"Macro Resonance of Micro Resonators: Singular Upscaling in Acoustics"
Mathematics, Mechanics, and Materials Unit (Fried Unit) would like to invite you to a Seminar by Dr. Andrés Baldelli, CNRS - Centre national de la recherche scientifique, France.
Date: Friday, July 13, 2018
Venue: C756, Level C, Lab3
Dr. Andrés Baldelli, CNRS - Centre national de la recherche scientifique, France.
Macro Resonance of Micro Resonators
We will take the chance to discuss a mechanical problem that relates microscopic small bodies (or elementary Helmholtz resonators) to their overlying macroscopic system, in conditions in which resonators are distributed on a (codimension-1) manifold. The link is performed using tools of rational mechanics and analysis, in the scalar setting of acoustics.
Instead of focussing on the individual body (or the elementary resonator), we explore their collective behaviour in the frequency domain and establish that, within the scaling regime of ’tightly chocked necks’, emergent singularities determine an upscaling of information (micro to macro) in a way that not only they influence but they determine effective (boundary) conditions, at the dominant order of the macroscopic problem.
This work paves the way, in a rigorous and logic manner, to exposing some of the singularly emergent phenomena that underlie fundamental notions that hinge the structure of the current society (e.g. the notion of ‘value').