Frontiers in Mathematics Lecture Series

Date: March 2, 2015

Time: 4:00PM - 5:00PM

Location: BLOCKER 220

Speaker: Alain Goriely, University of Oxford

Title: Magnetic chains: from self-buckling to self-assembly (Graduate Lecture)

Abstract: Spherical neodymium-iron-boron magnets are marketed as toys as they can be assembled into different shapes due to their high magnetic strength. In this talk, I will consider two simple structures, chains and cylinders of magnets. By manipulating these structures, it quickly appears that they exhibit an elastic response to small deformations. Indeed, chains buckle on their own weight, rings oscillate, and cylinders resist bending but recover their shape after poking. Akin to the fundamental problem of materials science that consists in relating microscopic properties to macroscopic response, a natural question is to understand these macroscopic behaviours based on the individual physical properties of the magnets. I will show through illustrative experiments and simple model calculations that the idea of an effective magnetic bending stiffness is, in fact, an excellent macroscopic characterisation for the mechanical response of magnetic chains. I will then propose a more formal approach of the problem by considering discrete-to-continuum asymptotic analysis to derive a continuum model for the energy of a deformed chain of magnets based on the magnetostatic interactions between individual spheres.