PhD Thesis Presentation: Development of Dynamical Self-Consistent Field-Theory for Active Rods and its Application to Finger-Like Pattern Formation in Bacteria Colonies at a Glass-Agar Interface
Date and Time
We develop a dynamical self-consistent field theory (dSCFT) for studying the fascinating finger-like patterns observed at the edge of a Pseudomonas aeruginosa bacteria colony confined at a glass-agar interface. A main result of this thesis is the derivation of a set of dynamical mean field equations for this problem through a saddle-point approximation to a functional integral describing the dynamics of interacting active rods (bacteria) and passive particles (agar). As part of the suite of numerical methods we employ to simulate these equations, we developed a method to tackle the challenging, but important, calculation of the mean bacteria-bacteria interaction. As an initial demonstration of the theory, we show this interaction leads to an isotropic-nematic phase transition at sufficiently high rod density, in a pure rod system. The active force produces non-trivial transient behavior during the approach to the equilibrium nematic phase. Adding agar, we are able to demonstrate both phase separation between the bacteria and the agar, and the existence of polar order in the bacteria domains. With these two key features in hand, we then show that a perturbation to a flat interface between uniform agar and bacteria, which are aligned perpendicular to the interface, is unstable. Under the influence of the active force the interface breaks up into regular, finger-like protrusions of dense regions of bacteria with polar order. By introducing randomness into the strength of the agar adhesion with the glass, we can produce more realistic finger patterns, similar to those seen in experiment. We compare our results to various measured properties of the fingers. We find that the agar interaction parameters have little effect on our results. The main influence on the finger-tip velocity is from the magnitude of the active force. The width of the fingers is sensitive to the length scale we build into the randomness in the agar. Based on these simulation results, we propose an interpretation of some of the trends in the finger properties with agar concentration observed in the experiments.
- Dr. Leonid Brown, Chair
- Dr. Robert Wickham, Advisor
- Dr. John Dutcher, Advisory Committee
- Dr. Allan Willms, Graduate Faculty
- Dr. Andrew Rutenberg, External Examiner (Dalhousie University)