Active Interface Equations

Equilibrium and non-equilibrium (moving) interfaces are an established paradigm in statistical physics.

The fluctuating height of the interface is described by the Edwards Wilkinson (noisy diffusion) equation in the equilibrium case and Kardar-Parisi-Zhang equation (which includes a nonlinear growth term)  in the nonequilibrium case.

Motivated by the dynamics of cell membranes, through which cells grow, move and crawl, we explore the generalisation to active interface equations which describe interfaces which are self-driven by active elements.

I will discuss a simple lattice model in which inclusions embedded in the interface activate growth and have their own dynamics. Thus a continuum description is given by coupled height and density stochastic equations. I will show how this leads to novel phenomena of clustering of particles, waves and surfing on the interface, and oscillations of the interface width.

If time allows,  I will also consider a moving interface interacting with a fluctuating membrane and show how this can give rise to a new roughness exponent for a driven interface different from the established KPZ value.