Interface growth driven by a single active particle

Renormalization group study of the dynamics of active membranes: Universality classes and scaling laws

Motivated by experimental observations of patterning at the leading edge of motile eukaryotic cells, we introduce a general model for the dynamics of nearly-flat fluid membranes driven from within by an ensemble of activators. We include, in particular, a kinematic coupling between activator density and membrane slope which generically arises whenever the membrane has a nonvanishing normal speed. We unveil the phase diagram of the model by means of a perturbative field-theoretical renormalization group analysis. Due to the aforementioned kinematic coupling the natural early-time dynamical scaling is acoustic, that is the dynamical critical exponent is 1. However, as soon as the the normal velocity of the membrane is tuned to zero, the system crosses over to diffusive dynamic scaling in mean field. Distinct critical points can be reached depending on how the limit of vanishing velocity is realized: in each of them corrections to scaling due to nonlinear coupling terms must be taken into account. The detailed analysis of these critical points reveals novel scaling regimes which can be accessed with perturbative methods, together with signs of strong coupling behavior, which establishes a promising ground for further nonperturbative calculations. Our results unify several previous studies on the dynamics of active membrane, while also identifying nontrivial scaling regimes which cannot be captured by passive theories of fluctuating interfaces and are relevant for the physics of living membranes.