Abramowitz M. & Stegun I. 1970 Handbook of Mathematical Functions, 9th edn., §3.3.7. Dover.
Bagnold R. A. 1954 Experiments on gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc. R. Soc. Lond. A 225, 49–63.
Bartelt P. & McArdell B. W. 2009 Granulometric investigations of snow avalanches. J. Glaciol. 55 (193), 829–833.
Baxter J., Tüzün U., Heyes D., Hayati I. & Fredlund P. 1998 Stratification in poured granular heaps. Nature 391, 136.
Bertran P. 2003 The rock-avalanche of February 1995 at Claix (French Alps). Geomorphology 54, 339–346.
Branney M. J. & Kokelaar B. P. 1992 A reappraisal of ignimbrite emplacement: progressive aggradation and changes from particulate to non-particulate flow during emplacement of high-grade ignimbrite. Bull. Volcanol. 54, 504–520.
Bridgwater J. 1976 Fundamental powder mixing mechanisms. Powder Technol. 15, 215–236.
Cagnoli B. & Manga M. 2005 Vertical segregation in granular mass flows: A shear cell study. Geophys. Res. Lett. 32, L10402.
Cagnoli B. & Romano G. P. 2010 Effect of grain size on mobility of dry granular flows of angular rock fragments: An experimental determination. J. Volcanol. Geotherm. Res. 193 (1–2), 18–24.
Calder E. S., Sparks R. S. J. & Gardeweg M. C. 2000 Erosion, transport and segregation of pumice and lithic clasts in pyroclastic flows inferred from ignimbrite at Lascar Volcano, Chile. J. Volcanol. Geotherm. Res. 104, 201–235.
Cas R. A. & Wright J. V. 1987 Volcanic Successions. Allen & Unwin.
Chadwick P. 1976 Continuum Mechanics. Concise Theory and Problems. Allen & Unwin.
Cole J. D. 1951 On a quasilinear parabolic equation occurring in aerodynamics. Q. Appl. Maths 9, 225–236.
Costa J. E. & Williams G. 1984 Debris flow dynamics. Tech. Rep. 84–606. (Videotape) US Geological Survey.
Courant R. & Hilbert D. 1962 Methods of Mathematical Physics, vol. 2. Interscience.
Dade W. B. & Huppert H. E. 1998 Long-runout rockfalls. Geology 26, 803–806.
Dolgunin V. N. & Ukolov A. A. 1995 Segregation modelling of particle rapid gravity flow. Powder Technol. 83, 95–103.
Drahun J. A. & Bridgwater J. 1983 The mechanisms of free surface segregation. Powder Technol. 36, 39–53.
Ehrichs E. E., Jaeger H. M., Karczmar G. S., Knight J. B., Kuperman V. Y. & Nagel S. R. 1995 Granular convection observed by magnetic-resonance-imaging. Science 267, 1632–1634.
Félix G. & Thomas N. 2004 Relation between dry granular flow regimes and morphology of deposits: formation of levées in pyroclastic deposits. Earth Planet. Sci. Lett. 221, 197–213.
Goddard J. D. 2003 Material instability in complex fluids. Annu. Rev. Fluid Mech. 35, 113–133.
Golick L. A. & Daniels K. E. 2009 Mixing and segregation rates in sheared granular materials. Phys. Rev. E 80 (4), 042301.
Goujon C., Dalloz-Dubrujeaud B. & Thomas N. 2007 Bidisperse granular avalanches on inclined planes: A rich variety of behaviours. Eur. Phys. J. E 23, 199–215.
Gray J. M. N. T. 1999 Loss of hyperbolicity and ill-posedness of the viscous-plastic sea ice rheology in uniaxial divergent flow. J. Phys. Oceanogr. 29 (11), 2920–2929.
Gray J. M. N. T. 2001 Granular flow in partially filled slowly rotating drums. J. Fluid Mech. 441, 1–29.
Gray J. M. N. T. 2010 Particle size segregation in granular avalanches: A brief review of recent progress. AIP Conf. Proc. 1227, 343–362.
Gray J. M. N. T. & Ancey C. 2009 Segregation, recirculation and deposition of coarse particles near two-dimensional avalanche fronts. J. Fluid Mech. 629, 387–423.
Gray J. M. N. T. & Chugunov V. A. 2006 Particle-size segregation and diffusive remixing in shallow granular avalanches. J. Fluid Mech. 569, 365–398.
Gray J. M. N. T. & Hutter K. 1997 Pattern formation in granular avalanches. Contin. Mech. Thermodyn. 9, 341–345.
Gray J. M. N. T. & Kokelaar B. P. 2010 a Large particle segregation, transport and accumulation in granular free-surface flows. J. Fluid Mech. 652, 105–137.
Gray J. M. N. T. & Kokelaar B. P. 2010 b Large particle segregation, transport and accumulation in granular free-surface flows – erratum. J. Fluid Mech. 657, 539.
Gray J. M. N. T., Shearer M. & Thornton A. R. 2006 Time-dependent solutions for particle-size segregation in shallow granular avalanches. Proc. R. Soc. Lond. A 462, 947–972.
Gray J. M. N. T., Tai Y. C. & Noelle S. 2003 Shock waves, dead-zones and particle-free regions in rapid granular free-surface flows. J. Fluid Mech. 491, 161–181.
Gray J. M. N. T. & Thornton A. R. 2005 A theory for particle size segregation in shallow granular free-surface flows. Proc. R. Soc. Lond. A 461, 1447–1473.
Gray J. M. N. T., Wieland M. & Hutter K. 1999 Free surface flow of cohesionless granular avalanches over complex basal topography. Proc. R. Soc. Lond. A 455, 1841–1874.
Grigorian S. S., Eglit M. E. & Iakimov Yu. L. 1967 A new formulation and solution of the problem of snow avalanche movement. Tr. Vysokogornogo Geofizicheskogo Instituta, vol. 12, 104–113.
Gruber U. & Bartelt P. 2007 Snow avalanche hazard modelling of large areas using shallow water numerical methods and GIS. Environ. Model. Softw. 22 (10), 1472–1481.
Herrmann H. J., Mantica G. & Bessis D. 1990 Space-filling bearings. Phys. Rev. Lett. 65 (26), 3223–3226.
Hill K. M., Gioia G. & Amaravadi D. 2004 Radial segregation patterns in rotating granular mixtures: Waviness selection. Phys. Rev. Lett. 93, 224301.
Hill K. M. & Kakalios J. 1995 Reversible axial segregation of rotating granular media. Phys. Rev. E 52 (4), 4393–4400.
Hill K. M., Kharkar D. V., Gilchrist J. F., McCarthy J. J. & Ottino J. M. 1999 Segregation driven organization in chaotic granular flows. Proc. Natl Acad. Sci. USA 96, 11701–11706.
Hiscott R. N. 2003 In Encyclopedia of Sediments and Sedimentary Rocks (ed. Middleton G. V.), pp. 333–335. Springer.
Hopf E. 1950 The partial differential equation u _{t} + uu _{x} = μu _{xx}. Commun. Pure Appl. Math. 3, 201–230.
Iverson R. M. 1997 The physics of debris-flows. Rev. Geophy. 35, 245–296.
Iverson R. M. 2003 The debris-flow rheology myth. In Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment (ed. Rickenmann D. & Chen C. L.), pp. 303–314. Millpress.
Iverson R. M. & Denlinger R. P. 2001 Flow of variably fluidized granular masses across three-dimensional terrain. 1. Coulomb mixture theory. J. Geophys. Res. 106 (B1), 553–566.
Iverson R. M., Logan M., LaHusen R. G. & Berti M. 2010 The perfect debris flow? aggregated results from 28 large-scale experiments. J. Geophys. Res. 115, F03005.
Iverson R. M. & Vallance J. W. 2001 New views of granular mass flows. Geology 29 (2), 115–118.
Jha A. K. & Puri V. M. 2010 Percolation segregation of multi-size and multi-component particulate materials. Powder Technol. 197 (3), 274–282.
Johanson J. R. 1978 Particle segregation . . . and what to do about it. Chem. Engng, May, pp. 183–188.
Jomelli V. & Bertran P. 2001 Wet snow avalanche deposits in the French Alps: Structure and sedimentology. Geografiska Annaler. A Phys. Geog. 83, 15–28.
Jop P., Forterre Y. & Pouliquen O. 2006 A constitutive relation for dense granular flows. Nature 44, 727–730.
Joseph D. D. & Saut J. C. 1990 Short-wave instabilities and ill-posed initial-value problems. Theor. Comput. Fluid Dyn. 1, 191–227.
Khakhar D. V., McCarthy J. J. & Ottino J. M. 1997 Radial segregation of granular mixtures in rotating cylinders. Phys. Fluids 9, 3600–3614.
Khakhar D. V., McCarthy J. J. & Ottino J. M. 1999 Mixing and segregation of granular materials in chute flows. Chaos 9, 594–610.
Kynch G. J. 1952 A theory of sedimentation. Trans. Faraday Soc. 48, 166–176.
Lax P. D. 1957 Hyperbolic systems of conservation laws 2. Commun. Pure Appl. Maths 10 (4), 537–566.
Makse H. A., Havlin S., King P. R. & Stanley H. E. 1997 Spontaneous stratification in granular mixtures. Nature 386, 379–382.
Mangeney A., Bouchut F., Thomas N., Vilotte J. P. & Bristeau M. O. 2007 Numerical modeling of self-channeling granular flows and of their levee-channel deposits. J. Geophys. Res. 112, F02017.
May L. B. H., Golick L. A., Phillips K. C., Shearer M. & Daniels K. E. 2010 Shear-driven size segregation of granular materials: Modeling and experiment. Phys. Rev. E 81 (5), 051301.
McCarthy J. J. 2009 Turning the corner in segregation. Powder Technol. 192 (2), 137–142.
Middleton G. V. 1970 Experimental studies related to problems of flysch sedimentation. In Flysch Sedimentology in North America (ed. Lajoie J.), pp. 253–272. Business and Economics Science Ltd.
Middleton G. V. & Hampton M. A. 1976 Subaqueous sediment transport and deposition by sediment gravity flows. In Marine Sediment Transport and Environmental Management (ed. Stanley D. J. & Swift D. J. P.), pp. 197–218. Wiley.
Morland L. W. 1992 Flow of viscous fluids through a porous deformable matrix. Surv. Geophys. 13, 209–268.
Newey M., Ozik J., Van der Meer S. M., Ott E. & Losert W. 2004 Band-in-band segregation of multidisperse granular mixtures. Eur. Phys. Lett. 66 (2), 205.
Palladino D. M. & Valentine G. A. 1995 Coarse-tail vertical and lateral grading in pyroclastic flow deposits of the Latera Volcanic Complex (Vulsini, Central Italy): origin and implications for flow dynamics. J. Volcanol. Geotherm. Res. 69 (3–4), 343–364.
Phillips J. C., Hogg A. J., Kerswell R. R. & Thomas N. H. 2006 Enhanced mobility of granular mixtures of fine and coarse particles. Earth Planet. Sci. Lett. 246, 466–480.
Pierson T. C. 1986 Flow behavior of channelized debris flows, Mount St. Helens, Washington. In Hillslope Processes (ed. Abrahams A. D.), pp. 269–296. Allen & Unwin.
Pitman E. B., Nichita C. C., Patra A., Bauer A., Sheridan M. & Bursik M. 2003 Computing granular avalanches and landslides. Phys. Fluids 15 (12), 3638–3646.
Pouliquen O. 1999 a Scaling laws in granular flows down rough inclined planes. Phys. Fluids 11 (3), 542–548.
Pouliquen O. 1999 b On the shape of granular fronts down rough inclined planes. Phys. Fluids 11 (7), 1956–1958.
Pouliquen O., Delour J. & Savage S. B. 1997 Fingering in granular flows. Nature 386, 816–817.
Pouliquen O. & Vallance J. W. 1999 Segregation induced instabilities of granular fronts. Chaos 9 (3), 621–630.
Rhee H. K., Aris R. & Amundson N. R. 1986 First-Order Partial Differential Equations, vol. 1: Theory and Applications of Single Equations. Prentice-Hall.
Rognon P. G., Roux J. N., Naaim M. & Chevoir F. 2007 Dense flows of bidisperse assemblies of disks down an inclined plane. Phys. Fluids 19, 058101.
Rosato A., Strandburg K. J., Prinz F. & Swendsen R. H. 1987 Why the Brazil nuts are on top: Size segregation of particulate matter by shaking. Phys. Rev. Lett. 58 (10), 1038–1040.
Savage S. B. & Hutter K. 1989 The motion of a finite mass of granular material down a rough incline. J. Fluid Mech. 199, 177–215.
Savage S. B. & Lun C. K. K. 1988 Particle size segregation in inclined chute flow of dry cohesionless granular solids. J. Fluid Mech. 189, 311–335.
Schröter M., Ulrich S., Kreft J., Swift J. B. & Swinney H. L. 2006 Mechanisms in the size segregation of a binary granular mixture. Phys. Rev. E 74 (1), 011307.
Schulze D. 2008 Powders and Bulk Solids. Springer.
Scott A. M. & Bridgwater J. 1975 Interparticle percolation: A fundamental solids mixing mechanism. Ind. Engng Chem. Fundam. 14 (1), 22–27.
Shearer M. & Dafermos C. 2010 Finite time emergence of a shock wave for scalar conservation laws. J. Hyperbolic Differ. Equ. 7 (1), 107–116.
Shearer M. & Giffen N. 2010 Shock formation and breaking in granular avalanches. Discr. Contin. Dyn. Sys. 27 (2, Special Issue), 693–714.
Shearer M., Gray J. M. N. T. & Thornton A. R. 2008 Stable solutions of a scalar conservation law for particle-size segregation in dense granular avalanches. Eur. J. Appl. Maths 19, 61–86.
Shinbrot T. & Muzzio F. J. 1998 Reverse buoyancy in shaken granular beds. Phys. Rev. Lett. 81 (20), 4365–4368.
Skeel R. D. & Berzins M. 1990 A method for the spatial discretization of parabolic equations in one space variable. SIAM J. Sci. Stat. Comput. 11 (1), 1–32.
Thornton A. R. & Gray J. M. N. T. 2008 Breaking size-segregation waves and particle recirculation in granular avalanches. J. Fluid Mech. 596, 261–284.
Thornton A. R., Gray J. M. N. T. & Hogg A. J. 2006 A three-phase mixture theory for particle size segregation in shallow granular free-surface flows. J. Fluid Mech. 550, 1–25.
Truesdell C. 1984 Rational Thermodynamics. Springer.
Vallance J. W. & Savage S. B. 2000 Particle segregation in granular flows down chutes. In IUTAM Symposium on Segregation in Granular Materials (ed. Rosato A. D. & Blackmore D. L.), pp. 31–51. Kluwer.
Whitham G. B. 1974 Linear and Nonlinear Waves. John Wiley.
Wiederseiner S., Andreini N., Epely-Chauvin G., Moser G., Monnereau M., Gray J. M. N. T. & Ancey C. 2011 Experimental investigation into segregating granular flows down chutes. Phys. Fluids 23, 013301.
Williams S. C. 1968 The mixing of dry powders. Powder Technol. 2, 13–20.
Wills B. A. 1979 Mineral Processing Technology. Pergamon.
Zanuttigh B. & Di Paolo A. 2006 Experimental analysis of the segregation of dry avalanches and implications for debris flows. J. Hydraul. Res. 44 (6), 796–806.
Zanuttigh B. & Ghilardi P. 2010 Segregation process of water-granular mixtures released down a steep chute. J. Hydrol. 391 (1–2), 175–187.
Zuriguel I., Gray J. M. N. T., Peixinho J. & Mullin T. 2006 Pattern selection by a granular wave in a rotating drum. Phys. Rev. E 73, 061302.