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43.It may happen that no such circle exists, which was occasionally observed for polydisperse systems. In this case we skip the corresponding neighbor-triangle from the statistics.
44.We use the following test to check if a triangle with edge lengths a, b, and c is acute: , where ɛ = 1 − 10−12 is used to account for numerical error.
45.The growth rate is defined as with the total system mass M.

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The channel size distribution in hard sphere systems, based on the local neighbor correlation of four particle positions, is investigated for all volume fractions up to jamming. For each particle, all three particle combinations of neighbors define channels, which are relevant for the concept of caging. The analysis of the channel size distribution is shown to be very useful in distinguishing between gaseous, liquid, partially and fully crystallized, and glassy (random) jammed states. A common microstructural feature of four coplanar particles is observed in crystalline and glassy jammed states, suggesting the presence of “hidden” two-dimensional order in three-dimensional random close packings.


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