This paper addresses the void fraction of polydisperse particles with a Weibull (or Rosin-Rammler) size distribution. It is demonstrated that the governing parameters of this distribution can be uniquely related to those of the lognormal distribution. Hence, an existing closed-form expression that predicts the void fraction of particles with a lognormal size distribution can be transformed into...

1 Abstract A random greedy algorithm, somewhat modiied, is analyzed by using a real time context and showing that the variables remain close to the solution of a natural diierential equation. Given a (k + 1)-uniform simple hypergraph on N vertices, regular of degree D, the algorithm gives a packing of disjoint hyperedges containing all but O(ND ?1=k ln c D) of the vertices. Let H = (V; E) be a ...

We have studied how two- and three-dimensional systems made up of particles interacting with finite range, repulsive potentials jam (i.e., develop a yield stress in a disordered state) at zero temperature and zero applied stress. At low packing fractions phi, the system is not jammed and each particle can move without impediment from its neighbors. For each configuration, there is a unique jamm...

We prove that the First Fit bin packing algorithm is stable under the input distribution U {k − 2, k} for all k ≥ 3, settling an open question from the recent survey by Coffman, Garey, and Johnson [3]. Our proof generalizes the multi-dimensional Markov chain analysis used by Kenyon, Rabani, and Sinclair to prove that Best Fit is also stable under these distributions [11]. Our proof is motivated...

The nature of randomness in disordered packings of frictional and frictionless spheres is investigated using theory and simulations of identical spherical grains. The entropy of the packings is defined through the force and volume ensemble of jammed matter and this is shown to be difficult to calculate analytically. A mesoscopic ensemble of isostatic states is then utilized in an effort to pred...

We answer the questions raised by Donev, Torquato, Stillinger, and Connelly (DTSC) in their preceding Comment on “Jamming at zero temperature and zero applied stress: The epitome of disorder” [Phys. Rev. E 70, 043301 (2004)] We emphasize that we follow a fundamentally different approach than they have done to reinterpret random close packing in terms of the “maximally random jammed” framework. ...

The simulation of granular materials requires an initial overlap-free packing of spherical particles at high volume packing fractions. In previous work, a dynamics-based collective approach, the Quasi-Dynamics Method (QDM), has been proposed to generate densely distributed spheres in an enclosed container. However, the stability and efficiency of the QDM were not fully addressed. In this paper,...

The high packing density of residues in proteins ought to be manifested in some order; to date this packing order has not been thoroughly characterized. The packing regularity in proteins is important because the internal organization of proteins can have a dominant effect on functional dynamics, and it can aid in the design, simulation and evaluation of structures. Packing metrics could also i...