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Quasi-long range order and sub-diffusion in systems of active particles in heterogeneous media
The rapidly expanding study of active particles has focused so far almost exclusively, theoretically as well as experimentally, on the statistical description of particle motion in idealized, homogeneous spaces. However, the great majority of natural active particle systems takes place, in the wild, in heterogeneous media : from active transport inside the cell, which occurs in a space that is filled by organelles and vesicles, to bacterial motion, which takes place in highly heterogeneous environments such as the soil or complex tissues such as in the gastrointestinal tract. I will show that the presence of spatial heterogeneities brings new physics unseen in homogeneous systems at the level of the transport properties and collective dynamics of such systems. I will show first that a random distribution of “obstacles” can lead to spontaneous trapping of active particles. Such “obstacles” represent undesirable areas that the active particles avoid and may correspond to a source of a repellent chemical, a light gradient, or whatever threat sensed by the moving particles. Inside traps, active particles exhibit a vortex-like motion and remain arbitrary long times. Particle motion then becomes genuinely sub-diffusive. We also find that the presence of such obstacles has a dramatic effect on the collective dynamics of usual self-propelled particle systems. In particular, we observe : i) the existence of an optimal (angular) noise amplitude that maximizes collective motion, and ii) quasi-long range order and the existence of two critical points.
This collection of results opens a new perspective for the design and control of active particle systems.
References :
- O. Chepizhko, E. Altmann, F. Peruani, PRL 110, 238101 (2013)
- O. Chepizhko, F. Peruani, (to appear in PRL) (2013)