# Percolation thresholds for discorectangles: Numerical estimation for a range of aspect ratios.

@article{Tarasevich2019PercolationTF, title={Percolation thresholds for discorectangles: Numerical estimation for a range of aspect ratios.}, author={Yuri Yu. Tarasevich and Andrei V. Eserkepov}, journal={Physical review. E}, year={2019}, volume={101 2-1}, pages={ 022108 } }

Using Monte Carlo simulation, we have studied the percolation of discorectangles. Also known as stadiums or two-dimensional spherocylinders, a discorectangle is a rectangle with semicircles at a pair of opposite sides. Scaling analysis was performed to obtain the percolation thresholds in the thermodynamic limits. We found that (i) for the two marginal aspect ratios ɛ=1 (disc) and ɛ→∞ (stick) the percolation thresholds coincide with known values within the statistical error and (ii) for…

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Yuri Yu. Tarasevich, ∗ Andrei V. Eserkepov, † Renat K. Akhunzhanov, ‡ Irina V. Vodolazskaya, § and Mikhail V. Ulyanov 3, ¶ Laboratory of Mathematical Modeling, Astrakhan State University, Astrakhan…

## References

SHOWING 1-10 OF 28 REFERENCES

### Continuum percolation of congruent overlapping spherocylinders.

- PhysicsPhysical review. E
- 2016

It is found ϕ_{c} is a universal monotonic decreasing function of α and is independent of the effective particle size and has implications in percolation theory for nonspherical particles and composite material design.

### Percolation Thresholds and Excluded Area for Penetrable Rectangles in Two Dimensions

- Mathematics
- 2015

The percolation threshold for penetrable rectangles in two dimensions is examined by way of an analogy to a lattice model that employs the averaged pairwise excluded area between particles as a key…

### Continuum Percolation Thresholds in Two Dimensions

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012

This work finds precise values of the percolation transition for disks, squares, rotated squares, and rotated sticks in two dimensions and confirms that these transitions behave as conformal field theory predicts.

### Percolation of binary disk systems: Modeling and theory.

- PhysicsPhysical review. E
- 2017

Monte Carlo simulations and spanning probability are used to extend prior models into regions of higher polydispersity than those previously considered and a correlation to predict the percolation threshold for binary disk systems is proposed.

### Precise percolation thresholds of two-dimensional random systems comprising overlapping ellipses

- Physics
- 2016

### Connectivity percolation of polydisperse anisotropic nanofillers.

- MathematicsThe Journal of chemical physics
- 2011

It is shown that for a given average length, a length distribution that is strongly skewed to shorter lengths produces the lowest threshold relative to the equivalent monodisperse one, and if the lengths and diameters of the particles are linearly correlated, polydispersity raises the percolation threshold and more so for a more skewed distribution toward smaller lengths.

### Percolation thresholds of two-dimensional continuum systems of rectangles.

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

It is confirmed that percolation thresholds are dominated by the average excluded areas for both homogeneous and heterogeneous rectangle systems (except for some special heterogeneous systems where the rectangle lengths differ too much from one another).

### Percolation of sticks: Effect of stick alignment and length dispersity

- PhysicsPhysical Review E
- 2018

Using Monte Carlo simulation, we studied the percolation of sticks, i.e. zero-width rods, on a plane paying special attention to the effects of stick alignment and their length dispersity. The stick…

### Finite-size scaling in stick percolation.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

A high-efficiency algorithm for Monte Carlo simulations is developed to investigate, with extensive realizations, the finite-size scaling behavior of stick percolation in large-size systems and results indicate that the spanning probability of stickPercolation on square systems with free boundary conditions falls on the same universal scaling function as that for lattice percolations.

### Connectedness percolation of hard convex polygonal rods and platelets.

- Materials ScienceThe Journal of chemical physics
- 2018

This work analytically calculates the percolation threshold of hard convex particles in terms of three single-particle measures and finds that the universal scaling of the perColation threshold is lowered by decreasing the number of sides of the particle cross section.