Non-Gaussian limit fluctuations in active swimmer suspensions

Hydrodynamic fluctuations in suspensions of swimming microorganisms (Chlamydomonas and E-coli) exhibit heavily-tailed distribution which is not Gauss nor Levy, for which both the classical and extended central limiting theories do not apply. In this study, the physical limit distribution, instead of mathematical ones, was derived in an analytical form by summing the general power-law interactions from field sources (here, swimming microorganisms) randomly distributed in general spatial dimensions. The origin of the non-Gaussianity is not just the power-law decay of hydrodynamic fields, but the summing procedure of the fields, which we refer to as the physical limit operation [1].
The non-Gaussian shape of the hydrodynamic fluctuations in active swimmer suspensions obeys the analytic theory concomitantly with independently determined parameters such as the strength of force generations and the concentration of swimmers. 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 fluctuations in active systems [2].
Fluctuations show up differently in different spatial dimensions since dimensionality affects the spatial correlations of fields and the population of field sources as a function of system size. Swimmers that resist to sedimentation or ordinary force-dipolar swimmers confined in 2D generate 1/r-decaying fields that are long-ranged in the sense that there is no thermodynamic limit. If time permitted, I will discuss the implication of our study for the dimensionality dependence of active fluctuations.

[1] T. Kurihara, et al. and D. Mizuno, Physical Review E. 95, 030601 (2017).
[2] I. Zaid and D. Mizuno T. Kurihara, Physical Review Letters 117, 030602 (2016).