# Percolation of overlapping squares or cubes on a lattice

@article{Koza2014PercolationOO, title={Percolation of overlapping squares or cubes on a lattice}, author={Zbigniew Koza and Grzegorz Kondrat and Karol Suszczy'nski}, journal={Journal of Statistical Mechanics: Theory and Experiment}, year={2014}, volume={2014} }

Porous media are often modeled as systems of overlapping obstacles, which leads to the problem of two percolation thresholds in such systems, one for the porous matrix and the other for the void space. Here we investigate these percolation thresholds in the model of overlapping squares or cubes of linear size k > 1 randomly distributed on a regular lattice. We find that the percolation threshold of obstacles is a nonmonotonic function of k, whereas the percolation threshold of the void space is…

## 16 Citations

### Site percolation on square and simple cubic lattices with extended neighborhoods and their continuum limit.

- PhysicsPhysical review. E
- 2021

By means of extensive Monte Carlo simulation, extended-range site percolation on square and simple cubic lattices with various combinations of nearest neighbors up to the eighth nearest neighbors for the square lattice and the ninth nearestNeighborhoods are found using a single-cluster growth algorithm.

### Bond percolation on simple cubic lattices with extended neighborhoods.

- PhysicsPhysical review. E
- 2020

The results show that the percolation thresholds of these and other three-dimensional lattices decrease monotonically with the coordination number z quite accurately according to a power-law p_{c}∼z^{-a} with exponent a=1.111.

### Point to point continuum percolation in two dimensions

- Physics
- 2016

The outcome of the classic percolation approach is several power-law curves with some universal (critical) exponents. Here, the universality means that these power laws as well as their critical…

### From discrete to continuous percolation in dimensions 3 to 7

- Mathematics, Computer Science
- 2016

The convergence of a discrete model to its continuous limit is controlled by a power-law dependency with a universal exponent θ=3/2, which allows us to estimate the continuous percolation thresholds in a model of aligned hypercubes in dimensions d=3,…,7 with accuracy far better than that attained using any other method before.

### Scaling and critical behavior of lattice and continuum porous media with different connectivity configurations

- PhysicsPhysica A: Statistical Mechanics and its Applications
- 2018

### Site and bond percolation thresholds on regular lattices with compact extended-range neighborhoods in two and three dimensions.

- PhysicsPhysical review. E
- 2022

Extended-range percolation on various regular lattices, including all 11 Archimedean lattices in two dimensions and the simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc)…

### Percolation through Voids around Randomly Oriented Polyhedra and Axially Symmetric Grains.

- GeologyPhysical review letters
- 2018

The critical number density per volume is calculated for a variety of axially symmetric shapes and faceted solids with the former including cylinders, ellipsoids, cones, and tablet shaped grains from highly oblate (platelike) to highly prolate (needlelike) extremes.

### Percolation of hyperspheres in dimensions 3 to 5: from discrete to continuous

- MathematicsJournal of Statistical Mechanics: Theory and Experiment
- 2022

We study the onset of percolation of overlapping discrete hyperspheres on hypercubic lattices in dimension D = 3, 4, 5. Taking the continuum limit of the thresholds for discrete hyperspheres we…

### Site and bond percolation on four-dimensional simple hypercubic lattices with extended neighborhoods

- PhysicsJournal of Statistical Mechanics: Theory and Experiment
- 2022

The asymptotic behavior of the percolation threshold p c and its dependence upon coordination number z is investigated for both site and bond percolation on four-dimensional lattices with compact…

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