Departmental Seminars & Events

Slender elastic filaments with intrinsic helical geometry are encountered in a wide range of physical and biological settings, ranging from coil springs in engineering to bacteria flagellar filaments. The equilibrium configurations of helical filaments under a variety of loading types have been well studied in the framework of the Kirchhoff rod equations. These equations are geometrically nonlinear and so can account for large, global displacements of the rod. This geometric nonlinearity also makes a mathematical analysis of the rod equations extremely difficult, so that much is still unknown about the dynamic behaviour of helical rods under external loading.

An important class of simplified models consists of 'equivalent-column' theories. These model the helical filament as a naturally-straight beam (aligned with the helix axis) for which the extensional and torsional deformations are coupled. Such theories have long been used in engineering to describe the free vibrations of helical coil springs, though their validity remains unclear, particularly when distributed forces and moments are present. In this talk, we show how such an effective theory can be derived systematically from the Kirchhoff rod equations using the method of multiple scales. Importantly, our analysis is asymptotically exact in the small-wavelength limit and can account for large, unsteady displacements. We then illustrate our theory with two loading scenarios: (i) a heavy helical rod deforming under its own weight; and (ii) axial rotation (twirling) in viscous fluid, which may be considered as a simple model for a bacteria flagellar filament. More broadly, our analysis provides a framework to develop reduced models of helical rods in a wide variety of physical and biological settings, as well as yielding analytical insight into their tensile instabilities.

The global COVID19 pandemic has highlighted the lethality and morbidity associated with infectious respiratory diseases. These diseases can lead to devastating syndrome known as the acute respiratory distress syndrome (ARDS) where bacterial/viral infections cause excessive lung inflammation, pulmonary edema, and severe hypoxemia (shortness of breath). Although ARDS patients require artificial mechanical ventilation, the complex biofluid and biomechanical forces generated by the ventilator exacerbates lung injury leading to high mortality. My group has used mathematical and computational modeling to both characterize the complex mechanics of lung injury during ventilation and to identify novel ways to prevent injury at the cellular level. We have used in-vitro and in-vivo studies to validate our mathematical predictions and have used engineering tools to understand the biological consequences of the mechanical forces generated during ventilation. In this talk I will specifically describe how our mathematical/computational approach has led to novel cytoskeletal based therapies and how coupling mathematics and molecular biology has led to the discovery of a gene regulatory mechanisms that can minimize ventilation induced lung injury. I will also describe how we are currently using nanotechnology and gene/drug delivery systems to enhance the lung’s native regulatory responses and thereby prevent lung injury during ARDS.

Tension-induced giant actuation in elastic sheets

Dr. Marc Suñé

Buckling is normally associated with a compressive load applied to a slender structure; from railway tracks in extreme heat to microtubules in cytoplasm, axial compression is relieved by out-of-plane buckling. However, recent studies have demonstrated that tension applied to structured thin sheets leads to transverse motion that may be harnessed for novel applications, such as kirigami grippers, multi-stable `groovy-sheets', and elastic ribbed sheets that close into tubes. Qualitatively similar behaviour has also been observed in simulations of thermalized graphene sheets, where clamping along one edge leads to tilting in the transverse direction. I will discuss how this counter-intuitive behaviour is, in fact, generic for thin sheets that have a relatively low stretching modulus compared to the bending modulus, which allows `giant actuation' with moderate strain.

It is well known that adding even small amounts of  long chain polymers (e.g. few parts per million) to Newtonian solvents can drastically change the flow behaviour by introducing elasticity. In particular,  two decades ago, experiments in curved geometries  demonstrated  that polymer flows can be  chaotic even at vanishingly small Reynolds numbers. The situation in `straight’ flows  such as pressure-driven flow down a channel is less clear  and hence an area of current focus. I will discuss recent progress.