Motivated by the search for best lattice sphere packings in Euclidean spaces of large dimensions we study randomly generated perfect lattices in moderately large dimensions (up to d=19 included). Perfect lattices are relevant in the solution of the problem of lattice sphere packing, because the best lattice packing is a perfect lattice and because they can be generated easily. Their number, how...

The bin packing structure arises in a wide range of service operational applications, where a set of items are assigned to multiple bins with fixed capacities. With random item weights, a chanceconstrained bin packing problem bounds, for each bin, the probability that the total weight of packed items exceeds the bin’s capacity. Different from the stochastic programming approaches relying on ful...

We investigate equal spheres packings generated from several experiments and from a large number of different numerical simulations. The structural organization of these disordered packings is studied in terms of the network of common neighbours. This geometrical analysis reveals sharp changes in the network’s clustering occurring at the packing fractions (fraction of volume occupied by the sph...

In previous papers analytical expressions were derived and validated for the packing fraction of bimodal hard spheres with small size ratio, applicable to ordered (crystalline) [H. J. H. Brouwers, Phys. Rev. E 76, 041304 (2007);H. J. H. Brouwers, Phys. Rev. E 78, 011303 (2008)] and disordered (random) packings [H. J. H. Brouwers, Phys. Rev. E 87, 032202 (2013)]. In the present paper the underly...

Understanding the properties of random packings of solid objects is of critical importance to a wide variety of fundamental scientific and practical problems. The great majority of the previous works focused, however, on packings of spherical and sphere-like particles. We report the first detailed simulation and characterization of packings of non-overlapping cubic particles. Such packings aris...

We introduce an algorithmic framework for tuning the spatial density of disks in a maximal random packing, without changing the sizing function or radii of disks. Starting from any maximal random packing such as a Maximal Poisson-disk Sampling (MPS), we iteratively relocate, inject (add), or eject (remove) disks, using a set of three successively more-aggressive local operations. We may achieve...

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 can be tested using numerical algorith...

Let X = {X(t), t ∈ RN} be a Gaussian random field with values in R defined by X(t) = ( X1(t), . . . , Xd(t) ) , ∀ t ∈ R , where X1, . . . , Xd are independent copies of a centered Gaussian random field X0. Under certain general conditions, Xiao (2007a) defined an upper index α∗ and a lower index α∗ for X0 and showed that the Hausdorff dimensions of the range X ( [0, 1] ) and graph GrX ( [0, 1] ...

in a graph g = (v,e), a subset s  v is said to be an open packing set if no two vertices of s have a common neighbour in g. the maximum cardinality of an open packing set is called the open packing number and is denoted by rho^o. this paper further studies on this parameter by obtaining some new bounds.

In a recent paper, we showed that every sufficiently large regular digraph G on n vertices whose degree is linear in n and which is a robust outexpander has a decomposition into edge-disjoint Hamilton cycles. The main consequence of this theorem is that every regular tournament on n vertices can be decomposed into (n − 1)/2 edge-disjoint Hamilton cycles, whenever n is sufficiently large. This v...