Eur. Phys. J. B (2018) 91: 27
https://doi.org/10.1140/epjb/e2017-80347-5

Regular Article

Relative distance between tracers as a measure of diffusivity within moving aggregates^★

¹ Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
² Institute of Supercomputing Technologies, Lobachevsky State University of Nizhny Novgorod, Gagarina Av. 23, Nizhny Novgorod 603140, Russia

^a e-mail: wolframp@pks.mpg.de

Received: 15 June 2017
Received in final form: 23 November 2017
Published online: 7 February 2018

Abstract

Tracking of particles, be it a passive tracer or an actively moving bacterium in the growing bacterial colony, is a powerful technique to probe the physical properties of the environment of the particles. One of the most common measures of particle motion driven by fluctuations and random forces is its diffusivity, which is routinely obtained by measuring the mean squared displacement of the particles. However, often the tracer particles may be moving in a domain or an aggregate which itself experiences some regular or random motion and thus masks the diffusivity of tracers. Here we provide a method for assessing the diffusivity of tracer particles within mobile aggregates by measuring the so-called mean squared relative distance (MSRD) between two tracers. We provide analytical expressions for both the ensemble and time averaged MSRD allowing for direct identification of diffusivities from experimental data.