Vol. 15, No. 1, 2022

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Hitting time of Brownian motion subject to shear flow

Despina Chouliara, Yishu Gong, Siming He, Alexander Kiselev, James Lim, Omar Melikechi and Keenan Powers

Vol. 15 (2022), No. 1, 131–140
Abstract

The 2-dimensional motion of a particle subject to Brownian motion and ambient shear flow transportation is considered. Numerical experiments are carried out to explore the relation between the shear strength, box size, and the particle’s expected first hitting time of a given target. The simulation is motivated by biological settings such as reproduction processes and the workings of the immune system. As the shear strength grows, the expected first hitting time converges to the expected first hitting time of the 1-dimensional Brownian motion. The dependence of the hitting time on the shearing rate is monotone, and only the form of the shear flow close to the target appears to play a role. Numerical experiments also show that the expected hitting time drops significantly even for quite small values of shear rate near the target.

Keywords
hitting time, shear flow
Mathematical Subject Classification
Primary: 35K10, 60G07, 92B05
Milestones
Received: 5 March 2021
Revised: 9 September 2021
Accepted: 22 September 2021
Published: 14 March 2022

Communicated by Suzanne Lenhart
Authors
Despina Chouliara
Duke University
Durham, NC
United States
Yishu Gong
Department of Mathematics
Duke University
Durham, NC
United States
Siming He
Department of Mathematics
Duke University
Durham, NC
United States
Alexander Kiselev
Department of Mathematics
Duke University
Durham, NC
United States
James Lim
Duke University
Durham, NC
United States
Omar Melikechi
Department of Mathematics
Duke University
Durham, NC
United States
Keenan Powers
Duke University
Durham, NC
United States