“…The largest rings are 24-rings (in net 26). Strong rings (Goetzke & Klien, 1991) are those which cannot be decomposed into sums of smaller circuits. The largest of these are the 20-rings occurring in net 25.…”
“…The largest rings are 24-rings (in net 26). Strong rings (Goetzke & Klien, 1991) are those which cannot be decomposed into sums of smaller circuits. The largest of these are the 20-rings occurring in net 25.…”
“…Rings have been variously called 'fundamental circuits', 'primitive rings' and 'fundamental rings' by other authors. Goetzke & Klien (1991) (Marians & Hobbs, 1990;Stixrude & Bukowinski, 1990;Goetzke & Klien, 1991).…”
A description is given of 4-connected nets with one kind of vertex in which the shortest rings containing each pair of edges are N-rings (N>4). Eleven uniform nets (66 ) are identified; seven of these are believed to be new. A further thirteen nets with one type of vertex and without 3-or 4-rings are described; nine of these are also believed to be new
“…[1,2,9,10,11,12,13,14,15,16,17]. These methods do not restrict the number of atoms to be considered, and are useful to classify the variety of many-body atomic structure in certain situations.…”
Abstract. Characterization of medium-range order in amorphous materials and its relation to short-range order is discussed. A new topological approach is presented here to extract a hierarchical structure of amorphous materials, which is robust against small perturbations and allows us to distinguish it from periodic or random configurations. The method is called the persistence diagram (PD) and it introduces scales into manybody atomic structures in order to characterize the size and shape. We first illustrate how perfect crystalline and random structures are represented in the PDs. Then, the medium-range order in the amorphous silica is characterized by using the PD. The PD approach reduces the size of the data tremendously to much smaller geometrical summaries and has a huge potential to be applied to broader areas including complex molecular liquid, granular materials, and metallic glasses.
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