Related papers: Multifractal Properties of the Random Resistor Net…
Recently, the percolation transition has been characterized on interacting networks both in presence of interdependent and antagonistic interactions. Here we characterize the phase diagram of the percolation transition in two Poisson…
The influence of fractal clusters of a normal phase on the dynamics of a magnetic flux trapped in a percolative superconductor is considered. The critical current distribution and the current-voltage characteristics of fractal…
The multifractal characterization of the distribution over disorder of the mean first-passage time in a finite chain is revisited. Both, absorbing-absorbing and reflecting-absorbing boundaries are considered. Two models of dichotomic…
We study the percolation behavior of two interdependent scale-free (SF) networks under random failure of 1-$p$ fraction of nodes. Our results are based on numerical solutions of analytical expressions and simulations. We find that as the…
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…
An exact method that analytically provides transfer matrices in finite networks of quasicrystalline approximants of any dimensionality is discussed. We use these matrices in two ways: a) to exactly determine the band structure of an…
Numerically we study the bulk current relaxation in percolative Random Resistor cum Tunneling Network (RRTN) model through a first-passage route. The RRTN considers an extra semi-classical barrier-crossing process over a voltage threshold…
Percolation theory characterizing the robustness of a network has applications ranging from biology, to epidemic spreading, and complex infrastructures. Percolation theory, however, only concern the typical response of a infinite network to…
Using the S_3-symmetry of Sierpinski fractal resistor networks we determine the current distribution as well as the multifractals spectrum of moments of current distribution by using the real space renormalization group technique based on…
We present here a detailed multifractal scaling study for the electronic transmission resonances with the system size for an infinitely large one dimensional perfect and imperfect quasiperiodic system represented by a sequence of…
We suggest treating a conducting network of oriented polymer chains as an anisotropic fractal whose dimensionality D=1+\epsilon is close to one. Percolation on such a fractal is studied within the real space renormalization group of Migdal…
We study a simple model of conducting polymers in which a single electron propagates through a randomly tangled chain. The model has the geometry of a small-world network, with a small density $p$ of crossings of the chain acting as…
The functionality of nodes in a network is often described by the structural feature of belonging to the giant component. However, when dealing with problems like transport, a more appropriate functionality criterion is for a node to belong…
We characterize the existence of certain geometric configurations in the fractal percolation limit set $A$ in terms of the almost sure dimension of $A$. Some examples of the configurations we study are: homothetic copies of finite sets,…
Using Monte-Carlo simulations, we determine the scaling form for the probability distribution of the shortest path, $\ell$, between two lines in a 3-dimensional percolation system at criticality; the two lines can have arbitrary positions,…
The probability density of a quantum particle moving freely within a circular ring can exhibit local flow patterns inconsistent with its angular momentum, a phenomenon known as quantum backflow. In this study, we examine a quantum particle…
We study random networks of nonlinear resistors, which obey a generalized Ohm's law, $V\sim I^r$. Our renormalized field theory, which thrives on an interpretation of the involved Feynman Diagrams as being resistor networks themselves, is…
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…
Using direct numerical simulations, we study the statistical properties of reversals in two-dimensional Rayleigh-B\'enard convection for infinite Prandtl number. We find that the large-scale circulation reverses irregularly, with the…
In this paper, we study the critical behavior of percolation on a configuration model with degree distribution satisfying an infinite second-moment condition, which includes power-law degrees with exponent $\tau \in (2,3)$. It is well known…