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 […]
From cylinder packings to auxetic periodic tensegrity structures Abstract I will present a chiral, triply-periodic tensegrity structure, which displays local reentrant geometry at its vertices. Our tensegrity structure is based on the β−Mn cylinder packing from structural chemistry, and contains all symmetries of the cylinder packing itself. The tensegrity structure is auxetic, as demonstrated by the modelling of a quasi-static extension and compression […]
The Wrinkle-to-Crumple Transition in Thin Elastic Solids Abstract The last decade has seen a renaissance in the buckling of thin elastic solids, in part because of its impact on the mechanics of synthetic skins, biological tissues, textiles, and 2D materials like graphene. Significant effort has been devoted to understanding and […]
Symmetry Making and Breaking in Seeded Syntheses of Metal Nanocrystals Abstract Crystal growth theory predicts that heterogeneous nucleation will occur preferentially at defect sites, such as the vertices rather than the faces of shape-controlled seeds. Platonic metal solids are generally assumed to have vertices with nearly identical chemical potentials, and […]