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We extend Feynman's analysis of the infinite ladder AC circuit to fractal AC circuits. We show that the characteristic impedances can have positive real part even though all the individual impedances inside the circuit are purely imaginary.…
The probability distributions of the masses of the clusters spanning from top to bottom of a percolating lattice at the percolation threshold are obtained in all dimensions from two to five. The first two cumulants and the exponents for the…
We present structural properties of two-dimensional polymers as far as they can be described by percolation theory. The percolation threshold, critical exponents and fractal dimensions of clusters are determined by computer simulation and…
In past decades, the application of fractals to electrode design for enhanced signaling and electrochemical performance was a popular subject and enabled the growth of consumer micro-electronics. Supercapacitors, which are energy storage…
We investigate a recent suggestion that the spatial distribution of earthquake hypocenters makes a fractal set with a structure and fractal dimensionality close to those of the backbone of critical percolation clusters, by analyzing four…
The effect of morphologic factors on magnetic flux dynamics and critical currents in percolative superconducting structures is considered. The superconductor contains the fractal clusters of a normal phase, which act as pinning centers. The…
In the parameter spaces of nonlinear dynamical systems, we investigate the boundaries between periodicity and chaos and unveil the existence of fractal sets characterized by a singular fractal dimension. This dimension stands out from the…
Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount…
Analytic approximations for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension $d$ ($1 \leq d \leq 3$) are developed as heuristic interpolations from the knowledge of…
We show that only considering the largest cluster suffices to obtain a first-order percolation transition. As opposed to previous realizations of explosive percolation our models obtain Gaussian cluster distributions and compact clusters as…
The effect of the fractal clusters of a normal phase, which act as pinning centers, on the dynamics of magnetic flux in percolative type-II superconductor is considered. The main features of these clusters are studied in detail: the cluster…
Classically, percolation critical exponents are linked to the power laws that characterize percolation cluster fractal properties. It is found here that the gradient percolation power laws are conserved even for extreme gradient values for…
Using simple space-time implementation of the random cascade model we investigate numerically influence of the possible fractal structure of the emitting source on Bose-Einstein correlations between identical particles. The results are then…
We investigate the properties of a two-state sandpile model subjected to a confining potential in two dimensions. From the microdynamical description, we derive a diffusion equation, and find a stationary solution for the case of a…
The effect of fractal clusters on magnetic and transport properties of percolative superconductors is studied. The superconductor contains percolative superconducting cluster carrying a transport current and clusters of a normal phase. It…
Polymer's network is treated as an anisotropic fractal with fractional dimensionality D = 1 + \epsilon close to one. Percolation model on such a fractal is studied. Using the real space renormalization group approach of Migdal and Kadanoff…
Explosive percolation (EP) has received significant research attention due to its rich and anomalous phenomena near criticality. In our recent study [Phys. Rev. Lett. 130, 147101 (2023)], we demonstrated that the correct critical behaviors…
The incipient infinite cluster appearing at the bond percolation threshold can be decomposed into singly-connected ``links'' and multiply-connected ``blobs.'' Here we decompose blobs into objects known in graph theory as 3-blocks. A 3-block…
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…
We study loop erased random walk (LERW) on the percolation cluster, with occupation probability $p\geq p_c$, in two and three dimensions. We find that the fractal dimensions of LERW$_p$ is close to normal LERW in Euclidean lattice, for all…