Raúl Montagne

Simple model for active nematics: quasi-long-range order and giant fluctuations.

We propose a simple microscopic model for active nematic particles similar in spirit to the Vicsek model for self-propelled polar particles. In two dimensions, we show that this model exhibits a Kosterlitz-Thouless-like transition to quasi-long-range orientational order and that in this nonequilibrium context, the ordered phase is characterized by giant density fluctuations, in agreement with the predictions of Ramaswamy et al.

Cross-Wavelet Bias Corrected by Normalizing Scales

AbstractThe cross-wavelet transform (XWT) is a powerful tool for testing the proposed connections between two time series. Because of XWT’s skeletal structure, which is based on the wavelet transform, it is suitable for the analysis of nonstationary periodic signals. Recent work has shown that the power spectrum based on the wavelet transform can produce a deviation, which can be corrected by choosing a proper rectification scale. In this study, it is shown that the standard application of the XWT can also lead to a biased result. A corrected version of the standard XWT was constructed using the scale of each series as normalizing factors. This correction was first tested with an artificial example involving two series built from combinations of two harmonic series with different amplitudes and frequencies. The standard XWT applied to this example produces a biased result, whereas the correct result is obtained with the use of the proposed normalization. This analysis was then applied to a real geophysica...

Collective Motion of Self-Propelled Particles with Memory

We show that memory, in the form of underdamped angular dynamics, is a crucial ingredient for the collective properties of self-propelled particles. Using Vicsek-style models with an Ornstein-Uhlenbeck process acting on angular velocity, we uncover a rich variety of collective phases not observed in usual overdamped systems, including vortex lattices and active foams. In a model with strictly nematic interactions the smectic arrangement of Vicsek waves giving rise to global polar order is observed. We also provide a calculation of the effective interaction between vortices in the case where a telegraphic noise process is at play, explaining thus the emergence and structure of the vortex lattices observed here and in motility assay experiments.

Two-layer stratified flows over pronounced obstacles at low-to-intermediate Froude numbers

Two-layer stratified flows over abrupt topographic obstacles, simulating relevant situations in oceanographic problems, are investigated numerically and experimentally in a simplified two-dimensional situation. Experimental results and numerical simulations are presented at low-to-intermediate Froude numbers for two different obstacles: one semicylindrical and the other prismatic. In both cases, four different flow regimes downstream of the obstacles are found: (I) subcritical flow, (II) internal hydraulic jump, (III) Kelvin–Helmholtz instability at the interface, and (IV) shedding of billows. The critical values of the Froude number for the transition between different regimes depend strongly on the shape of the obstacle. In regime (III), we show that the characteristics of the lee wave that appears past the obstacle can be explained with a theoretical stability analysis. Almost independence of the vortex shedding frequency with upstream velocity is observed and explained.

Diffusion Parameter Control of Spatiotemporal Chaos

The stabilization of periodic solutions in the regime of spatiotemporal chaos through a diffusion parameter control is studied. We show that unstable plane waves in the Complex Ginzburg–Landau equation can be effectively stabilized in choatic regimes such as phase turbulence and spatiotemporal intermittency or defect turbulence.

FREQUENCY TRANSITION OF COHERENT STRUCTURES IN FARADAY SURFACE WAVES

Proper Orthogonal Decomposition (POD) was used as a suitable tool to characterize the evolution of fingers regime in Faraday instability. The transition from harmonic to subharmonic resonant finger behavior was thus studied. A cluster algorithm and Voronoi neighbor statistics were used to characterize the surface peak distribution for the principal spatial pattern. The structural transition was analyzed for varying acceleration amplitude used as system control parameter.

Dynamic spectral analysis of phase turbulence

We analyze the time fluctuations associated to the power spectrum of a finite system governed by the complex Ginzburg–Landau equation (CGLE) in the phase turbulence region. It is shown that, for any given value of the parameters of the CGLE, these fluctuations follow an exponential law with the wavenumber. The exponent, α, is such that α→0 indicating a critical behavior when the system is approaching the defect turbulence region. On the contrary α→∞ near the Benjamin–Feir line.

Controlling spatio-temporal chaos

Several mechanisms have been proposed to control the spatio-temporal chaos. An analytical and numerical insight is given for the control of a vector field in an extended system modeled by a vector complex Ginzburg–Landau equation (VCGLE). We show how a non-linear diffraction term stabilizes unstable polarized standing waves and linearly polarized traveling waves in a chaotic scenery.

CONTROLLING SPATIOTEMPORAL CHAOS IN OPTICAL SYSTEMS

We investigate analytically and numerically a nonfeedback control technique for spatially extended systems. The method is suited for systems where some parameters can be modified. We apply the control scheme to a model used to describe vectorial transverse pattern formation in nonlinear optical systems, the Vector Complex Ginzburg–Landau Equation (VCGLE). Our scheme stabilizes a periodic regime where otherwise a chaotic regime is observed. We confirm by analytical calculation and direct simulation how this scheme, based in the use of a nonlinear diffraction term, stabilizes unstable polarized standing waves and linearly polarized traveling waves in a chaotic scenery.

Chaos-induced coherence in two independent food chains.

Coherence evolution of two food web models can be obtained under the stirring effect of chaotic advection. Each food web model sustains a three-level trophic system composed of interacting predators, consumers, and vegetation. These populations compete for a common limiting resource in open flows with chaotic advection dynamics. Here we show that two species (the top predators) of different colonies chaotically advected by a jetlike flow can synchronize their evolution even without migration interaction. The evolution is characterized as a phase synchronization. The phase differences (determined through the Hilbert transform) of the variables representing those species show a coherent evolution.