Calculation of the Voronoi boundary for lens-shaped particles and spherocylinders

@article{Portal2013CalculationOT,
  title={Calculation of the Voronoi boundary for lens-shaped particles and spherocylinders},
  author={Louis Portal and Maximilien Danisch and Adrian Baule and Romain Mari and Hern{\'a}n A. Makse},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  year={2013},
  volume={2013},
  pages={11009}
}
We have recently developed a mean-field theory to estimate the packing fraction of non-spherical particles (Baule et al 2013 Nature Commun. 4 2194). The central quantity in this framework is the Voronoi excluded volume, which generalizes the standard hard-core excluded volume appearing in Onsager's theory. The Voronoi excluded volume is defined from an exclusion condition for the Voronoi boundary between two particles, which is usually not tractable analytically. Here, we show how the technical… 

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References

SHOWING 1-10 OF 23 REFERENCES
Random packings of spheres and spherocylinders simulated by mechanical contraction.
  • S. R. Williams, A. Philipse
  • Materials Science, Medicine
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2003
TLDR
A simulation technique for creating dense random packings of hard particles is introduced, particularly suited to handle particles of different shapes, and Comparisons between the equilibrium phase diagram for hard spherocylinders and the densest possible amorphous packings have interesting implications on the crystallization of sphero cylinders as a function of aspect ratio.
Mean-field theory of random close packings of axisymmetric particles.
TLDR
A mean-field formalism is presented to estimate the packing density of axisymmetric non-spherical particles, derived from an analytic continuation from the sphere that provides a phase diagram predicting that, for the same coordination number, the density of monodisperse random packings follows the sequence of increasing packing fractions.
Experiments on random packings of ellipsoids.
TLDR
A novel way of determining packing density for a finite sample that minimizes surface effects is introduced and fabricated ellipsoids are fabricated and it is shown that, in a sphere, the radial packing fraction phi(r) can be obtained from V(h), the volume of added fluid to fill the sphere to height h.
Influence of particle shape on the packing and on the segregation of spherocylinders via Monte Carlo simulations
Knowledge of the properties of granular materials is important for efficient and safe design of industrial equipment. In this work, the Monte Carlo method is used for simulating granular systems of
Model of random packings of different size balls.
TLDR
A model to describe the properties of random assemblies of polydisperse hard spheres that allows to determine the optimal packing over different distributions and may help to treat packing problems of nonspherical particles which are notoriously difficult to solve.
THE EFFECTS OF SHAPE ON THE INTERACTION OF COLLOIDAL PARTICLES
Introdzution. The shapes of colloidal particles are often reasonably compact, so that no diameter greatly exceeds the cube root of the volume of the particle. On the other hand, we know many coiloids
Organizing principles for dense packings of nonspherical hard particles: not all shapes are created equal.
  • S. Torquato, Y. Jiao
  • Mathematics, Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2012
TLDR
General organizing principles enable us to construct analytically the densest known packings of certain convex nonspherical particles, including spherocylinders, "lens-shaped" particles, square pyramids, and rhombic pyramids and it is shown how to apply these principles to infer the high-density equilibrium crystalline phases of hard convex and concave particles.
Predictive Self-Assembly of Polyhedra into Complex Structures
TLDR
145 convex polyhedra whose assembly arises solely from their anisotropic shape are investigated, demonstrating a remarkably high propensity for thermodynamic self-assembly and structural diversity.
A phase diagram for jammed matter
TLDR
This work presents a statistical description of jammed states in which random close packing can be interpreted as the ground state of the ensemble of jammed matter and demonstrates that random packings of hard spheres in three dimensions cannot exceed a density limit of ∼63.4 per cent.
Jammed hard-particle packings: From Kepler to Bernal and beyond
This review describes the diversity of jammed configurations attainable by frictionless convex nonoverlapping (hard) particles in Euclidean spaces and for that purpose it stresses individual-packing
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