Towards a statistical physics of slender animal behaviour

Slenderness is a common morphological trait shared by diverse animal species, including several commonly studied model organisms, in which individuals are much larger in one dimension than in the other two. This property can be exploited to describe a slender animal's mechanical configuration in terms of two scalar fields, measuring strain and curvature along the body axis. To build a statistical field theoretic description of slender animal movement, we choose to work within a "Riewe" theory space, in which driven and/or dissipative Langevin dynamics can be derived from a complex action functional containing higher- and fractional-order derivatives. In the spirit of effective field theory, we write down a generic action functional for the strain and curvature fields then follow through with a renormalisation procedure. This allows us to predict and explain the coarse-grained behavioural dynamics of slender animals that dominate at low frequencies and long wavelengths.