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Packing problems, such as how densely objects can fill a volume, are among the most ancient and persistent problems in mathematics and science. For equal spheres, it has only recently been proved that the face-centered cubic lattice has the highest possible packing fraction phi=pi/18 approximately 0.74. It is also well known that certain random (amorphous)(More)
the conditional probability of finding a particle at position x after time t with the particle located for t ϭ 0 at x ϭ 0. In Fig. 3A, we show the result of p(x, t) for ⌫ ϭ 4 at four different times, which are all greater than t c. Self-diffusion of particles causes p(x, t) to broaden with time. Despite the simplicity of the physical situation describing SF(More)
In this Letter, we report on the densest-known packings of congruent ellipsoids. The family of new packings consists of crystal arrangements of spheroids with a wide range of aspect ratios, and with density phi always surpassing that of the densest Bravais lattice packing phi approximately equal to 0.7405. A remarkable maximum density of phi approximately(More)
Quasicrystalline structures may have optical bandgap properties-frequency ranges in which the propagation of light is forbidden-that make them well-suited to the scientific and technological applications for which photonic crystals are normally considered. Such quasicrystals can be constructed from two or more types of dielectric material arranged in a(More)
Tetrahedra may be the ultimate frustrating, disordered glass forming units. Our experiments on tetrahedral dice indicate the densest (volume fraction phi=0.76+/-.02, compared with phi(sphere)=0.64), most disordered, experimental, random packing of any set of congruent convex objects to date. Analysis of MRI scans yield translational and orientational(More)
Spontaneous formation of colonies of bacteria or flocks of birds are examples of self-organization in active living matter. Here, we demonstrate a form of self-organization from nonequilibrium driving forces in a suspension of synthetic photoactivated colloidal particles. They lead to two-dimensional "living crystals," which form, break, explode, and(More)
COMMUNICATION Rossi and Philipse et al. Cubic crystals from cubic colloids The metal nano-antennas confi ne optical energy to a scale smaller than the exciting wavelength. The interaction between the photosensitive polymer material placed above and the localized near fi eld leads to a mass transport resulting in reversible topography changes on a nanometer(More)
New functional materials can in principle be created using colloids that self-assemble into a desired structure by means of a programmable recognition and binding scheme. This idea has been explored by attaching 'programmed' DNA strands to nanometre- and micrometre- sized particles and then using DNA hybridization to direct the placement of the particles in(More)
Hexagons can easily tile a flat surface, but not a curved one. Introducing heptagons and pentagons (defects with topological charge) makes it easier to tile curved surfaces; for example, soccer balls based on the geodesic domes of Buckminster Fuller have exactly 12 pentagons (positive charges). Interacting particles that invariably form hexagonal crystals(More)
Recent simulations indicate that ellipsoids can pack randomly more densely than spheres and, remarkably, for axes ratios near 1.25:1:0.8 can approach the densest crystal packing (fcc) of spheres, with a packing fraction of 74%. We demonstrate that such dense packings are realizable. We introduce a novel way of determining packing density for a finite sample(More)