Percolation Theory

1984 ◽  
pp. 94-136 ◽  
Author(s):  
Boris I. Shklovskii ◽  
Alex L. Efros
Keyword(s):  
Percolation Theory

Giant Anisotropy of Conductivity in Hydrogenated Nanocrystalline Silicon Thin Films

1998 ◽  
Vol 536 ◽  
Author(s):  
A. B. Pevtsov ◽  
N. A. Feoktistov ◽  
V. G. Golubev
Keyword(s):  
Thin Films ◽  
Film Thickness ◽  
Percolation Theory ◽  
Nanocrystalline Silicon ◽  
Spatial Light Modulators ◽  
Light Emitting ◽  
Light Modulators ◽  
Silicon Thin Films ◽  
Longitudinal Conductivity ◽  
Transverse Conductivity

AbstractThin (<1000 Å) hydrogenated nanocrystalline silicon films are widely used in solar cells, light emitting diodes, and spatial light modulators. In this work the conductivity of doped and undoped amorphous-nanocrystalline silicon thin films is studied as a function of film thickness: a giant anisotropy of conductivity is established. The longitudinal conductivity decreases dramatically (by a factor of 109 − 1010) as the layer thickness is reduced from 1500 Å to 200 Å, while the transverse conductivity remains close to that of a doped a- Si:H. The data obtained are interpreted in terms of the percolation theory.

Water-Retention of Fractal Soil Models Using Continuum Percolation Theory

2002 ◽  
Vol 1 (2) ◽  
pp. 252
Author(s):  
Allen G. Hunt ◽  
Glendon W. Gee
Keyword(s):  
Percolation Theory ◽  
Water Retention ◽  
Continuum Percolation

Polymer composites as sensing materials for liquid organic solvents – preliminary results

e-Polymers ◽  
2011 ◽  
Vol 11 (1) ◽  
Author(s):  
Stanislaw Frackowiak ◽  
Monika Maciejewska ◽  
Andrzej Szczurek ◽  
Marek Kozlowski
Keyword(s):  
Electrical Resistivity ◽  
Carbon Black ◽  
Polymer Composites ◽  
Percolation Theory ◽  
Liquid Mixtures ◽  
Organic Liquids ◽  
Volumetric Fraction ◽  
Factors Influencing ◽  
Benzene Toluene ◽  
Main Factors

AbstractCarbon black-filled polymer composites were investigated as sensing materials for organic liquids. Polypropylene and polystyrene which were selected as matrices and various amounts of carbon black were considered as the main factors influencing sensitivity of the composites in view of the percolation theory. Disposable filaments were produced of these materials. Change in their electrical resistivity was measured upon immersion in benzene, toluene, xylene, ethylbenzene and their mixtures. It has been found that studied materials were sensitive to the composition of liquid mixtures of organic solvent. Relationships between the filament response and volumetric fraction of the components were presented. The studied materials have shown promising sensing properties, which suggest their applicability for identification and quantification of multicomponent organic liquids.

scholarly journals Emergence of disconnected clusters in heterogeneous complex systems

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
István A. Kovács ◽  
Róbert Juhász
Keyword(s):  
Complex Systems ◽  
Percolation Theory ◽  
Contact Process ◽  
Heterogeneous Systems ◽  
Critical Dynamics ◽  
Magnetic Domains ◽  
3 Dimensional ◽  
Quantum Ising Model ◽  
Highly Correlated ◽  
Exact Renormalization Group

AbstractPercolation theory dictates an intuitive picture depicting correlated regions in complex systems as densely connected clusters. While this picture might be adequate at small scales and apart from criticality, we show that highly correlated sites in complex systems can be inherently disconnected. This finding indicates a counter-intuitive organization of dynamical correlations, where functional similarity decouples from physical connectivity. We illustrate the phenomenon on the example of the disordered contact process (DCP) of infection spreading in heterogeneous systems. We apply numerical simulations and an asymptotically exact renormalization group technique (SDRG) in 1, 2 and 3 dimensional systems as well as in two-dimensional lattices with long-ranged interactions. We conclude that the critical dynamics is well captured by mostly one, highly correlated, but spatially disconnected cluster. Our findings indicate that at criticality the relevant, simultaneously infected sites typically do not directly interact with each other. Due to the similarity of the SDRG equations, our results hold also for the critical behavior of the disordered quantum Ising model, leading to quantum correlated, yet spatially disconnected, magnetic domains.

scholarly journals Recent advances in percolation theory and its applications

2015 ◽  
Vol 578 ◽  
pp. 1-32 ◽  
Author(s):  
Abbas Ali Saberi
Keyword(s):  
Percolation Theory ◽  
Recent Advances

COEXISTENCE OF OPPOSITE GLOBAL SOCIAL FEELINGS: THE CASE OF PERCOLATION DRIVEN INSECURITY

2002 ◽  
Vol 13 (10) ◽  
pp. 1375-1385 ◽  
Author(s):  
STÉPHANE PAJOT ◽  
SERGE GALAM
Keyword(s):  
Percolation Theory ◽  
Local Environment ◽  
Infinite Clusters

A model of the dynamics of appearance of a new collective feeling, in addition and opposite to an existing one, is presented. Using percolation theory, the collective feeling of insecurity is shown to be able to coexist with the opposite collective feeling of safety. Indeed this coexistence of contradictory social feelings result from the simultaneous percolation of two infinite clusters of people who are respectively experiencing a safe and unsafe local environment. Therefore opposing claims on national debates over insecurity are shown to be possibly both valid.

Inequalities for Means of Restricted First-Passage Times in Percolation Theory

1999 ◽  
Vol 8 (4) ◽  
pp. 307-315 ◽  
Author(s):  
SVEN ERICK ALM ◽  
JOHN C. WIERMAN
Keyword(s):  
Half Space ◽  
Percolation Theory ◽  
First Passage Times ◽  
First Passage ◽  
Geometric Argument ◽  
Convexity And Concavity ◽  
Passage Times

A simple geometric argument establishes an inequality between the sums of two pairs of first-passage times. This result is used to prove monotonicity, convexity and concavity results for first-passage times with cylinder and half-space restrictions.

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