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MMAS

2015

Springer

2015

Springer

We compute the mean ﬁrst passage time (MFPT) for a Brownian particle inside a two-dimensional disk with reﬂective boundaries and a small interior trap that is rotating at a constant angular velocity. The inherent symmetry of the problem allows for a detailed analytic study of the situation. For a given angular velocity, we determine the optimal radius of rotation that minimizes the average MFPT over the disk. Several distinct regimes are observed, depending on the ratio between the angular velocity ω and the trap size ε, and several intricate transitions are analyzed using the tools of asymptotic analysis and Fourier series. For ω ∼ O(1), we compute a critical value ωc > 0 such that the optimal trap location is at the origin whenever ω < ωc and is oﬀ the origin for ω > ωc. In the regime 1 ω O(ε−1) the optimal trap path approaches the boundary of the disk. However, as ω is further increased to O(ε−1), the optimal trap path “jumps” closer to the origi...

Added |
14 Apr 2016 |

Updated |
14 Apr 2016 |

Type |
Journal |

Year |
2015 |

Where |
MMAS |

Authors |
J. C. Tzou, Theodore Kolokolnikov |

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