Fig. 2: Identification and geometric configurations of chain and arch structures.
From: Precursory arch-like structures explain the clogging probability in a granular hopper flow
a PDFs of \({\theta }_{i}\) (from right to the left, i = 1, 2, …, 5) for arches consisting of 6 particles. Inset: schematic diagram of a chain structure. b The correlation between \({\phi }_{i}\) and \({\phi }_{i+k}\) within an arch of different n at D/d = 3.8. The straight line corresponds to \(C(k)=0\). c The number of identified arches (red triangle) and chains (blue circle) as a function of \(\delta \theta\). Inset: PDF of \(\delta \theta\) at different D. The black dash line represents the threshold at \(\delta \theta =20^{\circ}\). d PDFs of \({\phi }_{i}\) for chains (triangle) and arches (square) at D = 3.49d. Inset: PDFs of \({\alpha }_{i}\) for chains (triangle) and arches (square) at the same D.
