Time parameterization and stationary distributions in a relativistic gas

In this paper we consider the effect of different time parameterizations on the stationary velocity distribution function for a relativistic gas. We clarify the distinction between two such distributions, namely the J\"{u}ttner and the modified J\"{u}ttner distributions. Using a recently proposed model of a relativistic gas, we show that the obtained results for the proper-time averaging does not lead to modified J\"{u}ttner distribution (as recently conjectured), but introduces only a Lorentz factor $\gamma$ to the well-known J\"{u}ttner function which results from observer-time averaging. We obtain results for rest frame as well as moving frame in order to support our claim.Comment: 5 pages, 2 figure

Activity-induced asymmetric dispersion in confined channels with constriction

Microorganisms, such as E.Coli, are known to display upstream behavior and respond rheotactically to shear flows. In particular, E.Coli suspensions have been shown to display strong sensitivity to spatial constrictions, leading to an anomalous densification past the constriction for incoming fluid velocities comparable to the microoganism's self propulsion speed. We introduce a Brownian dynamics model for ellipsoidal self-propelling particles in a confined channel subject to a constriction. The model allows to identify the relevant parameters that characterize the relevant dynamical regimes of the accumulation of the active particles at the constriction, and clarify the mechanisms underlying the experimental observations. We find that particles are trapped in butterfly-like attractors in front of the constriction, which is the origin of the symmetry breaking in the emerging density profiles of active particles passing the constriction. In addition, the probability of trapping and thus the strength of asymmetry is affected by size of the particles and geometry of the channel, as well as the ratio of fluid velocity to propulsion speed