相关论文: Percolation properties of the classic Sierpinski c…
We prove that the critical probability for the Sierpinski carpet lattice in two dimensions is uniquely determined. The transition is sharp. This extends the Kumagai's result to the original Sierpinski carpet lattice.
Self-organized criticality is a dynamical system property where, without external tuning, a system naturally evolves towards its critical state, characterized by scale-invariant patterns and power-law distributions. In this paper, we…
The classic Sierpinski triangle comprised of conducting bonds is multifractal. Thus the critical exponents and dimensions related to the conductivity are obtained asymptotically--that is, in the limit that the correlation length {\xi} of…
In this paper, we compute the next-nearest-neighboring site percolation (Connections exist not only between nearest-neighboring sites, but also between next-nearest-neighboring sites.) probabilities Pc on the two-dimensional Sierpinski…
The relative configurational entropy per cell as a function of length scale is a sensitive detector of spatial self-similarity. For Sierpinski carpets the equally separated peaks of the above function appear at the length scales that depend…
We study, on a square lattice, an extension to fully coordinated percolation which we call iterated fully coordinated percolation. In fully coordinated percolation, sites become occupied if all four of its nearest neighbors are also…
Recent advances in nanofabrication methods have made it possible to create complex two-dimensional artificial structures, such as fractals, where electrons can be confined. The optoelectronic and plasmonic properties of these exotic quantum…
Percolation refers to the emergence of a giant connected cluster in a disordered system when the number of connections between nodes exceeds a critical value. The percolation phase transitions were believed to be continuous until recently…
Uniform Harnack inequalities for harmonic functions on the pre- and graphical Sierpinski carpets are proved using a probabilistic coupling argument. Various results follow from this, including the construction of Brownian motion on…
In 2005, Liu et al. calculated the dimensionality of the intersection of Sierpinski carpet and a straight line with rational slope in the sense of Lebesgue measure.Sierpinski carpet is a self-similar set in two-dimensional planes obtained…
We introduce a simple lattice model in which percolation is constructed on top of critical percolation clusters, and show that it can be repeated recursively any number $n$ of generations. In two dimensions, we determine the percolation…
We extend Smirnov's proof of the existence and conformal invariance of the scaling limit of critical site-percolation on the triangular lattice to particular sequences of periodic graphs with more arbitrary large-scale structure, obtained…
The finite-size scaling behaviour for percolation and conduction is studied in two-dimensional triangular-shaped random resistor networks at the percolation threshold. The numerical simulations are performed using an efficient star-triangle…
Connections are found between the two-component percolation problem and the conductor/insulator percolation problem. These produce relations between critical exponents, and suggest formulae connecting the conductivity exponents in different…
Very often traditional approaches studying dynamics of self-similarity processes are not able to give their quantitative characteristics at infinity and, as a consequence, use limits to overcome this difficulty. For example, it is well know…
We investigate properties of two-dimensional finite-scale percolation systems whose size along the current flow is smaller than the perpendicular size. Successive thresholds of appearing multiple percolation channels in such systems have…
We study the critical behavior of the 3-state Potts model, where the spins are located at the centers of the occupied squares of the deterministic Sierpinski carpet. A finite-size scaling analysis is performed from Monte Carlo simulations,…
We present an "ultimate" proof of Cardy's formula for the critical percolation on the hexagonal lattice \cite{Smirnov01criticalpercolation}, showing the existence of the universal and conformally invariant scaling limit of crossing…
We define a percolation problem on the basis of spin configurations of the two dimensional XY model. Neighboring spins belong to the same percolation cluster if their orientations differ less than a certain threshold called the conducting…
Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some…