January 30, 2026 — ISQGD–DL06 — Distinguished Lecture by Professor Patrick D Shipman

Описание: Title: Geometry, Fractals, and Dynamics from Nucleation and Growth

Abstract:
We begin by observing patterns, motion, fractals, and a variety of geometric structures in a series of chemical experiments ranging from plant pigments under the influence of atmospheric pollutants to microtornados. A common theme of these experiments is nucleation from the vapor or liquid phase of solid nanoparticles, followed by their subsequent growth. Applications of size-controlled, uniform nanoparticles are vast. Yet the chemical mechanisms governing particle formation—and how to control particle size distributions—have long remained an unsolved problem in materials chemistry. We introduce Bayesian-enabled mechanism-enabled population balance modeling (BE-MEPBM), which allows us to determine previously inaccessible chemical mechanisms directly from measured particle size distributions. Mathematically, BE-MEPBM is based on coupled integro–partial differential equations describing nucleation, growth, and transport, and can be viewed as an infinite-dimensional dynamical system evolving in time (and, in many cases, space). Determining these parameters from experimental data leads naturally to a PDE-constrained inverse problem. By embedding the model within a Bayesian framework, we obtain uncertainty-aware reconstructions of kinetic mechanisms, posterior distributions over parameters, and quantitative assessments of identifiability and predictive reliability. Many of these experiments originated in discussions on developing engaging activities for applied mathematics courses, where chemical pattern formation serves as a concrete setting for dynamical systems, inverse problems, and uncertainty quantification. We close with reflections on this pedagogical endeavor and its role in connecting mathematical structure to visually compelling physical phenomena.