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Non Linear Physics Group - Eric Falcon

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Solitary waves and Nonlinear waves  (papers by our group)

Depression solitary wave

160 years after the first observation of a solitary wave hump (positive) on the surface of water, we observed for the first time a solitary wave of depression type (negative). It was nevertheless known since 1895 that dispersion could change sign, and thus the shape of the wave (positive or negative) if the effect of the surface tension is important. These results were widely commented in the scientific press.    MORE and papers

Axisymmetric solitons

Solitary waves or solitons are localized nonlinear waves that propagate almost without deformation due to the balance between the nonlinearity and the dispersion. Solitons are ubiquitous in hydrodynamics, optics and condensed matter. However, most of them propagates within a quasi-one-dimensional plane system. Observation of axisymmetric solitary waves is much more scarce. We have designed an experiment to observe axisymmetric solitary waves on the surface of a cylindrical magnetic fluid layer. Generally, in a usual fluid, a cylindrical fluid layer is unstable and droplets appear (Rayleigh-Plateau instability). By using a ferrofluid (a colloidal suspension of magnetic nanoparticles), it is possible to stabilize this cylindrical fluid layer. To wit, a metallic tube carrying an electrical current creates a magnetic field which stabilizes the cylindrical layer of ferrofluid around the tube due to the magnetic centripetal force. Both the shape and the speed of the solitary waves are modified by the strength of the magnetic field. Such a system allows us to observe for the first time the axisymmetric magnetic solitary waves predicted theoretically in the 80s. The study of collisions between these new type of solitary waves should be of particular interest.    MORE and papers

Sommerfeld precursors

  Sommerfeld precursors
One feature of the propagation of linear waves in dispersive medium is the existence of precursors (or forerunners). This terminology traces back to the fact that they generally arrive earlier than the main signal. This transient response is due to the propagation of the fastest high frequency components of the spectrum of the initial excitation. Although predicted since 1914 by Sommerfeld and Brillouin, the experimental observations remain rare and qualitative, and relate to mainly the electromagnetic waves in a dielectric medium.

We observed two types of Sommerfeld precursors on the surface of a layer of mercury. They are interpreted within the framework of the analysis first introduced by Sommerfeld and Brillouin. This study also makes it possible to connect the precursor concept of electromagnetic waves to the well-known transient phenomena of hydrodynamic surface waves, and their applications to the submarine eruptions.  MORE and papers



Solitary waves in a chain of beads  

Dynamical behaviors linked to the contact between beads (Hertz contact):  
Collective processes of collision and solitary waves propagation in granular media.


PUBLICATIONS on Solitary Waves and Nonlinear Waves

Surface waves:

For wave turbulence papers see here


11. M. F. Bonnefoy, A. Tikan, F. Copie, P. Suret, G. Ducrozet, G. Pradehusai, G. Michel, A. Cazaubiel, E. Falcon, G. El & S. Randoux 2019
submitted to Physical Review Fluids
(2019)
From Benjamin-Feir instability to focusing dam breaks in water waves

13. A. Cazaubiel, G. Michel, S. Lepot, B. Semin, S. Aumaître, M. Berhanu, F. Bonnefoy & E. Falcon 2018
      Physical Review Fluids 3, 114802 (2018)
      Coexistence of solitons and extreme events in deep water surface waves

12.
T. Jamin, L. Gordillo, G. Ruiz Chavarria, M. Berhanu & E. Falcon 2015
     
Proceedings of the Royal Society A 471, 20150069 (2015)
     
Experiments on generation of surface waves by an underwater moving bottom

11. L. Deike, J.-C. Bacri & E. Falcon 2013
      Nonlinear waves on the surface of a fluid covered by an elastic sheet
      Journal of Fluid Mechanics 733, 394 (2013)

10. Bourdin, E, Bacri, J.-C. & Falcon E. 2010:
      
Observation of axisymmetric solitary waves on the surface of a ferrofluid,
       Physical Review Letters
104, 094502 (2010)

9. Falcon, E., Laroche, C. & Fauve, S. 2003:
        Observation of Sommerfeld precursors on a fluid surface
        Physical Review Letters 91, 064502 (2003)

8. Falcon, E., Laroche, C. & Fauve, S. 2003:
        Observation d'ondes solitaires dépressions à la surface d'une fine couche de fluide
        in 6ème Rencontre du Non-Linéaire 2003, Non Linéaire Publications , Orsay, pp. 119-124, (2003) (in french).

7. Falcon, E., Laroche, C. & Fauve, S. 2002:
        Observation of a depression solitary surface waves on a thin fluid layer
        Physical Review Letters 89, 204501 (2002)

Internal Waves:

6. Gostiaux, L.,  Dauxois T., Falcon, E. & Garnier, N. 2005:
        Mesure quantitative de gradients de densité en fluides stratifiés bi-dimensionnels
        Actes du Colloque FLUVISU 11, 7-9 Juin 2005 ECL, Ecully, France (2005) (in French)

5. Gostiaux, L.,  Dauxois T. & Falcon, E. 2005:
        Réflexion critique d'ondes internes de gravité en fluides stratifiés
         in 8ème Rencontre du Non-Linéaire 2005, Non Linéaire Publications, Orsay, pp. 103-108 (2005) (in french)

4.
Dauxois, T., Didier, A. & Falcon, E. 2004:
        Observation of near-critical reflection of internal waves in a stably stratified fluid
        Physics of Fluids 16,  1936-1941 (2004)

In granular chain:

3. Falcon, E. 1997:
Comportements dynamiques associés au contact de Hertz : processus collectifs de collision et propagation d'ondes solitaires dans les milieux granulaires.
PhD Thesis Université Claude Bernard Lyon I (1997) (in french).

2. Coste, C., Falcon, E. & Fauve, S. 1997:
Solitary waves in a chain of beads under Hertz contact.
Physical Review E56, 6104-6117 (1997).

1. Coste, C., Falcon, E. & Fauve, S. 1995:
Propagations d'ondes non-linéaires dans une chaîne de billes en contact de Hertz.
in Petit, C., Pijaudier-Cabot, G. & Reynouard, J.-M., editors,
Des géomatériaux aux ouvrages : expérimentations et modélisations, 33-52. Hermes, Paris (1995) (in french).

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