Effects of advection on non-equilibrium systems
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Date
22/06/2012Author
Barrett-Freeman, Conrad
Freeman, Conrad Barrett
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Abstract
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.