Effects of advection on non-equilibrium systems
Freeman, Conrad Barrett
We study a number of non-equilibrium models of interest to both active matter and biological physicists. Using microscopic agent-based simulation as well as numerical integration of stochastic PDEs, we uncover the non-trivial behaviour exhibited when active transport, or an advection field, is added to out of equilibrium systems. When gravity is included in the celebrated Fisher-Kolmogoro Petrovsky Piscouno (F-KPP) equation, to model sedimentation of active bacteria in a container, we observe a discontinuous phase transition between a `sedimentation' and a `growth' phase, which should in principle be observable in real systems. With the addition of multiplicative noise, the resulting model contains, as its limits, both the bacterial sedimentation previously described and the fluctuating hydrodynamic description of Directed Percolation (DP), an important and well-studied non-equilibrium system whose physics incorporate many universal features which are typical of systems with absorbing states. We map out the phase diagram describing all the systems in between these two limiting cases, finding that adding an advection term, however small, immediately lifts the resulting system out of the DP universality class. Furthermore, we find two distinct low-density phases separated by a dynamical phase transition reminiscent of a spinodal transition. Finally, we attempt to improve the current diffusion-limited model for the growth of filopodia, which are intriguing networks of actin fibres used by moving cells to sense their environment. By the addition of directed transport of actin monomers to the fibre tip complex by myosin molecular motors, we show that, under appropriate conditions, the resulting dynamics may be more efficient that transport by diffusion alone, which would result in filopodial lengths better corresponding to experimental observation.