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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
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Abstract |
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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
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Mathematical Subject Classification
Primary: 35K10, 60G07, 92B05
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Milestones
Received: 5 March 2021
Revised: 9 September 2021
Accepted: 22 September 2021
Published: 14 March 2022
Communicated by Suzanne Lenhart
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Authors |
| Despina Chouliara | |
| Duke University Durham, NC United States |
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| Yishu Gong | |
| Department of Mathematics Duke University Durham, NC United States |
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| Siming He | |
| Department of Mathematics Duke University Durham, NC United States |
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| Alexander Kiselev | |
| Department of Mathematics Duke University Durham, NC United States |
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| James Lim | |
| Duke University Durham, NC United States |
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| Omar Melikechi | |
| Department of Mathematics Duke University Durham, NC United States |
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| Keenan Powers | |
| Duke University Durham, NC United States |
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