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. 2012 Aug 8;2(6):715–725. doi: 10.1098/rsfs.2012.0026

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Figure 4. — Topological model with angular resolution. The ensemble S(i) is defined in the following way. Let j and k be the first and second nearest neighbours of particle i(, , ). If we call μ a threshold parameter and α the angle , then i interacts only with j if (a), while it interacts with j and k if (b). This rule is iteratively applied to all the pairs of neighbours of i, choosing the nearest one every time that the angle between the particles is smaller than the threshold. The value of μ also fixes the average number of interacting neighbours . One can show that approximately . (Online version in colour.)

Inline graphic — Topological model with angular resolution. The ensemble S(i) is defined in the following way. Let j and k be the first and second nearest neighbours of particle i(, , ). If we call μ a threshold parameter and α the angle , then i interacts only with j if (a), while it interacts with j and k if (b). This rule is iteratively applied to all the pairs of neighbours of i, choosing the nearest one every time that the angle between the particles is smaller than the threshold. The value of μ also fixes the average number of interacting neighbours . One can show that approximately . (Online version in colour.)