arXiv subjects

P. Coullet

Publications and source records attributed to P. Coullet.

3 recordsLinked to original sources

arXiv2005

How much information can one store in a non-equilibrium medium?

It has recently been emphasized again that the very existence of stationary stable localized structures with short range interactions might allow to store information in non-equilibrium media, opening new perspectives on information storage. We show how to use generalized topological entropies to measure aspects of the quantities of storable and non-storable information. This leads us to introduce a measure of the long term stably storable information. As a first example to illustrate these concepts, we revisit a mechanism for the appearance of stationary stable localized structures that is related to the stabilization of fronts between structured and unstructured states (or between differently structured states).

nlin.CD↗

arXiv2004

Hydro-dynamical models for the chaotic dripping faucet

We give a hydrodynamical explanation for the chaotic behaviour of a dripping faucet using the results of the stability analysis of a static pendant drop and a proper orthogonal decomposition (POD) of the complete dynamics. We find that the only relevant modes are the two classical normal forms associated with a Saddle-Node-Andronov bifurcation and a Shilnikov homoclinic bifurcation. This allows us to construct a hierarchy of reduced order models including maps and ordinary differential equations which are able to qualitatively explain prior experiments and numerical simulations of the governing partial differential equations and provide an explanation for the complexity in dripping. We also provide a new mechanical analogue for the dripping faucet and a simple rationale for the transition from dripping to jetting modes in the flow from a faucet.

physics.flu-dyn↗

arXiv2001

Zig-zag instability of an Ising wall in liquid crystals

We present a theoretical explanation for the interfacial zigzag instability that appears in anisotropic systems. Such an instability has been experimentally highlighted for an Ising wall formed in a nematic liquid crystal cell under homeotropic anchoring conditions. From an envelope equation, relevant close to the Freedericksz transition, we have derived an asymptotic equation describing the interface dynamics in the vicinity of its bifurcation. The asymptotic limit used accounts for a strong difference between two of the elastic constants. The model is characterized by a conservative order parameter which satisfies a Cahn-Hilliard equation. It provides a good qualitative understanding of the experiments.

nlin.PS↗