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

Recent advances in management of cryptococcal meningitis: commentary

Cryptococcal meningitis remains a substantial health burden with high morbidity, particularly in developing countries. Antifungal treatment regimens are guided by host factors, severity of illness (including presence of complications), and causative cryptococcal species. Recent clinical studies indicate the need for rapidly fungicidal induction therapy regimens using amphotericin B in combination with flucytosine for optimal outcomes. Maintenance therapy with fluconazole is necessary until recovery of immune function. Cryptococcus gattii meningitis requires prolonged induction/eradication therapy. Prompt control of raised intracranial pressure or hydrocephalus is essential. Clinicians should be vigilant for immune restoration-like features. Adjuvant surgery, corticosteroids, and/or recombinant interferon-gamma may be required for large cryptococcomas, cerebral edema, or refractory infection

A Precise Packing Sequence for Self-Assembled Convex Structures

Molecular simulations of the self-assembly of cone-shaped particles with specific, attractive interactions are performed. Upon cooling from random initial conditions, we find that the cones self assemble into clusters and that clusters comprised of particular numbers of cones (e.g. 4 - 17, 20, 27, 32, 42) have a unique and precisely packed structure that is robust over a range of cone angles. These precise clusters form a sequence of structures at specific cluster sizes- a precise packing sequence - that for small sizes is identical to that observed in evaporation-driven assembly of colloidal spheres. We further show that this sequence is reproduced and extended in simulations of two simple models of spheres self-assembling from random initial conditions subject to certain convexity constraints. This sequence contains six of the most common virus capsid structures obtained in vivo including large chiral clusters, and a cluster that may correspond to several non-icosahedral, spherical virus capsid structures obtained in vivo. Our findings suggest this precise packing sequence results from free energy minimization subject to convexity constraints and is applicable to a broad range of assembly processes.Comment: 23 pages, 3 figure

Biomolecule-directed assembly of nanoscale building blocks studied via lattice Monte Carlo simulation

We perform lattice Monte Carlo simulations to study the self-assembly of functionalized inorganic nanoscale building blocks using recognitive biomolecule linkers. We develop a minimal coarse-grained lattice model for the nanoscale building block (NBB) and the recognitive linkers. Using this model, we explore the influence of the size ratio of linker length to NBB diameter on the assembly process and the structural properties of the resulting aggregates, including the spatial distribution of NBBs and aggregate topology. We find the constant-kernel Smoluchowski theory of diffusion-limited cluster–cluster aggregation describes the aggregation kinetics for certain size ratios. © 2004 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70812/2/JCPSA6-121-8-3919-1.pd