Criterion for noise-induced synchronization: application to colloidal alignment

Abstract

Colloidal bodies of irregular shape rotate as they descend under gravity in solution. This rotational response provides a means of bringing a dispersion of identical bodies into a synchronized rotation with the same orientation using programmed forcing. We use the notion of statistical entropy to derive bounds on the rate of synchronization. These bounds apply generally to dynamical systems with stable periodic motion with a phase $\varphi (t)$, when subjected to an impulsive perturbation. The impulse causes a change of phase expressible as a phase map $\psi (\varphi )$. We derive an upper limit on the average change of entropy $⟨\Delta H⟩$ in terms of this phase map; when this limit is negative, alignment must occur. For systems that have achieved a low entropy, the $⟨\Delta H⟩$ approaches this upper limit.

References in corpus (5)

• Noise-Induced Synchronization and Clustering in Ensembles of Uncoupled Limit-Cycle Oscillators
• Phase coherence in an ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses
• Experimental synchronization of circuit oscillations induced by common telegraph noise
• Hydrodynamic Interactions between Two Forced Objects of Arbitrary Shape: I Effect on Alignment
• Averaging approach to phase coherence of uncoupled limit-cycle oscillators receiving common random impulses

Cited by in corpus (5)

• A review of shaped colloidal particles in fluids: Anisotropy and chirality
• Predicting tensorial electrophoretic effects in asymmetric colloids
• Stochastic synchronization induced by noise
• Chiral motion in colloidal electrophoresis
• Effective synchronization amid noise-induced chaos