PERCOLATION TRANSITION AND TOPOLOGY

A number of bidimensional random structures with increasing densities are simulated to explore possible links between Euler-Poincare characteristic (EPC), or connectivity, and percolation threshold. For each structure model, the percolation threshold is compared with a number of typical points (extrema, zero crossings...) of the EPC curve. From these exercises, it can be concluded that the percolation threshold cannot be generally predicted using the evolution of the EPC.

[1]  M. Stampanoni,et al.  Topology of evolving pore networks , 2012 .

[2]  Mark A. Miller,et al.  Topological characteristics of model gels , 2010, Journal of physics. Condensed matter : an Institute of Physics journal.

[3]  Klaus Mecke,et al.  Topological estimation of percolation thresholds , 2007, 0708.3250.

[4]  D. Jeulin,et al.  Percolation d'agrégats multi-échelles de sphères et de fibres – Application aux nanocomposites , 2006 .

[5]  K. Mecke,et al.  Fluids in porous media: a morphometric approach , 2005 .

[6]  J. Jernot,et al.  Morphological transformations on a randomly filled 3D network , 1993 .

[7]  Klaus Mecke,et al.  Euler characteristic and related measures for random geometric sets , 1991 .

[8]  Dominique Jeulin,et al.  Caractéristiques morphologiques des constituants et comportement à la limite élastique d'un matériau biphasé Fe/Ag , 1989 .

[9]  K. Mendelson,et al.  Statistics of the percolation threshold , 1981 .

[10]  C. Lantuéjoul,et al.  On the use of the geodesic metric in image analysis , 1981 .

[11]  J. Clerc,et al.  Electrical conductivity of a mixture of conducting and insulating spheres: an application of some percolation concepts , 1978 .

[12]  Kamal K. Bardhan,et al.  Quantum and semi-classical percolation and breakdown in disordered solids , 2009 .

[13]  J. Jernot,et al.  Etude de la connexité de structures aléatoires , 1995 .

[14]  P. Jouannot.  Etude topologique de structures aleatoires biphasees , 1994 .

[15]  H. Hadwiger.  Vorlesungen über Inhalt, Oberfläche und Isoperimetrie , 1957 .