Claudio Falcón

Additive Noise Induces Front Propagation

The propagation of a front connecting a stable homogeneous state with a stable periodic state in the presence of additive noise is studied. The mean velocity was computed both numerically and analitically. The numerics are in good agreement with the analitical prediction.

Capillary wave turbulence on a spherical fluid surface in low gravity

We report the observation of capillary wave turbulence on the surface of a fluid layer in a low-gravity environment. In such conditions, the fluid covers all the internal surface of the spherical container that is submitted to random forcing. The surface wave amplitude displays power law spectrum over two decades in frequency, corresponding to wavelength from millimeters to a few centimeters. This spectrum is found in roughly good agreement with wave turbulence theory. Such a large-scale observation without gravity waves has never been reached during ground experiments. When the forcing is periodic, two-dimensional spherical patterns are observed on the fluid surface such as subharmonic stripes or hexagons with wavelength satisfying the capillary wave dispersion relation.

Localized patterns and hole solutions in one-dimensional extended systems

The existence, stability properties, and bifurcation diagrams of localized patterns and hole solutions in one-dimensional extended systems is studied from the point of view of front interactions. An adequate envelope equation is derived from a prototype model that exhibits these particle-type solutions. This equation allow us to obtain an analytical expression for the front interaction, which is in good agreement with numerical simulations.

Localized states in bistable pattern forming systems

We present a unifying description close to a spatial bifurcation of localized states, appearing as large amplitude peaks nucleating over a pattern of lower amplitude. Localized states are pinned over a lattice spontaneously generated by the system itself. We show that the phenomenon is generic and requires only the coexistence of two spatially periodic states. At the onset of the spatial bifurcation, a forced amplitude equation is derived for the critical modes, which accounts for the appearance of localized peaks.

Fluctuations of energy flux in wave turbulence.

We report that the power driving gravity and capillary wave turbulence in a statistically stationary regime displays fluctuations much stronger than its mean value. We show that its probability density function (PDF) has a most probable value close to zero and involves two asymmetric roughly exponential tails. We understand the qualitative features of the PDF using a simple Langevin-type model.

Symmetry Induced Four-Wave Capillary Wave Turbulence

We report theoretical and experimental results on 4-wave capillary wave turbulence. A system consisting of two immiscible and incompressible fluids of the same density can be written in a Hamiltonian way for the conjugated pair (eta, Psi). Adding the symmetry z --> -z, the set of capillary waves display a Kolmogorov-Zakharov spectrum k(-4) in wave vector space and f(-8/3) in the frequency domain. The wave system is studied experimentally with two immiscible fluids of almost equal densities (water and silicon oil) where the capillary surface waves are excited by a low-frequency random forcing. The probability density function of the local wave amplitude shows a quasi-Gaussian behavior and the power spectral density is shows a power-law behavior in frequency with a slope of -2.75. Theoretical and experimental results are in fairly good agreement with each other.

Fluctuations of energy flux in a simple dissipative out-of-equilibrium system.

We report the statistical properties of the fluctuations of the energy flux in an electronic RC circuit driven with a stochastic voltage. The fluctuations of the power injected in the circuit are measured as a function of the damping rate and the forcing parameters. We show that its distribution exhibits a cusp close to zero and two asymmetric exponential tails, with the asymmetry being driven by the mean dissipation. This simple experiment allows one to capture the qualitative features of the energy flux distribution observed in more complex dissipative systems. We also show that the large fluctuations of injected power averaged on a time lag do not verify the fluctuation theorem even for long averaging time. This is in contrast to the findings of previous experiments due to their small range of explored fluctuation amplitude. The injected power in a system of N components either correlated or not is also studied to mimic systems with large number of particles, such as in a dilute granular gas.

Emergence of spatiotemporal dislocation chains in drifting patterns

One-dimensional patterns subjected to counter-propagative flows or speed jumps exhibit a rich and complex spatiotemporal dynamics, which is characterized by the perpetual emergence of spatiotemporal dislocation chains. Using a universal amplitude equation of drifting patterns, we show that this behavior is a result of a combination of a phase instability and an advection process caused by an inhomogeneous drift force. The emergence of spatiotemporal dislocation chains is verified in numerical simulations on an optical feedback system with a non-uniform intensity pump. Experimentally this phenomenon is also observed in a tilted quasi-one-dimensional fluidized shallow granular bed mechanically driven by a harmonic vertical vibration.

Effective-parametric resonance in a non-oscillating system

We present a mechanism for the generation of oscillations and nonlinear parametric amplification in a non-oscillating system, which we term effective-parametric resonance. Sustained oscillations appear at a controlled amplitude and frequency, related directly to the external forcing parameters. We present an intuitive explanation for this phenomenon, based on an effective equation for a driven oscillation and discuss its relation to other approaches. More precisely, a high-frequency forcing can generate an effective oscillator, which may have a parametric resonance with the applied forcing. We point out the main ingredients for the development of effective-parametric resonance in non-oscillating systems and show its existence in a simple model. Theoretically, we calculate the appearance of this nonlinear oscillation by computing its stability curve, which is confirmed by numerical simulations and experimental studies on a vertically driven pendulum.

Wave-vortex interaction

We present an experimental study of the effect of an electromagnetically generated vortex flow on parametrically amplified waves at the surface of a vertically vibrated fluid layer. The underlying vortex flow, generated by a periodic Lorentz force, creates spatiotemporal fluctuations that nonlinearly interact with the standing surface waves. We measure the power spectral density of the surface wave amplitude and we characterize the bifurcation diagram by recording the subharmonic response of the surface to the external vibration. We show that the parametric instability is delayed in the presence of spatiotemporal fluctuations due to the vortex flow. In addition, the dependence of the amplitude of the subharmonic response on the distance to the instability threshold is modified. This shows that the nonlinear saturation mechanism of the waves is modified by the vortex flow.