Special Soft Matter Seminar

Abstract:

In this talk, I will talk about two problems that lie at the interface of soft-matter physics, geometry, and asymptotics.  In the first problem, I will consider thermal fluctuations of mechanical frameworks at the nanoscale, i.e., deformable assemblies of stiff bars connected by joints undergoing thermal fluctuations.  When the holonomic constraints in a framework cease to be linearly independent, singularities can appear in its configuration space and the framework becomes softer.  In the presence of thermal fluctuations, I will discuss how the free-energy landscape of these frameworks is dominated by the neighborhoods of points that correspond to these singularities, opening up ways to improve the design of nanoframeworks for various applications.

In the second problem, I will consider the propagation of waves on singly curved thin elastic structures with varying curvature.  Using semiclassical/WKB asymptotics, I will discuss how a varying curvature profile can be used to trap waves at points where the absolute curvature of the structure has a minimum.  As the trapped waves remain localized irrespective of the boundary conditions, in very long structures, we expect them to resemble a robust set of discrete, bound states that coexist with a quasicontinuum of delocalized states.  These findings are expected to help craft acoustic structures with desirable properties by fine-tuning their geometry.