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<b><i>"A Tale of Two Journeys: Random Particles in Complex Domains"</i></b></div>
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<b>Bryan Quaife</b></div>
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Dept. of Scientific Computing,</div>
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Florida State University (FSU)</div>
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Please feel free to forward/share this invitation with other groups/disciplines that might be interested in this talk/topic. All are welcome to attend. </div>
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NOTE: In-person attendance is requested in our 499 Dirac Science Library (DSL) Seminar Room. Zoom access is intended for external (non-departmental) participants only. </div>
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<b>https://fsu.zoom.us/j/94273595552 </b></div>
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Meeting # <b>942 7359 5552 </b></div>
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🎦 Colloquium recordings will be made available here, <a href="https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.sc.fsu.edu%2Fcolloquium&data=05%7C02%7Csc-seminar-announce%40lists.fsu.edu%7Ceef44829ba0a4925372a08de2469270e%7Ca36450ebdb0642a78d1b026719f701e3%7C0%7C0%7C638988231225235857%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=zteJVcu8wPDq6Ryno1kXIUcq%2F0u%2Fz6w3RAzhWT7IcMQ%3D&reserved=0" originalsrc="https://www.sc.fsu.edu/colloquium">
https://www.sc.fsu.edu/colloquium</a></div>
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<b>Wednesday, Nov 19, 2025, Schedule: </b></div>
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☕ Nespresso & Teatime - 417 DSL Commons </div>
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* 3:00 to 3:30 PM Eastern Time (US and Canada) </div>
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<b>🕟 Colloquium - 499 DSL Seminar Room </b></div>
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<b>* 3:30 to 4:30 PM Eastern Time (US and Canada) </b></div>
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<b>Abstract: </b></div>
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Random motion plays a central role in many physical and biological systems, from molecular diffusion in crowded environments to organisms or particles navigating complex landscapes. In this talk, I will present two such "journeys", each involving stochastic
particles trying to reach their own "best of times".</div>
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The first journey is that of Brownian particles navigating an unbounded domain while trying to reach a target domain (their "best of times") without wandering too far off to infinity (their "worst of times"). The probability density of the particles' arrival
time has a very long tail, necessitating a numerical method that can solve a PDE for this probability at very late times. I will describe one such method that avoids standard time stepping altogether. Examples will illustrate how complex geometric arrangements
can funnel, shield, or delay particles on their way to an absorbing target.</div>
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The second journey explores a generalization of the classical "N bugs on a square" problem. Here, the particles are randomly initialized on a compact manifold and pursue one another cyclically. Depending on their initial conditions, all particles either converge
to one another (their "best of times"), or they end up in an infinite pursuit with particles not catching the ones they pursue (their "worst of times").</div>
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Together, these two stories highlight how randomness interacts with geometry to produce unexpected pathways, delays, and patterns.</div>
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<img id="image_0" style="max-width: 917px;" size="37560" src="cid:6cc0f32f-4e8e-4100-9255-bc2ad52d2c8f"></div>
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Additional colloquium details can be found here,</div>
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