Bond percolation in±JIsing square lattices diluted by frustration

1998 ◽  
Vol 58 (13) ◽  
pp. 8475-8480 ◽  
Author(s):  
E. E Vogel ◽  
S. Contreras ◽  
M. A. Osorio ◽  
J. Cartes ◽  
F. Nieto ◽  
...  
Keyword(s):  
Bond Percolation

scholarly journals Phase transitions in a two-component site-bond percolation model

2000 ◽  
Vol 62 (13) ◽  
pp. 8719-8724 ◽  
Author(s):  
H. M. Harreis ◽  
W. Bauer
Keyword(s):  
Phase Transitions ◽  
Percolation Model ◽  
Bond Percolation ◽  
Two Component

Site-bond percolation in two-dimensional kagome lattices: Analytical approach and numerical simulations

2021 ◽  
Vol 104 (1) ◽  
Author(s):  
M. I. González-Flores ◽  
A. A. Torres ◽  
W. Lebrecht ◽  
A. J. Ramirez-Pastor
Keyword(s):  
Numerical Simulations ◽  
Analytical Approach ◽  
Bond Percolation ◽  
Two Dimensional

scholarly journals Pathogen Mutation Modeled by Competition Between Site and Bond Percolation

2013 ◽  
Vol 110 (10) ◽  
Author(s):  
Laurent Hébert-Dufresne ◽  
Oscar Patterson-Lomba ◽  
Georg M. Goerg ◽  
Benjamin M. Althouse
Keyword(s):  
Bond Percolation

Critical Probabilities of 1-Independent Percolation Models

2012 ◽  
Vol 21 (1-2) ◽  
pp. 11-22 ◽  
Author(s):  
PAUL BALISTER ◽  
BÉLA BOLLOBÁS
Keyword(s):  
Infinite Graph ◽  
Percolation Model ◽  
Bond Percolation ◽  
Locally Finite

Given a locally finite connected infinite graphG, let the interval [pmin(G),pmax(G)] be the smallest interval such that ifp>pmax(G), then every 1-independent bond percolation model onGwith bond probabilityppercolates, and forp<pmin(G) none does. We determine this interval for trees in terms of the branching number of the tree. We also give some general bounds for other graphsG, in particular for lattices.

On spàtial general epidemics and bond percolation processes

1984 ◽  
Vol 21 (4) ◽  
pp. 911-914 ◽  
Author(s):  
Kari Kuulasmaa ◽  
Stan Zachary
Keyword(s):  
Lower Bound ◽  
Bond Percolation ◽  
Percolation Process ◽  
Percolation Probability ◽  
Percolation Processes

We show that a lower bound for the probability that a spatial general epidemic never becomes extinct is given by the percolation probability of an associated bond percolation process.

scholarly journals The SI and SIR epidemics on general networks

2018 ◽  
Vol 37 (2) ◽  
pp. 229-234
Author(s):  
David Aldous
Keyword(s):  
Recent Result ◽  
Parameter Space ◽  
Epidemic Model ◽  
Small Proportion ◽  
High Probability ◽  
Bond Percolation ◽  
Sir Epidemic ◽  
Sir Epidemic Models ◽  
Lower Dimensional ◽  
General Networks

THE SI AND SIR EPIDEMICS ON GENERAL NETWORKSIntuitively one expects that for any plausible parametric epide mic model, there wil l be some region in parameter-space where the epidemicaffects with high probability only a small proportion of a largepopulation, another region where it affects with high probability a nonnegligible proportion, with a lower-dimensional “critical” interface. This dichotomy is certainly true in well-studied specific models, but we know o fno very general results. A recent result stated for a bond percolation modelcan be restated as giving weak conditions under which the dichotomy holdsfor an SI epidemic model on arbitrary finite networks. This result suggestsa conjecture for more complex and more realistic SIR epidemic models, and the purpose of this article is to record the conjecture.

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