Physarum polycephalum percolation as a paradigm for topological phase transitions in transportation networks

Physical Review Letters

Volumn 109, Issue 7, 2012, Pages

  Fessel, Adrian ^a,b   Oettmeier, Christina ^a,b   Bernitt, Erik ^a,b   Gauthier, Nils C ^b   Döbereiner, Hans Günther ^a,b  

^a UNIVERSITY OF BREMEN   (Germany)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

CONFIGURATION MODEL; EXACT SOLUTION; PERCOLATION TRANSITION; PHYSARUM POLYCEPHALUM; SLIME MOLD; TOPOLOGICAL PHASE; TRANSPORTATION NETWORK; VASCULAR NETWORK;

GRAPH THEORY;

SOLVENTS;

EID: 84865227626     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.109.078103     Document Type: Article

References (26)

1. M. Newman, SIAM Rev. 45, 167 (2003). SIREAD 0036-1445 10.1137/S003614450342480
2. R. Albert and A.-L. Barabasi, Rev. Mod. Phys. 74, 47 (2002). RMPHAT 0034-6861 10.1103/RevModPhys.74.47
3. M. Barthélemy, Phys. Rep. 499, 1 (2011). PRPLCM 0370-1573 10.1016/j.physrep.2010.11.002
4. S. Dorogovtsev and J. Mendes, Adv. Phys. 51, 1079 (2002). ADPHAH 0001-8732 10.1080/00018730110112519 (Pubitemid 34759032)
5. W. Risau and I. Flamme, Annu. Rev. Cell Dev. Biol. 11, 73 (1995). ARDBF8 1081-0706 10.1146/annurev.cb.11.110195.000445
6. A. Tero, S. Takagi, T. Saigusa, K. Ito, D.P. Bebber, M.D. Fricker, K. Yumiki, R. Kobayashi, and T. Nakagaki, Science 327, 439 (2010). SCIEAS 0036-8075 10.1126/science.1177894
7. J. Jones, Artif. Life ARLIEY 1064-5462 16, 127 (2010). 10.1162/artl.2010.16.2.16202
8. F.L. Howard, Am. J. Bot. 18, 116 (1931). AJBOAA 0002-9122 10.2307/2435936
9. W. Marwan, Science 327, 419 (2010). SCIEAS 0036-8075 10.1126/science. 1185570
10. T. Nakagaki, H. Yamada, and Ágota Tóth, Nature (London) NATUAS 0028-0836 407, 470 (2000). 10.1038/35035159
11. T. Saigusa, A. Tero, T. Nakagaki, and Y. Kuramoto, Phys. Rev. Lett. 100, 018101 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.100.018101 (Pubitemid 351388317)
12. A. Adamatzky and J. Jones, J. Bionic Eng. 1672-6529 5, 348 (2008). 10.1016/S1672-6529(08)60180-8
13. A. Takamatsu, E. Takaba, and G. Takizawa, J. Theor. Biol. 256, 29 (2009). JTBIAP 0022-5193 10.1016/j.jtbi.2008.09.010
14. M. Ito, R. Okamoto, and A. Takamatsu, J. Phys. Soc. Jpn. 80, 074801 (2011). JUPSAU 0031-9015 10.1143/JPSJ.80.074801
15. W. Baumgarten, T. Ueda, and M.J.B. Hauser, Phys. Rev. E PLEEE8 1539-3755 82, 046113 (2010). 10.1103/PhysRevE.82.046113
16. D. Stauer, Phys. Rep. 54, 1 (1979). PRPLCM 0370-1573 10.1016/0370- 1573(79)90060-7
17. G. Serini, D. Ambrosi, E. Giraudo, A. Gamba, L. Preziosi, and F. Bussolino, EMBO J. 22, 1771 (2003). EMJODG 0261-4189 10.1093/emboj/cdg176 (Pubitemid 36460134)
18. C. Oettmeier and H.-G. Döbereiner (unpublished).
19. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevLett.109.078103 for detailed methods.
20. E. Bernitt, C. Oettmeier, and H.-G. Döbereiner, IFMBE Proc. 1680-0737 31, 1133 (2010). 10.1007/978-3-642-14515-5-288
21. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevLett.109.078103 for movies of (i) Fig. and its skeleton (movie 1), (ii) the skeleton along with the fraction of its largest component (movie 2), as well as (iii) the supplemental movie of with overlaid skeleton.
22. M. Molloy and B. Reed, Random Struct. Algorithms RSALFD 1042-9832 6, 161 (1995). 10.1002/rsa.3240060204
23. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevLett.109.078103 for (i) Fig. s1 for histograms of p k at percolation and (ii) Fig. s2 for a distribution of percolation times as a function of plating density.
24. A. Fessel and H.-G. Döbereiner (unpublished).
25. R. Folberg, M.J. Hendrix, and A.J. Maniotis, Am. J. Pathol. 156, 361 (2000). AJPAA4 0002-9440 10.1016/S0002-9440(10)64739-6
26. B. Bussolati, C. Grange, and G. Camussi, FASEB J. FAJOEC 0892-6638 25, 2874 (2011). 10.1096/fj.10-180323