Using old tricks to understand new dogs: Explaining two biophysical phenomena with multiscale asymptotics

Part of the Leeds Applied Nonlinear Dynamics seminar series.


Mohit Dalwadi, University College London


In this talk I discuss two problems: each related to fundamental biophysical problems involving nonlinear dynamics, and linked to one another via the multiscale techniques I use to analyse them.

In the first part, I discuss the problem of spatio-temporal variations in biological pattern formation, linked to the general idea first explored by Turing in the 1950s. How do cells decode spatio-temporally varying signals into functionally robust patterns in the presence of confounding effects caused by unpredictable or heterogeneous environments? Through multiscale analysis, I will present a general theory of pattern formation in the presence of spatio-temporal variations, and show how robustness in the output manifests inherently from Turing bifurcations over unusual intermediate timescales. Moreover, I will show how general dynamics can be classified based on the types of bifurcation in the system.

In the second part, I investigate how the rapid 3D spinning of microswimmers in shear flow affects their emergent (observed) trajectories and how this relates to the classic Jeffery's orbits for inert ellipsoids, first explored by Jeffery in the 1920s. To understand this fluid mechanics problem, I will use a technical multiple scales analysis for systems. I will show that the short-scale rapid spinning behaviour exhibited by many microswimmers can have a significant effect on longer-scale trajectories, despite the common neglect of this spinning in mathematical models. I will show how these rapid short-scale effects can be systematically incorporated into modified versions of Jeffery's original equations.