Extinction on a rough front
Consider growth of two species (active and inactive) on a flat front
The active particles have selective advantage s but mutate to inactive form at rate μ; their fraction f evolves as
f =0 is an absorbing state; corresponding to extinction of active particles;
transitions to adsorbing states belong to the Directed Percolation universality class, descrived by
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How is this picture modified due to roughness of the front?
Generic form of equation governing roughness of a growing front is
Leading couplings in a gradient expansion between height and concentration fluctuations at the front, lead to
"Bacterial range expansions on a growing front: Roughness, Fixation, and Directed Percolation,"
J. Horowitz &M.Kardar PRE 99, 042134 (2019) (off-line)
Related equations were proposed and studied in connection with binary alloy ordering for a growing film:
"Interplay between phase ordering and roughening on growing films,"
B. Drossel & M.Kardar, Eur. J. Phys. B 36, 401 (2003) (off-line)
Non-linear terms are relevant below 4 dimensions, different criticality from standard directed percolation expected.
Renormalization group flows are to strong coupling, with no pertinent fixed point perturbatively accessible.