Effective Geometries in Elasticity: Wrinkled Shells and Shape-Morphing Kirigami What do wrinkled shells and shape-morphing kirigami sheets have in common? The answer is fine scale buckling — a patterned response driven by mechanical instabilities enabling macroscopic shape change beyond bulk elasticity. This talk will present two recent developments on (i) […]
Optimal packing of a finite collection of deformable objects How should space-filling, deformable objects be packed so as to minimize the area of the interfaces between them? In 3D the search for a packing of equal-volume shapes with minimum surface area is known as the Kelvin problem. In 2D the […]
Measures of order for imperfect two-dimensional patterns Motivated by patterns with defects in natural and laboratory systems, we develop two quantitative measures of order for imperfect Bravais lattices in the plane. A tool from topological data analysis called persistent homology combined with the sliced Wasserstein distance, a metric on point […]
Mathematical Modelling of Programmable Polymorphism of Protein Cages Protein cages, convex polyhedral protein containers self-assembled from multiple copies of identical protein subunits, are pillars of nanotechnology. They include naturally occurring virus capsids (virus-like particles, VLPs) which are spherical as well as a plethora of particles with diverse symmetries such as […]
Cumulative Geometric Frustration and the Intrinsic Approach to Physical Assemblies Geometric frustration arises whenever the constituents of a physical assembly locally favor an arrangement that is incompatible with the geometry or topology of the space in which it resides.  It naturally arises in a variety of fields ranging from macromolecular assemblies to liquid-crystals to spin models, yet in distinct systems, geometric frustration may […]
The topological origin of the Peierls-Nabarro barrier Crystals and other condensed matter systems described by density waves often exhibit dislocations. Here we show, by considering the topology of the ground state manifolds (GSMs) of such systems, that dislocations in the density phase field always split into disclinations, and that the […]
Geometry, Topology and Defects in the Programmable Assembly of Nanoparticles Materials whose fundamental units are nanocrystals (NC)s, instead of atoms or molecules, are emerging as major candidates to solve many of the technological challenges of our century. Those materials display unique structural, dynamical and thermodynamical properties, often reflecting deep underlying […]
Fractional defect charges for liquid crystals on cones We study two-dimensional liquid crystals with p-fold rotational symmetry (p-atics) on the surfaces of cones, and find both the ground state(s) and a ladder of quantized metastable states as a function of both the cone angle and the liquid crystal symmetry p. […]
Colloidal clusters from confined self-assembly: Structure – Thermodynamics – Formation kinetics The spontaneous organization of individual building blocks into ordered structures is extensively used in nature and found at all length scales, from crystallization processes, via composite materials, to living cells constituting complex tissue. Understanding the relationship between building blocks, […]
Slimming down through frustration Abstract In many diseases, proteins aggregate into fibers. Why? One could think of molecular reasons, but here we try something more general. We propose that when particles with complex shapes aggregate, geometrical frustration builds up and fibers generically appear. Such a rule could be very useful […]