Topologically transitive

ELECTRONIC TOPOLOGICAL TRANSITIONS AND COMPOSITIONAL ORDER IN CiiPd AND CuPt ALLOYS... 

I.A.Abrikosov, Yu.H.Vehkov, P.A.Korzhavyi, A.V.Ruban and L.E.Shilkrot, Ab-initio calculations of the electronic topological transition in Li-Mg alloys , Sohd State Commun. 83 867 (1992) ... 

Fig. 8.18 Neighborhood partitioning. In the same way a.s outer sites can be considered separately for value transitions, we may, for topology transitions, distinguish between those sites belonging to both i and j (g Aij) and those belonging to one of the two sites but not both (G liij) In this way we obtain the analogous totalislic (T), outer-totalistic (OT), and an additional type called restricted totalistic (RT).

Angelov, D., Vitolo, J.M., Mutskov, V., Dimitrov, S., and Hayes, J.J. (2001) Preferential interaction of the core histone tail domains with linker DNA. Proc. Natl. Acad. Sci. USA 98, 6599-6604. Tobias, I., Coleman, B.D., and Olson, W. (1994) The dependence of DNA tertiary structure on end conditions theory and implications for topological transitions. J. Chem. Phys. 101, 10990-10996. Coleman, B.D., Tobias, I., and Swigon, D. (1995) Theory of the influence of end conditions on selfcontact in DNA loops. J. Chem. Phys. 103, 9101-9109. 

Figure 1 2 1. The different types of 2.5 Lifshitz electronic topological transition (ETT) The upper panel shows the type (I) ETT where the chemical potential EF is tuned to a Van Hove singularity (vHs) at the bottom (or at the top) of a second band with the appearance (or disappearance) of a new detached Fermi surface region. The lower panel shows the type (II) ETT with the disruption (or formation) of a neck in a second Fermi surface where the chemical potential EF is tuned at a vHs associated with the gradual transformation of the second Fermi surface from a two-dimensional (2D) cylinder to a closed surface with three dimensional (3D) topology characteristics of a superlattice of metallic layers...

A recent XRD study of CL/DNA complexes has revealed that the addition of linear lambda-phage DNA (48, 502 bp, contour length=16.5 pm) (Raedler et al., 1997) or plasmid DNA (Lin et al., 2000) to binary mixtures of cationic liposomes (mean diameter of 70 nm), consisting of mixtures of neutral lipid DOPC and cationic DOTAP, induces a topological transition from liposomes into collapsed condensates in the form of optically birefringent liquid crystalline (LC) globules with sizes on the order of 1pm. 

An order-of-magnitude estimate of the critical stirring rate can be obtained from the balance between the typical flow velocity and the speed of the propagating fronts. The assumption behind this is that the flow produces a topological transition by generating a quasi-one-dimensional filamental structure. This naturally leads to the break down of coexistence, due to the different invasion velocities of the fronts separating the patches of different strains. 

The topological transition (Fig. 1) from polymeric solids in compounds containing linked polyhedral homoatomic clusters to discrete molecular (soluble) clusters can be conveniently studied by using as examples compounds rich in elements of the main-groups 13 to 15. It is possible for main-group elements in the middle of the periodic table to form homoatomic molecules or ions with localized homonuclear 2c-2e bonds. At higher valence-electron concentrations, fewer bonding and more free-electron pairs are formed. As electron deficiency increases, however, the formation of delocalized bonds becomes necessary, a situation typical of elements on the left of the periodic table. 

Figure 1. Topological transition from a diamond network (left) to polyhedral homoatomic clusters (right). Some bonds between the tetravalent atoms break by adding electrons (middle). The formation of progressively more and more lone pairs eventually results in discrete cluster anions (right).

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