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

## TL;DR

This paper introduces a method to measure the diffusivity of particles within moving aggregates by analyzing the mean squared relative distance between tracers, accounting for aggregate motion.

## Contribution

The authors develop an analytical framework for assessing tracer diffusivity within mobile environments using relative distance measurements.

## Key findings

- Analytical expressions for ensemble and time-averaged MSRD provided.
- Method effectively distinguishes tracer diffusivity from aggregate motion.
- Applicable to experimental data involving moving particle systems.

## 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.