[1] A W Jenike, Gravity Flow of Bulk Solids, University of Utah Engineering Experiment Station, Bull. 108 (1961), and Bulletin 123 (1964).

[2] W A Beverloo, H A Leniger, J van de Velde, The flow of granular solids through orifices, Chem. Eng. Sci. 15, 260 (1961).

[3] J Wu, J Binbo, J Chen, Y Yang, Multi-scale study of particle flow in silos, Advanced Pow. Tech. 20, 62 (2009).

[4] G H Ristow, Outflow rate and wall stress for two-dimensional hoppers, Phys. A 235, 319 (1997).

[5] K To, P-Y Lai, Jamming pattern in a two-dimensional hopper, Phys. Rev. E 66, 011308 (2002).

[6] S-C Yang, S-S Hsiau, The simulation and experimental study of granular materials discharged from a silo with the placement of inserts, Pow. Tech. 120, 244 (2001).

[7] A Garcimartin, I Zuriguel, L A Pugnaloni, A Janda, Shape of jamming arches in two-dimensional deposits of granular materials, Phys. Rev. E 82, 031306 (2010).

[8] R O Unac, O A Benegas, A M Vidales and I Ippolito, Experimental study of discharge rate fluctuations in a silo with different hopper geometries, Pow. Tech. 225, 214 (2012).

[9] R L Brown, J C Richards, Profile of flow of granulates through apertures, Trans. Inst. Chem. Eng. 38, 243 (1960).

[10] P W Cleary, M L Sawley, DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge, Appl. Math. Model. 26, 89 (2002).

[11] A Anand, J S Curtis, C R Wassgren, B C Hancock, W R Ketterhagen, Predicting discharge dynamics from a rectangular hopper using the discrete element method (DEM), Chem. Eng. Sci. 63, 5821 (2008).

[12] R O Unac, A M Vidales and L. A. Pugnaloni, The effect of packing fraction on the jamming of granular flow through small apertures, J. Stat. Mech. P4008 (2012).

[13] C Mankoc, A Janda, R Arevalo, J M Pastor, I Zuriguel, A Garcimartin, D Maza, The flow rate of granular materials through an orifice, Gran. Matt. 9, 407 (2007).

[14] A P Huntington, N M Rooney, Chemical Engineering Tripos Part 2, Research Project Report, University of Cambridge (1971).

[15] F C Franklin, L N Johanson, Flow of granular material through a circular orifice, Chem. Eng. Sci. 4, 119 (1955).

[16] S Humby, U Tuzun, A B Yu, Prediction of hopper discharge rates of binary granular mixtures, Chem. Eng. Sci. 53, 483 (1998).

[17] A Mehta, G C Barker, J M Luck, Cooperativity in sandpiles: statistics of bridge geometries, J. Stat. Mech. P10014 (2004).

[18] G H Ristow, H J Herrmann, Density patterns in two-dimensional hoppers, Phys. Rev. E 50, R5 (1994).

[19] A Medina, J A Cordova, E Luna, C Trevino, Velocity field measurements in granular gravity flow in a near 2D silo, Phys. Lett. A 250 111 (1998).

[20] L Babout, K. Grudzien, E Maire, P J Withers, Influence of wall roughness and packing density on stagnant zone formation during funnel flow discharge from a silo: An X-ray imaging study, Chem. Eng. Sci. 97, 210 (2013).

[21] SS Manna, D V Khakhar, Internal avalanches in a granular medium, Phys. Rev. E 58, R6935 (1998).

[22] Manna S S, Self-Organization in a Granular Medium by Internal Avalanches, Phase Transit. 75, 529 (2002).

[23] R O Unac, J G Benito, A M Vidales, L A Pugnaloni, Arching during the segregation of two-dimensional tapped granular systems: Mixtures versus intruders, Eur. Phys. J.E 37, 117 (2014).

[24] L A Pugnaloni, M G Valluzzi and L G Valluzzi, Arching in tapped deposits of hard disks, Phys. Rev. E 73, 051302 (2006).

[25] A Kudrolli, Size separation in vibrated granular material, Rep. Prog. Phys. 67, 209 (2004).

[26] J Duran, J Rajchenbach, E Clement, Arching effect model for particle size segregation, Phys. Rev. Lett. 70, 2431 (1993).

[27] J Duran, T Mazozi, E Clement, J Rajchenbach, Size segregation in a two-dimensional sandpile: Convection and arching effects, Phys.Rev. E 50, 5138 (1994).

[28] R O Unac, A M Vidales, L A Pugnaloni, Simple model for wet granular beds subjected to tapping, Gran. Matt. 11, 371 (2009).

[29] P Ribiere, P Richard, P Philippe, D Bideau, R Delannay, On the existence of stationary states during granular compaction, Eur. Phys. J. E 22, 249 (2007).