PIMS/AMI Seminar: Vkhtang Putkaradze

Abstract:

In this introductory lecture, I will explore some applications of geometry and mechanics to problems at the nanoscale (and perhaps larger scales as well!). First, we shall talk about recent work on dendronized polymers and study a model of contact dynamics assuming that the polymers roll rather than slide, much like crossing rubber strings. We then talk about the dynamics of molecular detectors based on oscillations of nanoresonator arrays. Finally, we discuss the dynamics of resonators built in the shape of tree-like structures and their possible applications to sensing and energy harvesting.  I shall concentrate on the unsolved problems and there will be more questions posed than answers provided. This lecture is aimed primarily to graduate students who are interested in getting an introduction to the rapidly developing field of geometric methods in nanotechnology, and will touch upon issues like geometry, PDEs and nonlinear dynamics.