Percolation Transition and Related Phenomena in Terms of Grossone Infinity Computations

2016 ◽  
pp. 239-266
Author(s):  
Dmitry I. Iudin ◽  
Yaroslav D. Sergeyev
Keyword(s):  
Percolation Transition

Influence of the Morphology on the Optical Properties of Nanocermet Films: A Renormalization Approach

1990 ◽  
Vol 195 ◽  
Author(s):  
S. Berthier ◽  
K. Driss-Khodja
Keyword(s):  
Optical Properties ◽  
Critical Exponents ◽  
Inhomogeneous Media ◽  
Experimental Results ◽  
Percolation Transition ◽  
Position Space ◽  
Renormalization Approach ◽  
2D And 3D ◽  
Good Agreement ◽  
Effective Medium Models

ABSTRACTIn order to take into account the actual morphology of the inhomogeneous media, we have developed, effective medium models based on a 2D and 3D position space renormalization /1,2/. These models predict the dipolar resonance and the percolation transition with critical exponents in good agreement with theoretical values and fairly reproduce most of the experimental results, whatever the concentration is. Further more, this allows a valuable comparison of the predictions of our models when applied on different lattices like real digitized TEM of cermet films or randomly occupied lattices.

scholarly journals Double Percolation Transition in Superconductor-Ferromagnet Nanocomposites

2010 ◽  
Vol 104 (3) ◽  
Author(s):  
Xiangdong Liu ◽  
Raghava P. Panguluri ◽  
Zhi-Feng Huang ◽  
Boris Nadgorny
Keyword(s):  
Percolation Transition ◽  
Double Percolation

Scaling of Complex Conductivity for A Percolating Metal-Insulator Composite with Inter granular Tunneling Above and Below the Superconducting Transition

1995 ◽  
Vol 411 ◽  
Author(s):  
D. S. Mclachlan ◽  
A. B. Pakhomov ◽  
I. I. Oblachova ◽  
F. Brouers ◽  
A. Sarychev
Keyword(s):  
Volume Fraction ◽  
Frequency Dispersion ◽  
Scaling Theory ◽  
Complex Conductivity ◽  
Superconducting Transition ◽  
Percolation Transition ◽  
Metal Insulator ◽  
Metal Volume ◽  
Metal Volume Fraction ◽  
Composite Samples

ABSTRACTThe complex conductivity was measured on 3d granular NbC-KCI composite samples at varying metal volume fraction p, frequency ω and temperature above and below the superconductivity critical Tc. The observed frequency dispersion is anomalous in that it is not in accord with the scaling theory of percolation transition. The results are compared with a recently developed scaling theory, which takes both intercluster tunneling and intercluster capacitance into account. The experimental estimates for the new critical exponents are in reasonable agreement with the theory. The very low value of the crossover frequency can also be understood. We also present the data showing the dispersion of the complex conductivity well below the superconducting transition Tc of NbC.

Concentration Phase Transition in a Two-Dimensional Ferromagnet

2020 ◽  
Vol 312 ◽  
pp. 244-250
Author(s):  
Alexander Konstantinovich Chepak ◽  
Leonid Lazarevich Afremov ◽  
Alexander Yuryevich Mironenko
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Thermal Effect ◽  
Spin State ◽  
Critical Concentration ◽  
Two Dimensional ◽  
Percolation Transition ◽  
Magnetic Cluster ◽  
The Monte Carlo Method

The concentration phase transition (CPT) in a two-dimensional ferromagnet was simulated by the Monte Carlo method. The description of the CPT was carried out using various order parameters (OP): magnetic, cluster, and percolation. For comparison with the problem of the geometric (percolation) phase transition, the thermal effect on the spin state was excluded, and thus, CPT was reduced to percolation transition. For each OP, the values ​​of the critical concentration and critical indices of the CPT are calculated.

scholarly journals Depth Penetration and Scope Extension of Failures in the Cascading of Multilayer Networks

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Wen-Jun Jiang ◽  
Run-Ran Liu ◽  
Chun-Xiao Jia
Keyword(s):  
Real World ◽  
Propagation Direction ◽  
Intervention Programs ◽  
Theoretical Studies ◽  
Percolation Transition ◽  
Multilayer Networks ◽  
Microscopic Mechanism ◽  
Network Layers ◽  
Avalanche Process ◽  
Random Failures

Real-world complex systems always interact with each other, which causes these systems to collapse in an avalanche or cascading manner in the case of random failures or malicious attacks. The robustness of multilayer networks has attracted great interest, where the modeling and theoretical studies of which always rely on the concept of multilayer networks and percolation methods. A straightforward and tacit assumption is that the interdependence across network layers is strong, which means that a node will fail entirely with the removal of all links if one of its interdependent nodes in other network layers fails. However, this oversimplification cannot describe the general form of interactions across the network layers in a real-world multilayer system. In this paper, we reveal the nature of the avalanche disintegration of general multilayer networks with arbitrary interdependency strength across network layers. Specifically, we identify that the avalanche process of the whole system can essentially be decomposed into two microscopic cascading dynamics in terms of the propagation direction of the failures: depth penetration and scope extension. In the process of depth penetration, the failures propagate from layer to layer, where the greater the number of failed nodes is, the greater is the destructive power that will emerge in an interdependency group. In the process of scope extension, failures propagate with the removal of connections in each network layer. Under the synergy of the two processes, we find that the percolation transition of the system can be discontinuous or continuous with changes in the interdependency strength across network layers, which means that a sudden system-wide collapse can be avoided by controlling the interdependency strength across network layers. Our work not only reveals the microscopic mechanism of global collapse in multilayer infrastructure systems but also provides stimulating ideas on intervention programs and approaches for cascade failures.

Percolation transition in fractal dimensions

2004 ◽  
Vol 332 (3-4) ◽  
pp. 310-319 ◽  
Author(s):  
Pascal Monceau ◽  
Pai-Yi Hsiao
Keyword(s):  
Fractal Dimensions ◽  
Percolation Transition
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