3D continuum percolation approach and its application to lava-like fuel-containing materials behaviour forecast

Abstract

The paper is devoted to the theoretical study of elementary permeable objects percolation and its application to real physical objects. Spheres and isotropic oriented capped sticks were chosen as elementary geometrical objects for percolation simulation, physically adequate for radiation defects behaviour description in brittle dielectrics, particularly in the so-called Lava-like Fuel Containing Materials (LFCM), where it effects their mechanical steadiness. LFCMs is high-radioactive glass, which was formed during active stage of well-known heavy nuclear accident, that occurred at Chornobyl nuclear facility in 1986. Physical processes taking place in the materials are of great practical interest. Furthermore, when applying percolation models to LFCM objects, an approximate behaviour forecast can be created. From the results of simulation, it appears that physical properties of the LFCM should drastically change within in the period of 2015÷2045 calendar years, depending on variations in nuclear fuel content.

Considerations on Oxygen Bubble Formation and Evolution on BiVO4 Porous Anodes Used in Water Splitting Photoelectrochemical Cells

“…Things may change when the electrode has an extremely porous structure because the real 3D percolation space could no longer be imagined as a 2D space. In this case, there are many possibilities of individual cells being connected to lead to percolation transition. − The immediate result is a decrease of the percolation parameter β c to values smaller than 0.59. Actually, there is no theory to predict the value of β c so that the percolation factor must be considered as an experimental parameter.…”

Ising Model for Conductive Percolation in Electrically Conductive Adhesives by Considering Random Arrangement of Conducting Particles

“…1 a discontinuity in the average coordination number at some volume fractions. The existence of this kind of discontinuity has also been discussed by Zhang et al (2008;2009). At high ξ, or ε pm >>ε p , the average coordination number quickly decreases to 4 (the coordination number of the diamond structure) when increasing the volume fraction of particles.…”

“…Since each arrangement is attributed to a specific coordination number, this speculation leads to the existence of an average coordination number. Indeed, the concept of average coordination number is logically accepted when we consider some previous reports related to average bond connection between particles per nodes (Dhydkov, 2009;Blumenfeld et al, 2005) and the concept of non permanent bonds (Coniglio et al, 2004). Lagemaat et al (2001) reported that in porous TiO 2 film, at a film porosity of 58%, about 10% of particles have two neighbors, 25% of the particles have four neighbors and less than 1% of the particles have eight neighbors and the average coordination number is 4.1.…”

“…The properties of composites of particles dispersed in continuum media have been reported by many authors several decades, covering numerous composites, such as conductive particles dispersed in insulating adhesives (electrically conductive adhesives) for microelectronic applications (Mikrajuddin et al, 2000;Yim et al, 2008;Lin and Chen, 2008;Li et al, 2008;Lin and Chiu, 2008;Morris and Lee, 2008;Zenner et al, 2008;Inoue et al, 2008;2009;Inoue and Suganuma, 2007;2009;Kim and Paik, 2008;Mundlein et al, 2002;Li et al, 1993;Tongxiang et al, 2008;Lee et al, 2005;Sander et al, 2002;, insulating particles dispersed in Ionic adhesive for use in solid batteries or fuel cells (Mikrajuddin et al, 2000;1999), colloidal systems (Lu et al, 2006;, pharmaceutical tablets (Stromme et al, 2003) and other composites such as fibers in concrete (Newman, 2002) and fly ash-concrete (Mohan et al, 2012). One interesting phenomenon exhibited by these composites is the occurrence of percolation threshold, a quantity which divides two strongly different states, such as conductive and insulating states (Mikrajuddin et al, 2000;1999), magnetic and nonmagnetic states (Thorpe, 1978), crystal and amorphous states, Surprisingly, in recent progress, the percolation phenomena are also applied to other fields, in the past of which likely did not show any relation with material composites such as communication systems such as the internet and other Peer-To-Peer networks (PastorSatorras and Vespignani, 2007), dynamics of epidemic spreading (Anderson and May, 1992;Meyers, 2007), HIV infection to AIDS (Kamp and Bornholdt, 2002), social networks …”

Percolation of Spheres in Continuum

“…Кроме того, найдены значения среднего количества соседей сферы B c [24][25][26] на пороге перколяции для каждого значения толщины оболочки (рис. 5).…”