Inhomogeneous Site Percolation on an Irregular Bethe Lattice with Random Site Distribution

Ren, Jing; Zhang, Liying

doi:10.1007/s10955-017-1803-1

Cited by 8 publications

(3 citation statements)

References 29 publications

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“…where, ∂Y ∂β is the partial derivative of Y with respect to β, β Y is given to normalize the index by dimensionless [4], which can measure the sensitivity explicitly and objectively. By the definition, the larger absolute value of sensitivity index indicates quantitatively that the corresponding input factor has stronger impact on system output.…”

Section: Appendix C Sensitivity Analysis Of the Modelmentioning

confidence: 99%

“…Percolation is a powerful tool in statistical physics for dealing with phase transition and disorder property of complex systems. The percolation model often involves an underlying network, which has progressed from simple one-dimensional lattice [1], Bethe lattice [2][3][4], and square lattice [5,6]; to complex random network [7][8][9], bilayer network [10][11][12], and multilayer network [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

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Inhomogeneous percolation on multilayer networks

Zhang¹,

Ren²

2019

J. Stat. Mech.

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A generalization of high-order inhomogeneous bond percolation is studied on a multilayer finite fixed network (MFFN) and a multilayer infinite random network (MIRN). The inhomogeneous bond percolation means that edges in different layers are occupied or removed with distinct probabilities, independently and randomly. Firstly, an analytical approach to simplify the inhomogeneous bond percolation on MFFN is presented, by decomposing the layers into disjoint ones, fusing inhomogeneous bond percolation process and combining weighted layers together to form a monolayer network. Then employing generalised recursive approach, discrete-time dynamical system analysis and fixed-point iteration method, we derive the results for percolating probability and the critical occupation probability, demonstrate the percolation transition and critical phenomenon of inhomogeneous bond percolation on these two networks. It is found that, for inhomogeneous bond percolation on MFFN, the high fraction of intersection speeds up the percolating process; for inhomogeneous bond percolation on MIRN, the increasing mean degree will enlarge the supercritical region and enhance the intensity of percolating process.

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Section: Appendix C Sensitivity Analysis Of the Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Inhomogeneous percolation on multilayer networks

Zhang¹,

Ren²

2019

J. Stat. Mech.

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“…For percolation on irregular but static lattice, curious readers may refer to[33] and references therein 5. This is one of the main reasons why it is not straightforward to implement the propagation of 'civilisation', as we describe it in this paper, as the usual percolation on a square or cubic lattice found in textbooks on computational physics[26][27][28].…”

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confidence: 99%

Percolation of ‘civilisation’ in a homogeneous isotropic universe

Alinea,

Jadrin

2023

Eur. J. Phys.

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In this work, we consider the spread of a `civilisation' in an idealised homogeneous isotropic universe where all the planets of interest are habitable. Following a framework that goes beyond the usual idea of percolation in common undergraduate computational physics textbooks, we investigate the behaviour of the number of colonised planets with time, and the total colonisation time for three types of universes. These include static, dark energy-dominated, and matter-dominated universes. For all these types of universes, we find a remarkable fit with the Logistic Growth Function for the number of colonised planets with time. This is in spite of the fact that for the matter- and dark-energy dominated universes, the space itself is expanding. For the total colonisation time, T, the case for a dark energy-dominated universe is marked with divergence beyond the linear regime characterised by small values of the Hubble parameter, H. Not all planets in a spherical section of this universe can be `colonised' due to the presence of a shrinking Hubble sphere. In other words, the recession speeds of other planets go beyond the speed of light making them impossible to reach. On the other hand, for a matter-dominated universe, while there is an apparent horizon, the Hubble sphere is growing instead of shrinking. This leads to a finite total colonisation time that depends on the Hubble parameter characterising the universe; in particular, we find T ~ H for small H and T ~ H^2 for large H.

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