W lipcu, w ramach programu IDUB, gościem Instytutu Matematycznego UWr. będzie Prof. Andrew Wade z Durham University (UK).
W ramach wizyty wygłosi wykład otwarty pt. Deposition, diffusion, and nucleation on an interval w ramach seminarium „Rekurencja i samopodobieństwo w procesach stochastycznych“, które odbędzie się w czwartek 10 lipca o godz. 14:15 w sali 602.
Wszystkich chętnych serdecznie zapraszamy.
Ponadto Profesor Wade wygłosi też cykl wykładów dla studentów i doktorantów. Wykłady odbędą się w październiku w formie on-line. Szczegóły zostaną podane we wrześniu.
Streszczenie wykładu:
I will talk about an interacting particle model motivated by nanoscale growth of ultra-thin films. Particles are deposited (according to a space-time Poisson process) on an interval substrate and perform Brownian motions until any two meet, when they nucleate to form a static island, which acts as an absorbing barrier to subsequent particles. This is a continuum version of a lattice model popular in the applied literature. We are interested in the induced interval-splitting process. In particular, we show that the long-time evolution converges to a Markovian interval-splitting process, which we describe. The density that appears in this description is derived from an exit problem for planar Brownian motion from a right-angled triangle, extending work of Smith and Watson. The splitting density has a compact Fourier series expansion but, apparently, no simple closed form. The nucleation problem is rather physical in its application - although one can observe a link as the dynamics of "epitaxy" is used to construct nanomaterial whose remarkable optical, electrical and thermal properties are important in modern nano-scale technologies which can constitute the hardware used in AI.
This talk is based on joint work with Nicholas Georgiou (Durham).