DOI

1

Suction in Darcy and Stokes interfacial flows: Maximum growth rate versus minimum dissipation - Ben Amar, M. and Boudaoud, A.

EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS 166, 83-88 (2009)

Abstract : Two-dimensional flows with suction or mass loss are investigated within Darcy's or Stokes' framework. Examples include a Hele-Shaw cell with a lifted plate or extraction of lipids from a lipid bilayer. An initially circular patch ret-racts due to the suction and might undergo an instability whereby it becomes undulating. The selection of the wavelength of undulations is investigated with the help of an extremum principle, the minimization of the generalized dissipation, from which derive the flow equations.

EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS 166, 83-88 (2009)

Abstract : Two-dimensional flows with suction or mass loss are investigated within Darcy's or Stokes' framework. Examples include a Hele-Shaw cell with a lifted plate or extraction of lipids from a lipid bilayer. An initially circular patch ret-racts due to the suction and might undergo an instability whereby it becomes undulating. The selection of the wavelength of undulations is investigated with the help of an extremum principle, the minimization of the generalized dissipation, from which derive the flow equations.

DOI

2

Thermalization of incoherent nonlinear waves - Picozzi, A. and Barviau, B. and Kibler, B. and Rica, S.

EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS 173, 313-340 (2009)

Abstract : The subject of incoherent nonlinear optics received a renewed interest since the first experimental demonstration of incoherent solitons in slowly responding photorefractive crystals. Several theories have been successfully developed to provide a detailed description of the dynamics of incoherent optical solitons. However, such theories leave unanswered the question regarding the long term evolution of a partially incoherent optical field propagating in a nonlinear medium. In analogy with kinetic gas theory, an incoherent optical field evolves, owing to nonlinearity, towards a thermodynamic equilibrium state. Wave turbulence theory describes the essential properties of this irreversible process of thermal wave relaxation to equilibrium. Such irreversible behavior is expressed by a H-theorem of entropy growth, whose origin is analogous to the celebrated Boltzmann's H-theorem. In this review we analyze the thermalization of incoherent nonlinear optical fields in various circumstances. We shall begin with the simplest case where the optical field is ruled by the scalar NonLinear Schrodinger (NLS) equation. In this case wave thermalization is characterized by a condensation process of the optical field, whose thermodynamic properties are analogous to those of Bose-Einstein condensation, despite the fact that the considered optical wave is completely classical. We then study the thermalization of an ensemble of incoherent fields governed by the vector NLS equation. The influence of the relative intensity of the coupled fields reveals the existence of a process of coherence absorption: The condensation of the optical field is induced by the presence of another small-amplitude field, which absorbs almost all the noise of the system. Such a coherence absorption effect is shown to also occur in thermal quantum Bose gases. The influence of convection (group-velocity difference) on the thermalization process is also analyzed. A set of incoherent wave-packets is shown to irreversibly evolve towards an equilibrium state in which they propagate with an identical group-velocity. This velocity-locking effect has a thermodynamic origin and thus appears as a generic property of a system of incoherent nonlinear waves. The influence of a coherent coupling on wave thermalization leads to an unexpected process of spontaneous polarization of unpolarized incoherent light, without loss of energy. Finally, the influence of higher-order dispersion effects on optical thermalization is responsible for a dramatic spectral broadening phenomenon known as supercontinuum generation. This reveals that supercontinuum generation may be regarded as a consequence of the natural thermalization of an optical field to equilibrium. We finally show that the thermodynamic properties of incoherent nonlinear waves may be analyzed by means of the fundamental T dS equation of thermodynamics.

EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS 173, 313-340 (2009)

Abstract : The subject of incoherent nonlinear optics received a renewed interest since the first experimental demonstration of incoherent solitons in slowly responding photorefractive crystals. Several theories have been successfully developed to provide a detailed description of the dynamics of incoherent optical solitons. However, such theories leave unanswered the question regarding the long term evolution of a partially incoherent optical field propagating in a nonlinear medium. In analogy with kinetic gas theory, an incoherent optical field evolves, owing to nonlinearity, towards a thermodynamic equilibrium state. Wave turbulence theory describes the essential properties of this irreversible process of thermal wave relaxation to equilibrium. Such irreversible behavior is expressed by a H-theorem of entropy growth, whose origin is analogous to the celebrated Boltzmann's H-theorem. In this review we analyze the thermalization of incoherent nonlinear optical fields in various circumstances. We shall begin with the simplest case where the optical field is ruled by the scalar NonLinear Schrodinger (NLS) equation. In this case wave thermalization is characterized by a condensation process of the optical field, whose thermodynamic properties are analogous to those of Bose-Einstein condensation, despite the fact that the considered optical wave is completely classical. We then study the thermalization of an ensemble of incoherent fields governed by the vector NLS equation. The influence of the relative intensity of the coupled fields reveals the existence of a process of coherence absorption: The condensation of the optical field is induced by the presence of another small-amplitude field, which absorbs almost all the noise of the system. Such a coherence absorption effect is shown to also occur in thermal quantum Bose gases. The influence of convection (group-velocity difference) on the thermalization process is also analyzed. A set of incoherent wave-packets is shown to irreversibly evolve towards an equilibrium state in which they propagate with an identical group-velocity. This velocity-locking effect has a thermodynamic origin and thus appears as a generic property of a system of incoherent nonlinear waves. The influence of a coherent coupling on wave thermalization leads to an unexpected process of spontaneous polarization of unpolarized incoherent light, without loss of energy. Finally, the influence of higher-order dispersion effects on optical thermalization is responsible for a dramatic spectral broadening phenomenon known as supercontinuum generation. This reveals that supercontinuum generation may be regarded as a consequence of the natural thermalization of an optical field to equilibrium. We finally show that the thermodynamic properties of incoherent nonlinear waves may be analyzed by means of the fundamental T dS equation of thermodynamics.

DOI

3

Noise induced rolls propagation - Clerc, M. G. and Falcon, C. and Escaff, D. and Tirapegui, E.

EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS 143, 171-179 (2007)

Abstract : Interfaces in two-dimensional systems exhibit unexpected complex dynamical behaviors. We present a robust effect of noise in two dimensional extended systems: the motion of a static front connecting a stripe pattern with uniform state due to fluctuations. Numerical simulations of a prototype,model show that noise induces rolls propagation. To give a unified description of this robust effect we place ourselves at the onset of the spatial bifurcation and we derive an stochastic normal form, which exhibits the same dynamics. Close to the Maxwell point, an interface equation is obtained, the over damping forced Sine-Gordon model, which allows us to explain origin of this stochastic phenomenon.

EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS 143, 171-179 (2007)

Abstract : Interfaces in two-dimensional systems exhibit unexpected complex dynamical behaviors. We present a robust effect of noise in two dimensional extended systems: the motion of a static front connecting a stripe pattern with uniform state due to fluctuations. Numerical simulations of a prototype,model show that noise induces rolls propagation. To give a unified description of this robust effect we place ourselves at the onset of the spatial bifurcation and we derive an stochastic normal form, which exhibits the same dynamics. Close to the Maxwell point, an interface equation is obtained, the over damping forced Sine-Gordon model, which allows us to explain origin of this stochastic phenomenon.

DOI

4

Pattern formation and localized structures in monoatomic layer deposition - Clerc, M. G. and Tirapegui, E. and Trejo, M.

EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS 146, 407-425 (2007)

Abstract : We study the nonlinear robust behaviors of a model for the deposition of a monolayer of molecules on a surface which takes into account the interactions of the adsorbed molecules. The transport properties of the model lead to non Fickian diffusion. It is shown that we have generically Turing structures coexisting with uniform concentrations and consequently localized structures through the pinning mechanism. The characteristic lengths are in the nanometer region in agreement with recent experiments.

EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS 146, 407-425 (2007)

Abstract : We study the nonlinear robust behaviors of a model for the deposition of a monolayer of molecules on a surface which takes into account the interactions of the adsorbed molecules. The transport properties of the model lead to non Fickian diffusion. It is shown that we have generically Turing structures coexisting with uniform concentrations and consequently localized structures through the pinning mechanism. The characteristic lengths are in the nanometer region in agreement with recent experiments.

DOI

5

Patterns and supersolids - Josserand, C. and Pomeau, Y. and Rica, S.

EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS 146, 47-61 (2007)

Abstract : In the frame of the Gross - Pitaevskii equation with a non- local interaction term we study the crystallization induced by the non- local interaction and its connection with the theory of supersolids. The crystallization is well understood as the search of a ground- state of a certain energy functional, and uses the techniques of pattern- formation in the weak ( but finite) amplitude limit. In two space dimensions an hexagonal pattern is displayed, however, in three space dimensions density modulation displays an hexagonal- close- packing or hcp structure. We derive, using the technique of homogenization, an effective Lagrangian that provides the long- wave slow dynamics for the local density variations, the global wavefunction phase, and for the crystal deformation. As a classical crystal, our supersolid displays shear and compression waves for the elastic deformations, however the later are coupled with the wave function phase and the local density. Finally the system presents the quite remarkable property of non- classical rotational inertia ( NCRI) under rotation. Indeed under an uniform slow rotation the effective moment of inertia is less than the one of a classical rigid body.

EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS 146, 47-61 (2007)

Abstract : In the frame of the Gross - Pitaevskii equation with a non- local interaction term we study the crystallization induced by the non- local interaction and its connection with the theory of supersolids. The crystallization is well understood as the search of a ground- state of a certain energy functional, and uses the techniques of pattern- formation in the weak ( but finite) amplitude limit. In two space dimensions an hexagonal pattern is displayed, however, in three space dimensions density modulation displays an hexagonal- close- packing or hcp structure. We derive, using the technique of homogenization, an effective Lagrangian that provides the long- wave slow dynamics for the local density variations, the global wavefunction phase, and for the crystal deformation. As a classical crystal, our supersolid displays shear and compression waves for the elastic deformations, however the later are coupled with the wave function phase and the local density. Finally the system presents the quite remarkable property of non- classical rotational inertia ( NCRI) under rotation. Indeed under an uniform slow rotation the effective moment of inertia is less than the one of a classical rigid body.