We prove that the Cohn-Elkies linear programming bound for sphere packing is not sharp in dimension 6. The proof uses duality and optimization over a space of modular forms, generalizing a construction of Cohn- Triantafillou [Math. Comp. 91 (2021), pp. 491 ...
Why are materials with specific characteristics more abundant than others? This is a fundamental question in materials science and one that is traditionally difficult to tackle, given the vastness of compositional and configurational space. We highlight he ...
Hard-sphere colloids are model systems in which to study the glass transition and universal properties of amorphous solids. Using covariance matrix analysis to determine the vibrational modes, we experimentally measure here the scaling behavior of the dens ...
Thin colloidal photonic crystals were grown using shear-flow crystallization of polystyrene colloidal nanoparticles. The arrays consist of two types of domains, which are clearly visible on scanning electron microscopy patterns. Both domains have cubic clo ...
