Tiny Chaotic Swimmers Achieving Great Collective Order

Abstract

“From chaos, order can emerge”, a counterintuitive statement but also one laying the foundation for complex living systems. Individually acting agents can collectively produce organised structures at a larger scale. Possibly the most ubiquitous example of this phenomenon are bacterial colonies.
Everywhere around us, a pandemonium of pushing and pulling produces complex structures. The most researched bacterium is E. coli and partially due to its excellent swimming capabilities, the internal structure of its colony is predominantly shaped through mechanical repulsion coupled with
individual motility. In this thesis, we are interested in the emergent dynamics within a bacterial colony. Our focus will lie on how the colony's density \rho affects the internal structure and motility.
To study the colony's interior, we built a three-dimensional individual-based model (IBM) with self-propelling sphero-cylindrical agents representing E. coli bacteria and governed by mechanical interactions. A downside of IBM is its computational costliness, posing an optimisation challenge which will also be covered in this thesis.
A phase transition spontaneously occurs over time from isotropic to an aligned nematic phase. This transition takes longer for higher-density systems. We found a linear relation between the density and the local order for a colony in a quasi-infinite domain. Furthermore, after equilibration, the particles initially behave ballistically. However, this changes to diffusive behaviour in a later stadium. The Reynolds number Re ~ 10^-3 is two orders of magnitude larger than expected for E. coli, possibly due to underestimating the viscosity.
On a final note, the method to determine the moment of equilibrium tequi gives an underestimation in the case of a two-step phase transition; an improved method is proposed.