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 $ρ^{o}$. This paper further studies on this parameter by obtaining some new bounds.

Abstract Realistic yet efficient representation of particle shape is a major challenge for the Discrete Element Method. This paper uses angle-of-repose and direct-shear test simulations to describe influence several methods, their parameters, on bulk response granular assemblies. Three rolling resistance models, with varying coefficient friction, are considered spherical particles. For non-sphe...

It remains an open question whether statistical mechanics approaches apply to random packings of athermal particles. Although a jamming phase diagram has recently been proposed for hard spheres with varying friction, here we use a frictionless emulsion system in the presence of depletion forces to sample the available phase space of packing configurations. Using confocal microscopy, we access t...

This paper studies a variant of the three-dimensional bin packing problem (3D-BPP), where the bin height can be adjusted to the cartons it packs. The bins and cartons to be packed are assumed rectangular in shape. The cartons are allowed to be rotated into any one of the six positions that keep the carton edges parallel to the bin edges. This greatly increases the difficulty of finding a good s...

The title compound, C(16)H(20)N(2)O(4)S, exhibits a V-shape structure with a dihedral angle of 77.5 (11)° formed by the two benzenel rings. The mol-ecular packing is stabilized by intra-molecular and inter-molecular hydrogen bonds as well as π-π [3.738 (3) Å] and C-H⋯π inter-actions.

100% dry assembly using shape matching and van der Waals attraction for parts transfer has been performed to achieve high density parts packing (up to 92%) of thermoelectric cooling components. The feasibility of this approach has been examined for component sizes across a range of 130800μm.

We present a model of (modified) gravity on spacetimes with fractal structure based on packing of spheres, which are (Euclidean) variants of the Packed Swiss Cheese Cosmology models. As the action functional for gravity we consider the spectral action of noncommutative geometry, and we compute its asymptotic expansion on a space obtained as an Apollonian packing of 3-dimensional spheres inside ...

In this abstract, we present a rule-based modelling language for constraint programming, called Rules2CP [1], and a library PKML for modelling packing problems. Unlike other modelling languages, Rules2CP adopts a single knowledge representation paradigm based on logical rules without recursion, and a restricted set of data structures based on records and enumerated lists given with iterators. W...