# Percolation of disordered jammed sphere packings

@article{Ziff2016PercolationOD, title={Percolation of disordered jammed sphere packings}, author={Robert M. Ziff and Salvatore Torquato}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2016}, volume={50} }

We determine the site and bond percolation thresholds for a system of disordered jammed sphere packings in the maximally random jammed state, generated by the Torquato–Jiao algorithm. For the site threshold, which gives the fraction of conducting versus non-conducting spheres necessary for percolation, we find pc=0.3116(3), consistent with the 1979 value of Powell 0.310(5) and identical within errors to the threshold for the simple-cubic lattice, 0.311 608, which shares the same average…

## 40 Citations

### Critical pore radius and transport properties of disordered hard- and overlapping-sphere models.

- GeologyPhysical review. E
- 2021

This work quantifies geometrical and topological descriptors of the pore space of certain disordered and ordered distributions of spheres, including pore-size functions and the critical pore radius δ_{c), and confirms 〈δ^{2}〉 to be a promising candidate for convenient and reliable estimates of the fluid permeability for porous media with a well-connected porespace.

### Percolation in metal-insulator composites of disordered jammed spherocylindrical nanoparticles

- Physics
- 2020

While classical percolation is well understood, percolation effects in random jammed structures are much less explored. Here we investigate both experimentally and theoretically the electrical…

### Percolation in metal-insulator composites of randomly packed spherocylindrical nanoparticles

- PhysicsPhysical Review B
- 2021

While classical percolation is well understood, percolation effects in randomly packed or jammed structures are much less explored. Here we investigate both experimentally and theoretically the…

### Bulk modulus along jamming transition lines of bidisperse granular packings.

- PhysicsPhysical review. E
- 2022

We present three-dimensional discrete element method simulations of bidisperse granular packings to investigate their jamming densities ϕ_{J} and dimensionless bulk moduli K as functions of the size…

### Characterization of maximally random jammed sphere packings. III. Transport and electromagnetic properties via correlation functions.

- PhysicsPhysical review. E
- 2018

The analytic bounds of the MRJ sphere packings predict the qualitative trend in the physical properties associated with these structures, which provides guidance to more time-consuming simulations and experiments.

### Random sequential adsorption of lattice animals on a three-dimensional cubic lattice.

- Computer SciencePhysical review. E
- 2020

The presented results suggest that there is no correlation between the number of possible orientations m of the object and the corresponding values of the jamming density θ_{J}.

### Bond percolation between k separated points on a square lattice.

- MathematicsPhysical review. E
- 2020

We consider a percolation process in which k points separated by a distance proportional the system size L simultaneously connect together (k>1), or a single point at the center of a system connects…

### Exotic Ordered and Disordered Many-Particle Systems with Novel Properties

- Mathematics
- 2017

This dissertation presents studies on several statistical-mechanical problems, many of which involve exotic many-particle systems. In Chapter 2, we present an algorithm to generate Random Sequential…

### Perspective: Basic understanding of condensed phases of matter via packing models.

- Materials ScienceThe Journal of chemical physics
- 2018

This perspective reviews pertinent theoretical and computational literature concerning the equilibrium, metastable, and nonequilibrium packings of hard-particle packings in various Euclidean space dimensions and emphasizes the "geometric-structure" approach, which provides a powerful and unified means to quantitatively characterize individual packings via jamming categories and "order" maps.

### Local order metrics for two-phase media across length scales

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2022

The capacity to devise order metrics to characterize and classify microstructures of multiphase heterogeneous media across length scales is an outstanding but highly challenging task, given the…

## References

SHOWING 1-10 OF 88 REFERENCES

### Nonuniversality of density and disorder in jammed sphere packings

- Physics
- 2011

We show for the first time that collectively jammed disordered packings of three-dimensional monodisperse frictionless hard spheres can be produced and tuned using a novel numerical protocol with…

### Percolation and conduction on the 3D Voronoi and regular networks: a second case study in topological disorder

- Physics
- 1984

To assess the effect of random coordination percolation properties of the three-dimensional (3D) Voronoi network and the body-centred cubic with second-nearest-neighbour bonding (BCC2) are calculated…

### Bond and site percolation in three dimensions.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2013

The bond and site percolation models are simulated on a simple-cubic lattice with linear sizes up to L=512, and various universal amplitudes are obtained, including wrapping probabilities, ratios associated with the cluster-size distribution, and the excess cluster number.

### Dimer covering and percolation frustration.

- Computer Science, MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

A procedure for generating random dimer coverings of a given lattice is proposed and it is observed that the percolation frustration induced as a result of dimer covering is larger in the low-coordination-number square lattice.

### Distinctive features arising in maximally random jammed packings of superballs.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2010

It is found that the MRJ densities of such packings increase dramatically and nonanalytically as one moves away from the circular-disk and sphere point (p=1), and it is shown that such seemingly "special" packing configurations are counterintuitively not rare.

### Detailed characterization of rattlers in exactly isostatic, strictly jammed sphere packings.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2013

J jammed disordered packings of 100≤N≤2000 monodisperse hard spheres in three dimensions whose strictly jammed backbones are demonstrated to be exactly isostatic with unprecedented numerical accuracy by using the Torquato-Jiao (TJ) packing algorithm as a means of studying the maximally random jammed (MRJ) state.

### Fluctuations of the infinite network in percolation theory

- Physics
- 1980

For thermal phase transitions, fluctuations of the order parameter are well known to be related in a simple way to an appropriate susceptibility. For percolation, the infinite network plays the role…

### Jammed hard-particle packings: From Kepler to Bernal and beyond

- Computer Science
- 2010

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…

### High-precision percolation thresholds and Potts-model critical manifolds from graph polynomials

- Mathematics
- 2014

The critical curves of the q-state Potts model can be determined exactly for regular two-dimensional lattices G that are of the three-terminal type. This comprises the square, triangular, hexagonal…

### Maximally random jammed packings of Platonic solids: hyperuniform long-range correlations and isostaticity.

- Materials SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2011

It is found that as the number of facets of the particles increases, the translational order in the packings increases while the orientational order decreases, providing further evidence that hyperuniform quasi-long-range correlations are a universal feature of MRJ packings of frictionless particles of general shape.