A weighted planar stochastic lattice with scalefree, smallworld and multifractal properties
Abstract
We investigate a class of weighted planar stochastic lattice (WPSL1) created by random sequential nucleation of seed from which a crack is grown parallel to one of the sides of the chosen block and ceases to grow upon hitting another crack. It results in the partitioning of the square into contiguous and nonoverlapping blocks. Interestingly, we find that the dynamics of WPSL1 is governed by infinitely many conservation laws and each of the conserved quantities, except the trivial conservation of total mass or area, is a multifractal measure. On the other hand, the dual of the lattice is a scalefree network as its degree distribution exhibits a powerlaw $P(k)\sim k^{\gamma}$ with $\gamma=4.13$. The network is also a smallworld network as we find that (i) the total clustering coefficient $C$ is high and independent of the network size and (ii) the mean geodesic path length grows logarithmically with $N$. Besides, the clustering coefficient $C_k$ of the nodes which have degree $k$ decreases exactly as $2/(k1)$ revealing that it is also a nested hierarchical network.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.00936
 Bibcode:
 2021arXiv210700936M
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Physics  Physics and Society
 EPrint:
 10 pages, 9 captioned figures