Funct. Mater. 2022; 29 (4): 586-596.
Formation of a through conductive inclusion in a layered sample with sector conductive inclusions in single layers; conductive cluster
1Institute for Single Crystals, National Academy of Science of Ukraine, 60 Nauky Ave, 61072 Kharkiv, Ukraine
2V.N.Karazin Kharkiv National University, 4 Svobody Sq., 61022 Kharkiv, Ukraine
The results of studying the composition of a through conducting clster in a layered sample with sector conducting inclusions in round layers are presented. The case of a homogeneous and independent distribution of sector inclusions in each layer is considered. The values of the conductivity of the sample with inclusions and the values of the fraction of the conductive phase in the layer included in the through conductive cluster are obtained for various sets of the system parameters - the number of layers, the number of inclusions in the layer, and the size of the inclusions in the layers.
1. C.-W.Nan, Y.Shen, Jing Ma, IAnnu. Rev. Mater. Res., 40, 131 (2010). https://doi.org/10.1146/annurev-matsci-070909-104529 |
||||
2. E.Kroener, M.Ali Ahmed, A.Carminati, Phys. Rev. E, 91, 042706 (2015). https://doi.org/10.1103/PhysRevE.91.042706 |
||||
3. S.Marchenko, J.J.van Pelt Ward, Claremar Bjorn et al., Frontiers in Earth Science, 5, 16 (2017). https://doi.org/10.3389/feart.2017.00016 |
||||
4. H.G.Silva, A.M.Pereira, J.M.Teixeira et al., Phys. Rev. B, 82, 144432 (2013). https://doi.org/10.1103/PhysRevB.82.144432 |
||||
5. M.De Domenico, C.Granell, M.A.Porter, A.Arenas, Nat. Phys., 12, 901 (2016). https://doi.org/10.1038/nphys3865 |
||||
6. Yan-Yun Cao, Run-Ran Liu, Chun-Xiao Jia, Bing-Hong Wang, Communications in Nonlinear Science and Numerical Simulation, 92, 105492 (2021). https://doi.org/10.1016/j.cnsns.2020.105492 |
||||
7. R.R.Liu, D.A.Eisenberg, T.P.Seager et al., Sci. Rep., 8, 2111 (2018). https://doi.org/10.1038/s41598-018-20019-7 |
||||
8. Wang Xiao Juan, Guo Shi Ze, Jin Lei, Wang Zhen, Physica A: Statistical Mechanics and its Applications, 471, 233 (2017). https://doi.org/10.1016/j.physa.2016.11.051 |
||||
9. Andrea Santoro, Vincenzo Nicosia, Phys. Rev. Research, 2, 033122 (2020). https://doi.org/10.1103/PhysRevResearch.2.033122 |
||||
10. R.K.Akhunzhanov, A.V.Eserkepov, Y.Yu.Tarasevich, J. Phys. A: Math. Theor., 55, 204004 (2022). https://doi.org/10.1088/1751-8121/ac61b8 |
||||
11. R.M.Ziff, Physica A: Statistical Mechanics and its Applications, 568, 125723 (2021). https://doi.org/10.1016/j.physa.2020.125723 |
||||
12. H.E.Roman, F.Croccolo, Mathematics, 9, 3054 (2021). https://doi.org/10.3390/math9233054 |
||||
13. M.Dickison, S.Havlin, H.E.Stanley, Phys. Rev. E, 85, 066109 (2012). https://doi.org/10.1103/PhysRevE.85.066109 |
||||
14. S.-W.Son, G.Bizhani, C.Christensen et al., EPL, 97, 16006 (2012). https://doi.org/10.1209/0295-5075/97/16006 |
||||
15. P.Clusella, P.Grassberger, F.J.Perez-Reche, A.Politi, Phys. Rev. Lett., 117, 208301 (2016). https://doi.org/10.1103/PhysRevLett.117.208301 |
||||
16. D.Jeulin, M.Moreaud, Image Analysis and Stereology, 26, 121 (2007). https://doi.org/10.5566/ias.v26.p121-127 |
||||
17. A.Golovnev, M.E.Suss, J. Chem. Phys., 149, 144904 (2018). https://doi.org/10.1063/1.5041326 |
||||
18. D.Sangare, P.M.Adler, Phys. Rev. E Stat. Nonlin. Soft Matter. Phys., 79, 052101 (2009). https://doi.org/10.1103/PhysRevE.79.052101 |
||||
19. J.Tykesson, D.Windisch, Probability Theory and Related Fields, 154, 165 (2012). https://doi.org/10.1007/s00440-011-0366-3 |
||||
20. R.Ye.Brodskii, Funct. Mater., 27, 159 (2019). |
||||
21. R.Ye.Brodskii, Funct. Mater., 29, 419, 2022 |
||||
22. Y.S.Cho, S.Hwang, H.J.Herrmann, B.Kahng, Science, 339, 1185 (2013). https://doi.org/10.1126/science.1230813 |
||||
23. S.Armstrong, P.Dario, Comm. Pure Appl. Math., 71, 1717 (2018). https://doi.org/10.1002/cpa.21726 |
||||
24. M.Gorny, E.Maurel-Segala, A.Singh, Ann. Inst. H. Poincare Probab. Statist., 54, 2238 (2018). https://doi.org/10.1214/17-AIHP869 |
||||
25. Pengfei Tang, Ann. Probab., 47, 4115 (2019). https://doi.org/10.1214/19-AOP1354 |
||||
26. P.Trapman, Ann. Probab., 38, 1608 (2010). https://doi.org/10.1214/09-AOP517 |
||||
27. T.Fluschnik, S.Kriewald, A.Garcia Cantu Ros et al., ISPRS International Journal of Geo-Information, 5, 110 (2016). https://doi.org/10.3390/ijgi5070110 |
||||
28. N.Nisoh, V.Jarerattanachat, M.Karttunen, J.Wong-ekkabut, Biochimica et Biophysica Acta (BBA) - Biomembranes, 1862, 183328 (2020). https://doi.org/10.1016/j.bbamem.2020.183328 |
||||
29. S.Y.Lapshina, Lobachevskii J. Math., 40, 341 (2019). https://doi.org/10.1134/S1995080219030144 |
||||
30. X.J.Tan, Y.J.Deng, J.L.Jacobsen, Front. Phys., 15, 41501 (2020). https://doi.org/10.1007/s11467-020-0972-6 |
||||