UBC Mathematics Colloquium: Angelika Manhart

PDE models can be a powerful tool for understanding emerging structures and patterns, such as aggregates and traveling waves formed by large populations of cells. As a specific example, I will discuss myxobacteria, which, due to their co-operative nature, lie on the boundary between uni- and multicellular organisms. I will present a novel age-structured, continuous macroscopic model. The derivation is based on simple interaction rules and set within the SOH (Self-Organized Hydrodynamics) framework. The strength of this combined approach is that microscopic information can be incorporated into the particle model in a straight-forward manner, whilst the continuous model can be analyzed using mathematical tools, such as stability and asymptotic analysis.

It has been suggested that myxobacteria are not able to react to signals immediately after they have reversed their direction. Our analysis reveals that this insensitivity period is not necessary for wave formation, but is essential for wave synchronization. A more mathematical focus will be the existence and stability of such traveling waves moving in two opposing waves frames. Fascinatingly, while the wave profiles do not change, the wave composition does, and the fractions of reversible and non- reversible bacteria form waves traveling in the opposite direction. I will discuss the explicit construction of such waves and show simulation results.

This is joint work with Pierre Degond and Hui Yu.