensional Particle Image Velocimetry. In addition, we perform a Helmholtz-Hodge decomposition of the Lamb vector in order to explore its topological features. We compare the charge with the well-known Q criterion in order to assess its interest in detecting and characterizing coherent structure. Usefulness of this concept in studies of vortex dynamics is demonstrated.
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Surface waves in classical fluids experience a rich array of black/white hole horizon effects. The dispersion relation depends on the characteristics of the fluid as well as on the fluid depth and the wavelength regime. We focus on the... more
Surface waves in classical fluids experience a rich array of black/white hole horizon effects. The dispersion relation depends on the characteristics of the fluid as well as on the fluid depth and the wavelength regime. We focus on the shallow-water regime, and discuss the experimental proof that the circular hydraulic jump marks the transition between a supercritical and a subcritical flow regime. This finally confirms a theoretical conjecture formulated by Lord Rayleigh nearly 100 years ago. It also confirms that the circular jump corresponds to the spontaneous formation of a hydrodynamic white hole, with interesting characteristics from the point of view of analogue gravity. We study the dispersive regime, mention some lessons about the trans-Planckian issue and describe possible directions for future work.
The kinematics of particles refer to events and tangent vectors, while that of waves refer to dual gradient planes. Special relativity [1-3] applies to both objects alike. Here we show that spacetime exchange symmetry [7] implicit in the... more
The kinematics of particles refer to events and tangent vectors, while that of waves refer to dual gradient planes. Special relativity [1-3] applies to both objects alike. Here we show that spacetime exchange symmetry [7] implicit in the SIdefinition of length based on the universal constant c has profound consequences at low velocities. Galilean physics, exact in the limit c \to \infty, is mirrored by a dual so-called Carrollian superluminal kinematics [4-6] exact in the limit c \to 0. Several new results follow. The Galilean limit explains mass conservation in Newtonian mechanics, while the dual limit is a kinematical prerequisite for wavelike tachyonic motion [8, 9]. As an example, the Land\'e paradox [19, 20] of waveparticle duality has a natural resolution within special relativity in terms of superluminal, particlelike waves. It is emphasized that internal particle energy mc^2 can not be ignored, while kinetic energy leads to an extended Galilei group. We also demonstrate that Maxwell's equations have magnetic and electric limits covariant under Galilean and Carrollian symmetry.
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ABSTRACT
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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... 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 longitudin...