Non-Gaussian fluctuations in active suspensions

Thesis

An active particle converts energy to motion. An active suspension is a population of active particles, typically microscale, that are immersed in a viscous and/or elastic medium.

This thesis is about the statistics of active suspensions. Unlike a suspension at thermodynamic equilibrium, we show that an active suspension inherently has non-Gaussian fluctuations due to an interplay between self-driven constituents and microscopic physics. Consequently, the diffusion of a tracer in an active suspension is not Gaussian.

Our results explain some experiments with active suspensions that contain either swimming microorganisms or molecular motors. We provide different models for the fluctuations in dilute active suspensions, ranging from phenomenological to exact. The fundamental ingredient of such non-Gaussian fluctuations is an ultraslow convergence to the central limit theorem caused by truncated power-laws. Without any truncation, there is an intimate relation to the generalized central limit theorem.

We suggest similar effects occur in many other systems. These may be associated with probability distributions that appear to be exponential.

Authors: Zaid, I

• Publication date: 2012
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: Oxford University, UK
• Language: English
• Keywords: stochastic processes; statistical physics; fluid mechanics; elasticity; diffusion
• Subjects: Theoretical physics; Biophysics