Bacterial range expansions on a growing front: Roughness, fixation, and directed percolation
Name
PhysRevE.99.042134.pdf
Description
Published version
Size
1.36 MB
Format
Adobe PDF
Checksum (MD5)
5d240f0675afa0b5be44a0b47ffa81b7
Author(s)
Horowitz, Jordan M
Kardar, Mehran
Date Issued
2019
Journal
Physical Review E
Publisher
American Physical Society (APS)
Version
Final published version
Abstract
© 2019 American Physical Society. Directed percolation (DP) is a classic model for nonequilibrium phase transitions into a single absorbing state (fixation). It has been extensively studied by analytical and numerical techniques in diverse contexts. Recently, DP has appeared as a generic model for the evolutionary and ecological dynamics of competing bacterial populations. Range expansion - the stochastic reproduction of bacteria competing for space to be occupied by their progeny - leads to a fluctuating and rough growth front, which is known from experiment and simulation to affect the underlying critical behavior of the DP transition. In this work, we employ symmetry arguments to construct a pair of nonlinear stochastic partial differential equations describing the coevolution of surface roughness with the composition field of DP. Macroscopic manifestations (phenomenology) of these equations on growth patterns and genealogical tracks of range expansion are discussed; followed by a renormalization group analysis of possible scaling behaviors at the DP transition.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PHYSREVE.99.042134
