This paper introduces a stochastic adaptive dynamics model for the interplay of several crucial traits and mechanisms in bacterial evolution, namely dormancy, horizontal gene transfer (HGT), mutation and competition. In particular, it combines the re
cent model of Champagnat, Meleard and Tran (2021) involving HGT with the model for competition-induced dormancy of Blath and Tobias (2020). Our main result is a convergence theorem which describes the evolution of the different traits in the population on a `doubly logarithmic scale as piece-wise affine functions. Interestingly, even for a relatively small trait space, the limiting process exhibits a non-monotone dependence of the success of the dormancy trait on the dormancy initiation probability. Further, the model establishes a new `approximate coexistence regime for multiple traits that has not been observed in previous literature.
We study the coherent flow of a guided Bose-Einstein condensate incident over a disordered region of length L. We introduce a model of disordered potential that originates from magnetic fluctuations inherent to microfabricated guides. This model allo
ws for analytical and numerical studies of realistic transport experiments. The repulsive interaction among the condensate atoms in the beam induces different transport regimes. Below some critical interaction (or for sufficiently small L) a stationary flow is observed. In this regime, the transmission decreases exponentially with L. For strong interaction (or large L), the system displays a transition towards a time dependent flow with an algebraic decay of the time averaged transmission.
