A geometric probabilistic approach to random packing of hard disks in a plane
Literature Information
In this paper, the random packing fraction of hard disks in a plane is analyzed, following a geometric probabilistic approach. First, the random close packing (RCP) of equally sized disks is modelled. Subsequently, following the same methodology, a simple, statistical geometric model is proposed for the random loose packing (RLP) of monodisperse disks. This very basic derivation of RLP leads to a packing value (≈0.66) that is in very good agreement with values that have been obtained previously for 2D disk packings. The present geometrical model also enables a closed-form expression for the contact (coordination) number as a function of the packing density at different states of compaction. These predictions are thoroughly compared with empirical and simulation results, among others the Rényi parking model, yielding good agreement.
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Soft Matter
Soft Matter provides a unique forum for the communication of significant advances in interdisciplinary soft matter research. There is a particular focus on the interface between chemistry, physics, materials science, biology and chemical engineering. Research may report new soft materials or phenomena, encompass their design, synthesis, and use in new applications; or provide fundamental insight and observations on their behaviour. Experimental, theoretical and computational soft matter approaches are encouraged. The scope of Soft Matter covers the following. Soft matter assemblies, including colloids, granular matter, liquid crystals, gels & networks, polymers, hybrid materials, active matter and further examples Soft nanotechnology, soft robotics and devices Synthesis, self-assembly and directed assembly Biological aspects of soft matter including proteins, biopolymers, cells and tissues Surfaces, interfaces and interactions Phase behaviour, coacervation and rheological behaviour Sustainable soft materials including recycling, circular economy and end of life Mechanistic insights and modelling
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