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Non-Gaussian limit fluctuations in active swimmer suspensions

Takashi Kurihara1, Msato Aridome1, Heev Ayade1, Irwin Zaid2, and Daisuke Mizuno1,*

  • 1Kyushu University, Fukuoka 812-8581, Japan
  • 2Rudolf Peierls Center for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom

  • *Corresponding author: mizuno@phys.kyushu-u.ac.jp
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Phys. Rev. E 95, 030601(R) – Published 9 March, 2017

DOI: https://doi.org/10.1103/PhysRevE.95.030601

Abstract

We investigate the hydrodynamic fluctuations in suspensions of swimming microorganisms (Chlamydomonas) by observing the probe particles dispersed in the media. Short-term fluctuations of probe particles were superdiffusive and displayed heavily tailed non-Gaussian distributions. The analytical theory that explains the observed distribution was derived by summing the power-law-decaying hydrodynamic interactions from spatially distributed field sources (here, swimming microorganisms). The summing procedure, which we refer to as the physical limit operation, is applicable to a variety of physical fluctuations to which the classical central limiting theory does not apply. Extending the analytical formula to compare to experiments in active swimmer suspensions, we show that the non-Gaussian shape of the observed distribution obeys the analytic theory concomitantly with independently determined parameters such as the strength of force generations and the concentration of Chlamydomonas. Time evolution of the distributions collapsed to a single master curve, except for their extreme tails, for which our theory presents a qualitative explanation. Investigations thereof and the complete agreement with theoretical predictions revealed broad applicability of the formula to dispersions of active sources of fluctuations.

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Phys. Rev. E 95, 030601(R)– Published 9 March, 2017
  • Received 8 June 2016
  • Revised 18 January 2017

©2017 American Physical Society

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