From growing neurons and sunflowers to liquid crystal elastomers and elephant trunks: the fascinating dynamics of active filaments

We’re delighted to be hosting Alain Goriely for a talk via Teams.

Abstract: The natural and artificial world around us is full of active filamentary structures that respond to external stimuli and modify their internal structures through growth or remodeling to achieve specific functions. For instance, to survive and to thrive, plants rely on their ability to sense multiple environmental signals, such as gravity or light, and respond to them by growing in a particular direction and by changing their shape. Similarly, during development, neurons sense their environment to grow and interconnect different regions of the brain. Octopus arms and elephant trunks are other magnificent examples of the power and beauty of activated filamentary structures. In engineering structures, certain liquid crystal elastomers can be shaped into filaments that respond and bend towards incident light with enticing possibilities for new devices. These systems share the same slender geometry, the same mechanical constraints, and they all face three important challenges: how is the external signal transduced to the microstructure? How is it activated? How should the microstructure be organised/designed for a particular function?

In this talk, I will discuss a general mathematical theory of active filaments based on morphoelasticity and dimensional reduction. In this approach, multiple stimuli can be integrated at the microscopic level to produce curvature and torsion at the macroscopic level, thus modifying the filament shape and position with respect to the stimuli. General principles for microstructure organisation and activation can  then be obtained. More interestingly, this feedback loop of shape shifting based on external sources creates complex dynamics akin to actual natural behaviours and can be used to find elegant solutions to functional problems.