A weighted planar stochastic lattice with scale-free, small-world and multifractal properties

Mitra, Tushar; Hassan, Md. Kamrul

doi:10.1016/j.chaos.2021.111656

“…Interestingly, if we replace the center of each cell of the WPSL by a node and common border between cells by a link between the corresponding node then it emerges as a scale-free network. More recently, we have solved a class of models where by dividing the plane vertically or horizontally with equal probability the resulting network is not only scale-free with smaller exponent of the power-law degree distribution but also small-world [56,57]. It is small-world because we find that the mean geodesic path length increases logarithmically with system size and the total mean clustering coefficient is high and independent of system size.…”

Section: Kinetics Of Fragmentationmentioning

confidence: 86%

Recent development on fragmentation, aggregation and percolation

Hassan¹

2022

Preprint

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In this article, I have outlined how an accomplished researcher like Robert Ziff has influenced a new generation of researchers across the globe like gravity as an action-at-a-distance. In the 80s Ziff made significant contributions to the kinetics of fragmentation followed by the kinetics of aggregation. Here, I will discuss fractal and multifractal that emerges in fragmentation and aggregation processes where the dynamics is governed by non-trivial conservation laws. I have then discussed my recent works and results on percolation where I made extensive use of Newman-Ziff fast Monte Carlo algorithm. To this end, I have defined entropy which paved the way to define specific heat and show that the critical exponents of percolation obey Rushbrooke inequality. Besides, we discuss how entropy and order parameter together can help us to check whether the percolation is accompanied by order-disorder transition or not. The idea of entropy also help to explain why encouraging smaller cluster to grow faster than larger clusters makes the transition explosive.

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Analysis of the Evolution of the Status of ”The Belt and Road” in the World Trade Dependence Network

Zhang

¹

,

Han

²

2022

Emerging Markets Finance and Trade

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Recent development on fragmentation, aggregation and percolation

Hassan¹

2022

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

In this article, I have outlined how an accomplished researcher like Robert Ziff has influenced a new generation of researchers across the globe like gravity as an action-at-a-distance. In the 80s Ziff made significant contributions to the kinetics of fragmentation followed by the kinetics of aggregation. Here, I will discuss fractal and multifractal that emerges in fragmentation and aggregation processes where the dynamics is governed by non-trivial conservation laws. I have then discussed my recent works and results on percolation where I made extensive use of Newman-Ziff fast Monte Carlo algorithm. To this end, I have defined entropy which paved the way to define specific heat and show that the critical exponents of percolation obey Rushbrooke inequality. Besides, we discuss how entropy and order parameter together can help us to check whether the percolation is accompanied by order-disorder transition or not. The idea of entropy also help to explain why encouraging smaller cluster to grow faster than larger clusters makes the transition explosive.

show abstract

A weighted planar stochastic lattice with scale-free, small-world and multifractal properties

Cited by 3 publications

References 36 publications

Recent development on fragmentation, aggregation and percolation

Recent development on fragmentation, aggregation and percolation

Analysis of the Evolution of the Status of ”The Belt and Road” in the World Trade Dependence Network

Recent development on fragmentation, aggregation and percolation

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