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Updated: May 9, 2026

Evolution of Staircase Structures in Diffusive Convection

Evolution of Staircase Structures in Diffusive Convection

Published on: September 5, 2018

Noisy zigzag transition, fluctuations, and thermal bifurcation threshold.

Jean-Baptiste Delfau¹, Christophe Coste, Michel Saint Jean

¹Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|July 16, 2013

Summary

This study investigates the zigzag transition in particle systems, identifying a thermal threshold using noisy bifurcation theory. A divergence in fluctuation saturation time precisely defines this threshold, aligning with theoretical predictions.

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Area of Science:

Statistical Physics
Nonlinear Dynamics
Complex Systems

Background:

The zigzag transition in particle systems with screened electrostatic interactions is studied.
This transition at finite temperatures serves as a model for noisy supercritical pitchfork bifurcations.

Purpose of the Study:

To characterize the bifurcation region of the zigzag transition under thermal noise.
To precisely define and measure the thermal threshold influencing configurational phase transitions.

Main Methods:

Experimental measurements of transverse fluctuations in the particle system.
Analysis of fluctuation dynamics to identify the deterministic and thermal thresholds.
Application of noisy bifurcation theory for theoretical comparison.

Main Results:

The bifurcation region is fully described by analyzing transverse fluctuations.
A divergence in the saturation time of transverse fluctuations provides a precise definition of the thermal threshold.
Observed thermal threshold evolution with temperature agrees well with theoretical predictions.

Conclusions:

The study successfully defines a thermal threshold for the zigzag transition using fluctuation dynamics.
Noisy bifurcation theory accurately predicts the behavior of the system near the thermal threshold.
This work offers a robust method for characterizing phase transitions in noisy systems.