416 research outputs found
Complexity in surfaces of densest packings for families of polyhedra
Packings of hard polyhedra have been studied for centuries due to their
mathematical aesthetic and more recently for their applications in fields such
as nanoscience, granular and colloidal matter, and biology. In all these
fields, particle shape is important for structure and properties, especially
upon crowding. Here, we explore packing as a function of shape. By combining
simulations and analytic calculations, we study three 2-parameter families of
hard polyhedra and report an extensive and systematic analysis of the densest
packings of more than 55,000 convex shapes. The three families have the
symmetries of triangle groups (icosahedral, octahedral, tetrahedral) and
interpolate between various symmetric solids (Platonic, Archimedean, Catalan).
We find that optimal (maximum) packing density surfaces that reveal unexpected
richness and complexity, containing as many as 130 different structures within
a single family. Our results demonstrate the utility of thinking of shape not
as a static property of an object in the context of packings, but rather as but
one point in a higher dimensional shape space whose neighbors in that space may
have identical or markedly different packings. Finally, we present and
interpret our packing results in a consistent and generally applicable way by
proposing a method to distinguish regions of packings and classify types of
transitions between them.Comment: 16 pages, 8 figure
Dense packing crystal structures of physical tetrahedra
We present a method for discovering dense packings of general convex hard
particles and apply it to study the dense packing behavior of a one-parameter
family of particles with tetrahedral symmetry representing a deformation of the
ideal mathematical tetrahedron into a less ideal, physical, tetrahedron and all
the way to the sphere. Thus, we also connect the two well studied problems of
sphere packing and tetrahedron packing on a single axis. Our numerical results
uncover a rich optimal-packing behavior, compared to that of other continuous
families of particles previously studied. We present four structures as
candidates for the optimal packing at different values of the parameter,
providing an atlas of crystal structures which might be observed in systems of
nano-particles with tetrahedral symmetry
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