TY - JOUR
T1 - Run-and-tumble particles on a line with a fertile site
AU - Grange, Pascal
AU - Yao, Xueqi
N1 - Publisher Copyright:
© 2021 IOP Publishing Ltd Printed in the UK
PY - 2021/8
Y1 - 2021/8
N2 - We propose a model of run-and-tumble particles (RTPs) on a line with a fertile site at the origin. After going through the fertile site, a run-and-tumble particle gives rise to new particles until it flips direction. The process of creation of new particles is modelled by a fertility function (of the distance to the fertile site), multiplied by a fertility rate. If the initial conditions correspond to a single RTP with even probability density, the system is parity-invariant. The equations of motion can be solved in the Laplace domain, in terms of the density of right-movers at the origin. At large time, this density is shown to grow exponentially, at a rate that depends only on the fertility function and fertility rate. Moreover, the total density of RTPs (divided by the density of right-movers at the origin), reaches a stationary state that does not depend on the initial conditions, and presents a local minimum at the fertile site.
AB - We propose a model of run-and-tumble particles (RTPs) on a line with a fertile site at the origin. After going through the fertile site, a run-and-tumble particle gives rise to new particles until it flips direction. The process of creation of new particles is modelled by a fertility function (of the distance to the fertile site), multiplied by a fertility rate. If the initial conditions correspond to a single RTP with even probability density, the system is parity-invariant. The equations of motion can be solved in the Laplace domain, in terms of the density of right-movers at the origin. At large time, this density is shown to grow exponentially, at a rate that depends only on the fertility function and fertility rate. Moreover, the total density of RTPs (divided by the density of right-movers at the origin), reaches a stationary state that does not depend on the initial conditions, and presents a local minimum at the fertile site.
KW - Out-of-equilibrium statistical physics
KW - Run-and-tumble particles
KW - Stochastic processes
UR - http://www.scopus.com/inward/record.url?scp=85112042069&partnerID=8YFLogxK
U2 - 10.1088/1751-8121/ac0ebe
DO - 10.1088/1751-8121/ac0ebe
M3 - Article
AN - SCOPUS:85112042069
SN - 1751-8113
VL - 54
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 32
M1 - 325007
ER -