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
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.