BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Bryan Quaife (Florida State University) DTSTART:20260529T223000Z DTEND:20260529T233000Z DTSTAMP:20260604T191054Z UID:AppliedMath/90 DESCRIPTION:Title: Boundary Integral Methods for Particle Diffusion in Complex Geometrie s: Shielding\, Confinement\, and Escape\nby Bryan Quaife (Florida Stat e University) as part of SFU Mathematics of Computation\, Application and Data ("MOCAD") Seminar\n\nLecture held in K9509.\n\nAbstract\nMany problem s in Engineering and Biology necessitate solving the first passage time pr oblem\, which addresses questions such as the expected time for a Brownian particle in unbounded space to reach a target. I will present a boundary integral equation method for solving this mean first passage time with com plex geometries of absorbing and reflecting bodies. The method applies the Laplace transform to the time-dependent problem\, yielding a modified Hel mholtz equation which is solved with a boundary integral method. This appr oach circumvents the limitations of traditional time-stepping methods and effectively handles the long equilibrium timescales associated with diffus ion problems in unbounded domains. Returning to the time domain is achieve d by applying quadrature along the so-called Talbot contour. I will demons trate the method for various complex geometries formed by disjoint bodies of arbitrary shape on which either uniform Dirichlet or Neumann boundary c onditions are applied. The examples include geometries that guide diffusio n processes to particular absorbing sites\, absorbing sites that are shiel ded by reflecting bodies\, and finding the exits of confining geometries\, such as mazes.\n LOCATION:https://researchseminars.org/talk/AppliedMath/90/ END:VEVENT END:VCALENDAR