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We consider self-propelled particles undergoing run-and-tumble dynamics (as exhibited by E. coli) in one dimension. Building on previous analyses at drift-diffusion level for the one-particle density, we add both interactions and noise, enabling discussion of domain formation by "self-trapping," and other collective phenomena. Mapping onto detailed-balance systems is possible in certain cases.
Tailleur et al. (2008) studied this question.