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Hitting time of Brownian motion subject to shear flow. (English) Zbl 1504.35578

Summary: 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.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
92C32 Pathology, pathophysiology
92C35 Physiological flow
76Z05 Physiological flows
35K10 Second-order parabolic equations
60G07 General theory of stochastic processes
60J65 Brownian motion
92-08 Computational methods for problems pertaining to biology
35R60 PDEs with randomness, stochastic partial differential equations
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References:

[1] 10.1007/978-3-642-25847-3 · Zbl 1267.60004 · doi:10.1007/978-3-642-25847-3
[2] 10.1137/090776895 · Zbl 1387.35493 · doi:10.1137/090776895
[3] 10.1017/S0334270000001405 · Zbl 0359.60081 · doi:10.1017/S0334270000001405
[4] 10.1007/978-3-662-02574-1 · doi:10.1007/978-3-662-02574-1
[5] 10.1242/jeb.008516 · doi:10.1242/jeb.008516
[6] 10.1073/pnas.0304594101 · doi:10.1073/pnas.0304594101
[7] 10.1073/pnas.1018666108 · doi:10.1073/pnas.1018666108
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