Disorder topological

The second difference is related to the structure of the lamellar phase. The Euler characteristic has been assumed zero in the whole lamellar phase by Gompper and Kraus [47], whereas we show that it fluctuates strongly in the lamellar phase between the transition line and the topological disorder fine. The notion of the topological disorder line has not appeared in their paper. We think that the topological disorder line is much closer to the transition... 

R. Holyst, W. Gozdz. Fluctuating Euler characteristics, topological disorder line, and passages in lamellar phases. J Chem Phys 706 4773- 780, 1997. 

Figure 7. Topological fluctuations of the lamellar phase at different points of the phase diagram, (a) Single fusion between the lamellae by a passage (this configuration is close to the topological disorder line), (b) Configuration close to the transition to the disordered microemulsion phase the Euler characteristic is large and negative.

Topological disorder that leads to formation of amorphous phases... 

Physical gels, as exemplified by gelatin gels, exhibit many common features with chemical gels. Among them, we found the topological disorder of the network formed by the polymer chains, and the formal similarity of the process of gelation with a percolation problem. 

The general physical model of percolation theory applies to a broad range of phenomena that are rooted in spatially random events and topological disorder and that reflect long-range connectivity. One can picture the protonic process as being a transfer along threads of hydro-... 

H. Kawamura, in Topological Disorder in Condensed Matter, F. Yonezawa and T. Ninomiya, Eds. (Springer-Verlag, Berlin, 1983) p. 181. 

Figure 6.9 pictures the example of the triangular-square network taken from [6.38]. Some 4-coordinated sites are seen comprising inner boundaries of this LRC. It is easy to notice that there are two 5-coordinated atoms in the first coordination sphere of each 5-coordinated atom in LRC. This circumstance follows from the fact that, in P-polyhedra, we have an even number of squares leading to the formation of the MRO, which manifests itself in the formation of chains of 5-coordinated atoms. Collins and Kawamura studied the thermodynamic properties of triangular-square lattices. Kawamura established the existence of the first-order phase transition connected with the transformation of the crystalline structure into a topologically disordered one. 

H. Kawamura Topological Disorder in Condensed Matter, ed. by F. Yonesawa, T. Ninimia, Solid-State Sciences, 46 (Springer, Berlin, Heidelberg 1983) pp. 181-190... 

Hobbs LW, Sreeram AN, Jesumm CE, Berger, BA (1996) Structural freedom, topological disorder, and the irradiation-induced amorphization of ceramic stiuctures. Nucl Instr Meth Phys Res B116 18-25 Hong, HYP (1976) Crystal stiuctures and crystal chemistiy in the system Nai+xZr2SixP3-xOi2. Mater Res Bull 11 173-182... 

Hohhs, L. W. and Yuan, X., Topology and topological disorder in silica. In Defects in Si02 and Related Dielectrics Science and Technology, eds. Pacchioni, G., Skuja, L., and Griscom, D. L., NATO Science Series II Mathematics, Physics and Chemistry, Kluwer Academic Publishers, Dordrecht, the Netherlands, 2000, p. 37. Hosono, H., Ikuta, Y, Kinoshita, T., Kajihara, K., and Hirano, M., Physical disorder and optical properties in the vacuum ultraviolet region of amorphous SiOj, Phys. Rev. Lett. 87,175501 (2001). 

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