### Abstract

We introduce a class of discrete-continuous percolation models and an efficient Monte Carlo algorithm for computing their properties. The class is general enough to include well-known discrete and continuous models as special cases. We focus on a particular example of such a model, a nanotube model of disintegration of activated carbon. We calculate its exact critical threshold in two dimensions and obtain a Monte Carlo estimate in three dimensions. Furthermore, we use this example to analyze and characterize the efficiency of our algorithm, by computing critical exponents and properties, finding that it compares favorably to well-known algorithms for simpler systems.

Original language | English (US) |
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Article number | 022127 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 93 |

Issue number | 2 |

DOIs | |

State | Published - Feb 18 2016 |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Statistics and Probability

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*93*(2), [022127]. https://doi.org/10.1103/PhysRevE.93.022127

**Percolation thresholds for discrete-continuous models with nonuniform probabilities of bond formation.** / Szczygieł, Bartłomiej; Dudyński, Marek; Kwiatkowski, Kamil; Lewenstein, Maciej; Lapeyre, Gerald John; Wehr, Jan.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 93, no. 2, 022127. https://doi.org/10.1103/PhysRevE.93.022127

}

TY - JOUR

T1 - Percolation thresholds for discrete-continuous models with nonuniform probabilities of bond formation

AU - Szczygieł, Bartłomiej

AU - Dudyński, Marek

AU - Kwiatkowski, Kamil

AU - Lewenstein, Maciej

AU - Lapeyre, Gerald John

AU - Wehr, Jan

PY - 2016/2/18

Y1 - 2016/2/18

N2 - We introduce a class of discrete-continuous percolation models and an efficient Monte Carlo algorithm for computing their properties. The class is general enough to include well-known discrete and continuous models as special cases. We focus on a particular example of such a model, a nanotube model of disintegration of activated carbon. We calculate its exact critical threshold in two dimensions and obtain a Monte Carlo estimate in three dimensions. Furthermore, we use this example to analyze and characterize the efficiency of our algorithm, by computing critical exponents and properties, finding that it compares favorably to well-known algorithms for simpler systems.

AB - We introduce a class of discrete-continuous percolation models and an efficient Monte Carlo algorithm for computing their properties. The class is general enough to include well-known discrete and continuous models as special cases. We focus on a particular example of such a model, a nanotube model of disintegration of activated carbon. We calculate its exact critical threshold in two dimensions and obtain a Monte Carlo estimate in three dimensions. Furthermore, we use this example to analyze and characterize the efficiency of our algorithm, by computing critical exponents and properties, finding that it compares favorably to well-known algorithms for simpler systems.

UR - http://www.scopus.com/inward/record.url?scp=84959432607&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84959432607&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.93.022127

DO - 10.1103/PhysRevE.93.022127

M3 - Article

AN - SCOPUS:84959432607

VL - 93

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 2

M1 - 022127

ER -