Square lattice site percolation at increasing ranges of neighbor interactions

  title={Square lattice site percolation at increasing ranges of neighbor interactions},
  author={K.Malarz and S.Galam},
We report site percolation thresholds for square lattice with neighbor interactions at various increasing ranges. Using Monte Carlo techniques we found that nearest neighbors (N 2 ), next nearest neighbors (N 3 ), next next nearest neighbors (N 4 ) and fifth nearest neighbors (N 6 ) yield the same p c = 0 . 592 · · · . At odds, fourth nearest neighbors (N 5 ) give p c = 0 . 298 · · · . These results are given an explanation in terms of symmetry arguments. We then consider combinations of various… 

Figures and Tables from this paper

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

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

Alloying a single and a double perovskite: a Cu+/2+ mixed-valence layered halide perovskite with strong optical absorption†

A tiling model is proposed to describe how the Cu+, Cu2+, and In3+ coordination spheres can pack most favorably into a 2D perovskite lattice, which explains the unusual 1 : 2‬:‬1 ratio of these cations found in 1.

Influence of network defects on the conformational structure of nanogel particles: From "closed compact" to "open fractal" nanogel particles.

We propose an approach to generate a wide range of randomly branched polymeric structures to gain general insights into how polymer topology encodes a configurational structure in solution. Nanogel

Machine learning predictions of COVID-19 second wave end-times in Indian states

How the predictability of the SIR model changes with various parameters using a supervised learning algorithm is shown and the condition in which the model gives the least error in predicting the duration of the first wave of the COVID-19 pandemic in different states in India is estimated.

Noise induced unanimity and disorder in opinion formation

An opinion dynamics model based on Latané’s social impact theory is proposed, which shows that opinion formation and spread are influenced by both flow of information among actors and randomness in adopting opinions.

A cellular automaton for modeling non-trivial biomembrane ruptures

Results indicate that the CA can capture non-trivial rupture morphologies such as floral patterns and the saltatory dynamics of fractal avalanches observed in experiments, and provides insight into the poorly understood role of inter-layer adhesion, supporting the hypothesis that the density of adhesion sites governs rupture morphology.



Introduction To Percolation Theory

Preface to the Second Edition Preface to the First Edition Introduction: Forest Fires, Fractal Oil Fields, and Diffusion What is percolation? Forest fires Oil fields and fractals Diffusion in

Applications of Percolation Theory

Percolation theory for mathematicians

Statistical Mechanics:

AbstractPROF. R. H. FOWLER'S monumental work on statistical mechanics has, in this the second edition, in his own modest words, been rearranged and brought more up to date. But the new volume is much

) ; A . M . Vidales at al

  • Europhys . Lett .
  • 1999

Physica A 323 , 695 ( 2003 ) ; S . Galam , Physica A 336 , 49 ( 2004 ) ; S . Galam

  • Eur . Phys . J . B
  • 2002

Percolation in Fractals and Disordered Systems

  • Eds. A. Bunde and S. Hauling,
  • 1991


    Physica A 235

    • 573
    • 1997