Applied Math Seminar – Karl Glasner (University of Arizona)
November 15 @ 11:00 am - 12:00 pm
Mathematical Aspects of Nanoscale Self-Assembly
Self-assembly is a fundamental process for creation of both biological and synthetic materials. The latter are being employed in important biotechnological applications like drug delivery, as well as forming the basis for molecular sized machines. Recent advances in nanoscale fabrication in polymer systems, in particular, has lead to growing interest in the theoretical aspects of self-assembly.
This talk introduces continuum formulations of inhomogeneous polymer systems, which lead to questions in the calculus of variations and dynamics of PDEs and free boundary problems. These are studied using various model reduction strategies, in some cases leading to explicit quantitative predictions of morphology and microstructure. Applications involving bulk copolymer phases, nanoparticle aggregates, and amphiphilic structures will be discussed.