Chouliara, Despina; Gong, Yishu; He, Siming; Kiselev, Alexander; Lim, James; Melikechi, Omar; Powers, Keenan Hitting time of Brownian motion subject to shear flow. (English) Zbl 1504.35578 Involve 15, No. 1, 131-140 (2022). 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. Cited in 1 Document 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 Keywords:hitting time; shear flow PDFBibTeX XMLCite \textit{D. Chouliara} et al., Involve 15, No. 1, 131--140 (2022; Zbl 1504.35578) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.