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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)
We present a study of disordered jammed hard-sphere packings in four-, five-, and six-dimensional Euclidean spaces. Using a collision-driven packing generation algorithm, we obtain the first estimates for the packing fractions of the maximally random jammed (MRJ) states for space dimensions d=4, 5, and 6 to be phi(MRJ) approximately 0.46, 0.31, and 0.20,(More)
We present an efficient method for Monte Carlo simulations of diffusion-reaction processes. Introduced by us in a previous paper [Phys. Rev. Lett. 97, 230602 (2006)], our algorithm skips the traditional small diffusion hops and propagates the diffusing particles over long distances through a sequence of superhops, one particle at a time. By partitioning the(More)
Jamming in hard-particle packings has been the subject of considerable interest in recent years. In a paper by Torquato and Stillinger [J.Phys.Chem. B, 105 (2001)], a classification scheme of jammed packings into hierarchical categories of locally, collectively and strictly jammed configurations has been proposed. They suggest that these jamming categories(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)
Hard-particle packings have provided a rich source of outstanding theoretical problems and served as useful starting points to model the structure of granular media, liquids, living cells, glasses, and random media. The nature of ''jammed'' hard-particle packings is a current subject of keen interest. Elsewhere, we introduced rigorous and efficient(More)
Composite materials are ideally suited to achieve multifunctionality since the best features of different materials can be combined to form a new material that has a broad spectrum of desired properties. Nature's ultimate multifunctional composites are biological materials. There are presently no simple examples that rigorously demonstrate the effect of(More)
We study the approach to jamming in hard-sphere packings and, in particular, the pair correlation function g(2) (r) around contact, both theoretically and computationally. Our computational data unambiguously separate the narrowing delta -function contribution to g(2) due to emerging interparticle contacts from the background contribution due to near(More)
We apply the algorithm presented in the first part of this series of papers to systems of hard ellipses and ellipsoids. The theoretical machinery needed to treat such particles, including the overlap potentials, is developed in full detail. We describe an algorithm for predicting the time of collision for two moving ellipses or ellipsoids. We present(More)
Continuing on recent computational and experimental work on jammed packings of hard ellipsoids [Donev, Science 303, 990 (2004)] we consider jamming in packings of smooth strictly convex nonspherical hard particles. We explain why an isocounting conjecture, which states that for large disordered jammed packings the average contact number per particle is(More)