Modeling granular media on the computer

Continuum Mechanics and Thermodynamics

Volumn 10, Issue 4, 1998, Pages 189-231

  Herrmann, H J ^a   Luding, S ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032221899     PISSN: 09351175     EISSN: None     Source Type: Journal    
DOI: 10.1007/s001610050089     Document Type: Review

References (234)

1. Ahmad K, Smalley IJ (1973) Observation of particle segregation in vibrated granular systems. Powder Technol., 8:69
2. Alexander FJ, Garcia AL, Alder BJ (1995) A consistent Boltzmann algorithm. Phys. Rev. Lett., 74:5212
3. Allen MP, Tildesley DJ (1987) Computer Simulation of Liquids. Oxford University Press, Oxford
4. Alonso JJ, Herrmann HJ (1996) On the shape of the tail of a sand pile. Phys. Rev. Lett., 76:4911-4914
5. Alonso JJ, Hovi JP, Herrmann HJ (1998) Model for the calculation of the angle of repose from the microscopic grain properties. July 1998
6. Athey JD, Cutress JO, Pulfer RF (1966) X-ray investigation on flowing powders. Chem. Eng. Sci., 21:835
7. Bak P, Tang C, Wiesenfeld K (1987) Self-organized criticality: An explanation of 1 /f noise. Phys. Rev. Lett., 59(4):381-384
8. Bardet JP (1994) Observations on the effects of particle rotations on the failure of idealized granular materials. Mechanics of Materials. 18:159-182
9. Bardet JP, Proubet J ( 1991 ) A numerical investigation of the structure of persistent shear bands in granular media. Geotechnique, 41(4):599-613
10. Bashir YM, Goddard JD (1991) A novel simulation method for the quasi-static mechanics of granular assemblages. J. Rheol., 35(5):849-885
11. Bathurst RJ, Rothenburg L (1988) Micromechanical aspects of isotropic granular assemblies with linear contact interactions. J. Appl. Mech., 55:17
12. Baxter GW, Behringer RP (1990) Cellular automata models for granular flow. Phys. Rev. A (Rapid Communication), 42(2):1017
13. Baxter GW, Behringer RP (1991) Cellular automata models for the flow of granular materials. Physica D, 51:465
14. Baxter GW, Behringer RP, Fagert T, Johnson GA (1989) Pattern formation in flowing sand. Phys. Rev. Lett., 62(24):2825
15. Baxter GW, Leone R. Behringer RP (1993) Experimental test of time scales in flowing sand. Europhys. Lett., 21(5):569-574
16. Behringer RP, Jenkins JT, editors (1997) Powders & Grains 97. Balkema, Rotterdam
17. Bernu B, Mazighi R (1990) One-dimensional bounce of inelastically colliding marbles on a wall. J. Phys. A: Math. Gen., 23:5745
18. Bird GA (1994) Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon, Oxford
19. Blair-Fish P, Bransby P (1973) Flow patterns and wall stresses in a mass-flow bunker. J. Eng. for Industry. 95:17
20. Bouchaud JP ( 1994) Statics and dynamics of sandpiles: some phenomenological ideas. In Bardhan KK, Chakrabarti BK, Hansen A, editors, Lecture Notes in Physics, volume Non Linearity and Breakdown in Soft Condensed Matter, pages 47-53. Springer-Verlag, Berlin
21. Bouchaud JP, Gates ME, Claudin P (1995) Stress distribution in granular media and nonlinear wave equation. J.Phys.I, 5:639-656
22. Brennen CE, Ghosh S, Wassgren C (1993) Vertical oscillation of a bed of granular material. In Thornton C, editor, Powders & Grains 93, Rotterdam. Balkema
23. Bridgwater J (1976) Fundamental powder mixing mechanisms. Powder Technol., 15:215
24. Brown RL (1939) The fundamental principles of segregation. The Institute of Fuel, 13:15-19
25. Brown RL, Richards JC (1970) Principles of Powder Mechanics. Pergamon Press, Oxford
26. Buchholtz V, Pöschel T (1994) Nutfierical investigations of the evolution of sandpiles. Physica A, 202:390
27. Buchholtz V, Pöschel T, Tillemans HJ (1995) Simulation of rotating drum experiments using non-circular particles. Physica A, 216:199
28. Byerlee JD (1968) Brittle-ductile transition in rocks. J. Geophys. Res., 73:4741
29. Campbell CS (1990) Rapid granular flows. Annu. Rev. Fluid Mech., 22:57
30. Campbell CS, Brennen CE (1985) Computer simulation of granular shear flows. J. Fluid. Mech., 151:167
31. Caram H, Hong DC (1991) Random-walk approach to granular flows. Phys. Rev. Lett., 67(7):828
32. Chen W (1995) Experimental observation of self-localized structure in granular material. Phys. Lett. A, 196:321
33. Christensen K, Corral A, Frette V, Feder J, Jossang T (1996) Tracer dispersion in a self-organized critical system. Phys. Rev. Lett., 77(1):107-110
34. Clement E, Duran J, Rajchenbach J (1992) Experimental study of heaping in a two-dimensional "sandpile". Phys. Rev. Lett., 69(8): 1189
35. Clément E, Luding S, Blumen A, Rajchenbach J, Duran J (1993) Fluidization, condensation and clusterization of a vibrating column of beads. Int. J. of Mod. Phys. B, 7(9 &10):1807-1827
36. Clément E, Rajchenbach J (1991) Fluidization of a bidimensional powder. Europhys. Lett., 16(2): 133
37. Cundall PA (1974) Report ad/a - 001 602. Technical report, U.S. Nat. Tech. Information Service. Springfield VA
38. Cundall PA (1989) Numerical experiments on localization in factional materials. Ingenieur-Archiv, 59:148-159
39. Cundall PA, Strack O. DL (1979) A discrete numerical model for granular assemblies. Géotechnique, 29(1):47-65
40. Cutress O, Pulfer RF (1967) X-ray investigation on flowing powders. Powder Technol., 1:213
41. Désérable D, Martinez J (1993) Using a cellular automaton for the simulation of flow of granular media. In Thornton C, editor, Powders & Grains 93, page 345, Rotterdam. Balkema
42. Devillard P (1990) Scaling behaviour in size segregation ("Brazil Nuts") J. Phys. France, 51:369
43. Dinkelacker F, Hübler A. Lüscher E (1987) Pattern formation of powder on a vibrating disc. Biol. Cybern., 56:51
44. Dippel S, Luding S (1995) Simulations on size segregation: Geometrical effects in the absence of convection. J. Phys. I France, 5:1527
45. Dobry R, Ng TT (1989) Discrete modelling of stress-strain behaviour of granular media at small and large strains. In Proc. 1st U.S. Conf. on Discrete Element Meth., Nat. Sci. Found., Washington DC
46. Douady S, Fauve S, Laroche C (1989) Subharmonic instabilities and defects in a granular layer under vertical vibrations. Europhys. Lett., 8(7):621
47. Drake TG (1990) Structural features in granular flows. J. of Geophysical Research, 95(B6):8681-8696
48. Drescher A, de Josselin de Jong G (1972) Photoelastic verification of a mechanical model for the flow of a granular material. J. Mech. Phys. Solids, 20:337-351
49. Du Y, Li H, Kadanoff LP (1995) Breakdown of hydrodynamics in a one-dimensional system of inelastic particles. Phys. Rev. Lett., 74(8): 1268-1271
50. Duran J, Mazozi T, Clément E, Rajchenbach J (1994) Size segregation in a two-dimensional sandpile: convection and arching effects. Phys. Rev. E, 50(6):5138-5141
51. Duran J, Mazozi T, Luding S, Clément E, Rajchenbach J (1996) Discontinuous decompaction of a falling sandpile. Phys. Rev. E, 53(2): 1923
52. Duran J, Rajchenbach J, Clément E (1993) Arching effect model for particle size segregation. Phys. Rev. Lett., 70(16):2431-2434
53. Edwards SF (1991) Dynamics of complex flow. J. Stat. Phys., 62:889
54. Edwards SF, Mounfield CC (1996) A theoretical model for the stress distribution in granular matter. III: Forces in sandpiles. Physica A, 226:25
55. Edwards SF, Oakeshott R. BS ( 1989a) Theory of powders. Physica A, 157:1080
56. Edwards SF, Oakeshott R. BS (1989b) The transmission of stress in an aggregate. Physica D, 38:88-92
57. Ehrichs EE, Jaeger HM, Karczmar GS, Knight JB, Kuperman V, Nagel SR (1995) Granular convection observed by magnetic resonance imaging. Science, 267:1632-1634
58. Evesque P, Rajchenbach J (1989) Instability in a sand heap. Phys. Rev. Lett., 62(1 ):44
59. Faraday M (1831) On a peculiar class of acoustical figures: and on certain forms assumed by groups of particles upon vibrating elastic surfaces. Philos. Trans. R. Soc. London, 52:299
60. Flekkoy EG, Herrmann HJ (1993) Lattice Boltzmann models for complex fluids. Physica A, 199:1
61. Foerster SF, Louge MY, Chang H, Allia K (1994) Measurements of the collision properties of small spheres. Phys. Fluids, 6(3):1108-1115
62. Frette V, Christensen K, Malthe-Sorenssen A, Feder J, Jossang T, Meakin P (1996) Avalanche dynamics in a pile of rice. Nature, 379:49-51
63. Gallas J. AC, Herrmann HJ, Sokolowski SS (1992a) Molecular dynamics simulation of powder fluidization in two dimensions. Physica A, 189:437
64. Gallas J. AC, Herrmann HJ, Pöschel T, Sokolowski SS (1996) Molecular dynamics simulation of size segregation in three dimensions. J. Stat. Phys, 82:443
65. Gallas J. AC, Herrmann HJ, Sokolowski S (1992b) Convection cells in vibrating granular media. Phys. Rev. Lett., 69(9):1371
66. Gervois A, Bideau D (1992) Some geometrical properties of two-dimensional hard disk packings. In Bideau D, editor, Disorder and Granular Media, Amsterdam. North Holland
67. Goddard JD (1986) Microstructural origins of continuum stress fields - a brief history and some unresolved issues. In DeKee D, Kaloni PN, editors, Recent Developments in Structered Continua. Pitman Research Notes in Mathematics No. 143, page 179, New York. Longman, J. Wiley
68. Goddard JD ( 1990) Nonlinear elasticity and pressure-dependent wave speeds in granular media. Proc. R. Soc. Lond. A, 430:105
69. Goldhirsch I, Zanetti G (1993) Clustering instability in dissipative gases. Phys. Rev. Lett., 70(11):1619-1622
70. Goldshtein A, Shapiro M (1995) Mechanics of collisional motion of granular materials. Part I. General hydrodynamic equations J. Fluid Mech., 282:75-114
71. Grabinsky M (1992) Qunatifying rock stress and evaluating its significance in the geomechanical design of underground mines. PhD thesis, Univ. of Toronto
72. Grasselli Y, Herrmann HJ (1997) On the angles of dry granular heaps. Physica A, 246:301-312
73. Grasselli Y, Herrmann HJ (1998) Experimental study of granular stratification. Granular Matter, 1(1): 43-17
74. Haff PK (1983) Grain flow as a fluid-mechanical phenomenon. J. Fluid Mech., 134:401-430
75. Haff PK, Werner BT (1986) Computer simulation of the mechanical sorting of grains. Powder Technol., 48:239-245
76. Hanes DM, Inman DL (1985) Observations of rapidly flowing granular-fluid materials. J. Fluid Mech., 150:357
77. Hansen A, Bideau D, editors (1992) Disorder and Granular Media. North Holland, Amsterdam
78. Held GA, Solina DH, Keane DT, Haag WJ, Horn P, Grinstein GG (1990) Experimental study of critical-mass fluctuations in an evolving sandpile. Phys. Rev. Lett., 65(9): 1120-1123
79. Hemmingsson J, Herrmann HJ, Roux S (1997) On stress networks in granular media. J. Phys. I, 7:291-302
80. Herrmann HJ (1993) On the thermodynamics of granular media. J. Phys. II France, 3:427
81. Herrmann HJ (1995) Simulating granular media on the computer. In Garrido PL, Marro J, editors, 3rd Granada Lectures in Computational Physics, pages 67 - 114. Springer, Heidelberg
82. Herrmann HJ, Hong DC, Stanley HE (1984) Backbone and elastic backbone of percolation clusters obtained by the new method of 'burning'. J. Phys. A, 17:L261
83. Herrmann HJ, Hovi JP, Luding S, editors (1998) Physics of dry granular media - NATO ASI Series, E 350, Dordrecht. Kluwer Academic Publishers
84. Homsy GM, Jackson R, Grace JR (1992) Report of a symposium on mechanics of fluidized-beds J. Fluid Mech., 236:477
85. Hong DC ( 1993) Stress distribution of a hexagonally packed granular pile. Phys. Rev. E, 47(1):760-762
86. Hong DC, McLennan JA (1992) Molecular dynamics simulations of hard sphere granular particles. Physica A, 187:159
87. Huntley JM (1993) Vacancy effects on the force distribution in a two-dimensional granular pile. Phys. Rev. E, 48(51):4099-4101
88. Huthmann M, Zippelius A (1998) Dynamics of inelastically colliding rough spheres: Relaxation of translational and rotational energy. Phys. Rev. E, 56(6):6275-6278
89. Hutter K. Szidarovszky F, Yakowitz S ( 1986) Plane steady shear flow of a cohesionless granular material down an inclined plane: A model for flow avalanches. Part II: Numerical results. Acta Mechanica, 65:239-201
90. Hwang H, Hutter K (1995) A new kinetic model for rapid granular flow. Continuum Mech. Thermodyn., 7:357-384
91. Issa JA, Nelson RB (1989) Numerical analysis of micromechanical behaviour of granular materials. In Proc. 1st U.S. Conf. on Discrete Element Meth., Nat. Sci. Found., Washington DC
92. Jaeger HM, Liu C, Nagel SR (1989) Relaxation at the angle of repose. Phys. Rev. Lett.. 62(1):40-43
93. Jaeger HM, Nagel SR ( 1992) Physics of the granular state. Science, 255:1523
94. Jaeger HM, Nagel SR, Behringer RP (1996a) Granular solids, liquids, and gases. Reviews of Modern Physics, 68(4):1259-1273
95. Jaeger HM, Nagel SR, Behringer RP ( 1996b) The physics of granular materials. Physics Today, 49(4):32-38
96. Janssen HA (1895) Versuche über Getreidedruck in Silozellen. Zeitschr. d. Vereines deutscher Ingenieure. 39(35):1045-1049
97. Jenkins JT (1985) Grad's 13-moment system for a dense gas of inelastic spheres. Arch. Rat'l. Mech. Anal., 87:355
98. Jenkins JT, Cowin SC (1979) Theories for flowing granular materials. In Cowin SC, editor, Mechanics Applied to the Transport of Bulk Materials, New York. Am. Soc. Mech. Eng.
99. Jenkins JT, Savage SB (1983) A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles J. Fluid Mech., 130:187-202
100. Johnson KL (1989) Contact Mechanics. Cambridge Univ. Press, Cambridge
101. Jullien R, Meakin P (1992) Three-dimensional model for particle-size segregation by shaking. Phys. Rev. Lett., 69(4):640
102. Jullien R, Meakin P, Pavlovitch A (1993) Jullien and meakin and pavlovitch reply. Phys. Rev. Lett., 70(14):2195
103. Károly A, Kertész J (1994) Hydrodynamic cellular automata for granular media. In Gruber R, Tomassini M, editors, Proc. 6th Joint EPS-APS Int. Conf. of Phys. Comp., Geneva. EPS
104. Knight JB, Fandrich CG, Lau CN, Jaeger HM, Nagel SR (1995) Density relaxation in a vibrated granular material Phys Rev E, 51(5):3957-3962
105. Knight JB, Jaeger HM, Nagel SR (1993) Vibration-induced size separation in granular media: The convection connection Phys Rev. Lett., 70(24):3728-3731
106. Kohring GA (1994) Computer simulations of granular materials: the effect of mesoscopic forces. J. Phys. I, 4:1779
107. Kohring GA, Melin S, Puhl H, Tillemans HJ, Vermöhlen W(1995) Computer simulations of critical, non-stationary granular flow through a hopper. Comput. Methods in Appl. Mechanics and Eng., 124:2273
108. Kuhn MR, Mitchell JR (1989) Modelling of soil creep with the discrete element method. In Proc. 1st U.S. Conf. on Discrete Element Meth., Nat. Sci. Found., Washington DC
109. Labous L, Rosato AD, Dave R (1997) Measurements of collision properties of spheres using high-speed video analysis Phys Rev. E 56: 5715
110. Landau LD, Lifshitz EM (1975) Elasticity Theory. Pergamon Press, Oxford
111. Laroche C, Douady S, Fauve S (1989) Convective flow of granular masses under vertical vibrations. J. Phys., 50:699-706
112. Lee J (1995) Scaling behavior of granular particles in a vibrating box. Physica A, 219:305-326
113. Lee J, Cowin SC. Templeton JS (1974) An experimental study of a kinematics of flow through hoppers Trans Soc Rheol 18:247
114. Lee J, Herrmann HJ (1993) Angle of repose and angle of marginal stability: Molecular dynamics of granular particles J Phys A, 26:373
115. Lee J, Leibig M ( 1994) Density waves in granular flow: a kinetic wave approach. J. Phys. I France, 4:507
116. Lee M, Dufty JW (1996) Long wavelength instability for uniform shear flow, preprint
117. Liffman K, Chan D, Hughes BD-( 1994) On the stress depression under a sandpile. Powder Technol., 78:263-271
118. Liffman K, Chan D. YC, Hughes BD (1992) Force distribution in a two dimensional sandpile. Powder Technology. 72:255-267
119. Liu C, Nagel SR (1992) Sound in sand. Phys. Rev. Lett., 68( 15):2301-2304
120. Liu C. Nagel SR, Scheeler DA, Coppersmith SN, Majumdar S, Narayan O, Witten TA (1995) Force fluctuations in bead packs Science. 269:513
121. Lorig LJ, Brady B, HG (1984) A hybrid computational scheme for excavation and support design in jointed rock media. In Design and performance of underground excavations; ISRM Symposium, page 105, Cambridge. UK. London: British Geotech. Soc.
122. Lubachevsky BD (1991) How to simulate billards and similar systems. J. of Comp. Phys., 94(2):255
123. Luding S (1994) Models and Simulations of Granular Materials. PhD thesis. Universität Freiburg
124. Luding S (1995) Granular materials under vibration: Simulations of rotating spheres. Phys. Rev. E, 52(41):4442
125. Luding S (1996) Langkorn-oder Kurzkornreis? Lawinenstatistik in Reishaufen hängt von der Kornform ab Physikalische Blätter, 52(3):203
126. Luding S (1997) Stress distribution in static two dimensional granular model media in the absence of friction Phys Rev E 55(4):4720-4729
127. Luding S (1998) Collisions &contacts between two particles. In Herrmann HJ, Hovi JP, Luding S, editors, Physics of dry granular media - NATO ASI Series, Dordrecht, Kluwer Academic Publishers
128. Luding S, Clément E, Blumen A, Rajchenbach J, Duran J ( 1994c) Anomalous energy dissipation in molecular dynamics simulations of grains: The "detachment effect". Phys. Rev. E, 50:4113
129. Luding S, Clément E, Blumen A, Rajchenbach J, Duran J (1994b) The onset of convection in molecular dynamics simulations of grains. Phys. Rev. E, 50:R1762
130. Luding S, Clément E, Blumen A, Rajchenbach J, Duran J (1994a) Studies of columns of beads under external vibrations Phys Rev. E, 49(2):1634
131. Luding S, Clément E, Rajchenbach J, Duran J (1996a) Simulations of pattern formation in vibrated granular media Europhys Lett., 36(41):247-252
132. Luding S, Duran J, Clément E, Rajchenbach J (1996b) Computer simulations and experiments of dry granular media: Polydisperse disks in a vertical pipe. In Proc. of the 5th Chemical Engineering World Congress, San Diego. AIChE
133. Luding S, Duran J, Clément E, Rajchenbach J (1996c) Segregation of particulate solids: Segregation via convection. Pharin. Technol., 20(8):42-44. see also 20(9)
134. Luding S, Duran J, Clément E, Rajchenbach J (1996d) Simulations of dense granular flow: Dynamic arches and spin organization J. Phys. I France, 6:823-836
135. Luding S, Duran J, Mazozi T, Clément E, Rajchenbach J (1996e) Simulations of granular flow: Cracks in a falling sandpile. In Wolf DE, Schreckenberg M, Bachem A, editors, Traffic and Granular Flow, Singapore. World Scientific
136. Luding S, Herrmann HJ, Blumen A ( 1994d) Scaling behavior of 2-dimensional arrays of beads under external vibrations Phys Rev. E, 50:3100
137. Luding S, Matuttis HG (1997) The effect of interaction laws on the stresses in frictionless granular media. In Wolf DE, Grassberger P, editors, Friction, Arching and Contact Dynamics, pages 373-376, Singapore. World Scientific
138. Luding S, Müller M, McNamara S (1998) The validity of "molecular chaos" in granular flows. In Proceedings of the World Congress on Particle Technology. Brighton. Institution of Chemical Engineers, to appear
139. Makse HA, Herrmann HJ (1998) Microscopic model for granular flows of mixtures, submitted
140. Matuttis HG (1998) Simulations of the pressure distribution under a two dimensional sand-pile of polygonal particles. Granular Matter 1(2)
141. Matuttis HG, Luding S (1997) The effect of particle shape and friction on the stresses in heaps of granular media. In Wolf DE, Grassberger P, editors, Friction, Arching and Contact Dynamics, Singapore. World Scientific
142. Maw N, Barber JR, Fawcett JN (1976) The oblique impact of elastic spheres. Wear, 38:101
143. Maw N, Barber JR, Fawcctt JN (1981) The role of elastic tangential compliance in oblique impact. J. Lubrication Tech., 103:74
144. Mazighi R, Bernu B, Delyon F (1994) Steady state of a column of shaked inelastic spheres. Phys. Rev. E, 50:4551
145. McNamara S, Luding S (1998a,b) Energy flows in vibrated granular media. Phys. Rev. E 58: 813-822
146. McNamara S, Luding S (1998b) The ratio of translational to rotational kinetic energy in granular media. Phys. Rev. E, Aug. 1998
147. McNamara S, Young WR (1992) Inelastic collapse and clumping in a one-dimensional granular medium. Phys. Fluids A, 4(3):496
148. McNamara S, Young WR (1993) Kinetics of a one-dimensional granular medium in the quasielastic limit. Phys. Fluids A, 5(1):34
149. McNamara S, Young WR (1996) Dynamics of a freely evolving, two-dimensional granular medium. Phys. Rev. E, 53(5):5089-5100
150. Mehta A, editor (1994) Granular Matter. Springer, Berlin
151. Mehta A, Edwards SF (1989) Statistical mechanics of powder mixtures. Physica A, 157:1091
152. Melo F, Umbanhowar PB, Swinney HL (1994) Transition to parametric wave patterns in a vertically oscillated granular layer. Phys. Rev. Lett., 72(1): 172-175
153. Melo F, Umbanhowar PB, Swinney HL (1995) Hexagons, kinks, and disorder in oscillated granular layers. Phys. Rev. Lett., 75(21):3838-3841
154. Metcalf TH, Knight JB, Jaeger HM (1997) Standing wave patterns in shallow beds of vibrated granular material. Physica A, 236:202-210
155. Michalowski RL (1984) Flow of granular material through a plane hopper. Powder Technol., 39:29
156. Mindlin RD (1949) Compliance of elastic bodies in contact. J. of Appl. Mech., 16:259
157. Mindlin RD, Deresiewicz H ( 1953) Elastic spheres in contact under varying oblique forces. J. of Appl. Mech., 20:327
158. Müller M, Luding S, Herrmann HJ (1997) Simulations of vibrated granular media in 2d and 3d. In Wolf DE, Grassberger P, editors, Friction, Arching and Contact Dynamics, Singapore. World Scientific
159. Ogawa S (1978) Multitemperature theory of granular materials. In Cowin S, Satake M, editors, Proc. of US-Japan Symp. on Continuum Mechanics and Statistical Approaches to the Mechanics of Granular Media, page 208. Fukyu-kai. Gakujutsu Bunken
160. Oron G, Herrmann HJ (1998) Exact calculation offeree networks in granular media. Phys. Rev. E, July 1998
161. Ouaguenouni S, Roux JN (1997) Arching without friction: a simple model. In Wolf DE, Grassberger P, editors, Friction, Arching and Contact Dynamics, Singapore. World Scientific
162. Pak HK, Behringer PR (1994) Bubbling in vertically vibrated granular materials. Nature, 371:231-233
163. Pak HK, Behringer RP (1993) Surface waves in vertically vibrated granular materials. Phys. Rev. Lett., 71(12):1832-1835
164. Pak HK, van Doorn E, Behringer RP (1995) Effects of ambient gases on granular materials under vertical vibration. Phys. Rev. Lett., 74(23):4643-4646
165. Peng G, Herrmann HJ ( 1994) Density waves of granular flow in a pipe using lattice-gas automata. Phys. Rev. E, 49(3): 1796
166. Peng G, Herrmann HJ (1995) Density waves and 1/f density fluctuations in granular flow. Phys. Rev. E. 51(3):1745
167. Peng G, Ohta T (1997b) Velocity and density profiles of granular flow in channels using lattice gas automaton. Phys. Rev. E 55: 6811
168. Peng G, Ohta T (1998) Logarithmic density relaxation in compaction of granular materials. Phys. Rev. E 57: 829
169. Poliakov A, NB, Herrmann HJ (1994) Self-organized criticality in plastic shear bands. Geophys. Res. Lett., 21:2143-2146
170. Poliakov A. NB, Herrmann HJ, Podladchikov YY, Roux S (1994) Fractal plastic shear bands. Fractals, 2:567-581
171. Pöschel T (1993) Granular material flowing down an inclined chute: A molecular dynamics simulation. J. Phys. II, 3:27
172. Pöschel T (1994) Recurrent clogging and density waves in granular material flowing through a narrow pipe. J. Phys. I France,
173. Pöschel T, Buchholtz V (1993) Static friction phenomena in granular materials: Coulomb law vs. particle geometry. Phys. Rev. Lett., 71(24):3963
174. Pöschel T, Buchholtz V (1995a) Complex flow of granular material in a rotating cylinder. Chaos, Solitons, and Fractals, 5:1901
175. Pöschel T, Buchholtz V (1995b) Molecular dynamics of arbitrarily shaped granular particles. J. Phys. I France, 5(11): 1431-1455
176. Pöschel T, Herrmann HJ (1995) Size segregation and convection. Europhys. Lett., 29:123
177. Pöschel T, Rosenkranz DE (1997) Experimental study of horizontally shaken granular matter - the swelling effect. In: Parisi JM et al. (eds) A perspective look at nonlinear media in physics, chemistry, and biology. Springer, pp 96-109
178. Potapov AV, Campbell CS (1996) Propagation of elastic waves in deep vertically shaken particle beds. Phys. Rev. Lett., 77:4760
179. Pouliquen O, Renaut N (1996) Onset of granular flows on an inclined rough bed: dilatancy effects. J. Phys. II. 6: 923-935
180. Raafat T, Hulin JP, Herrmann HJ (1996) Density waves in dry granular media falling through a vertical pipe. Phys. Rev. E, 53:4345-4355
181. Raafat T, Terminassian V, Hulin JP, Herrmann HJ (1997) Pressure analysis for pneumatic instabilities during dry granular flows in vertical pipes, preprint
182. Radjai F, Jean M, Moreau JJ, Roux S (1996) Force distribution in dense two-dimensional granular systems. Phys. Rev. Lett., 77(2):274
183. Radjai F, Schäfer J, Dippel S, Wolf D (1997) Collective friction of an array of particles: A crucial test for numerical algorithms. J. Phys. I France, 7:1053
184. Rajchenbach J (1991) Dilatant process for convective motion in a sand heap. Europhys. Lett., 16(2):149
185. Rapaport DC (1995) The Art of Molecular Dynamics Simulation. Cambridge University Press. Cambridge
186. Rátkai G (1976) Particle flow and mixing in vertically vibrated beds. Powder Technol., 15:187
187. Reynolds O (1885) On the dilatancy of media composed of rigid particles in contact. Philos. Mag. Ser. 5, 50-20:469
188. Ristow GH (1992a) Molecular dynamics simulations of granular materials on the intel ipsc/860. Int. J. of Mod. Phys. C, 3(6): 1281
189. Ristow GH (1992b) Simulating granular flow with molecular dynamics. J. Phys. I, 2(6):649
190. Ristow GH (1994) Granular dynamics: A review about recent molecular dynamics simulations of granular materials. In Stauffer D, editor. Annual Reviews of Computational Physics I, Singapore. World Scientific
191. Ristow GH, Herrmann HJ (1994) Density patterns in two-dimensional hoppers. Phys. Rev. E, 50(1):R5-R8
192. Ristow GH, Herrmann HJ (1995) Forces on the walls and stagnation zones in a hopper filled with granular material. Physica A,
193. Rosato AD, Lan Y (1993) Discrete element modeling of vibrating granular beds. In Thornton C, editor, Powders & Grains 93, page 241, Rotterdam. Balkema
194. Rosato AD, Prinz F, Standburg KJ, , Swendsen R (1986) Monte carlo simulation of paniculate matter segregation Powder Technol., 49:59
195. Rosato AD, Strandburg KJ, Prinz F, Swendsen RH (1987) Why the Brazil nuts are on top: Size segregation of paniculate matter by shaking. Phys. Rev. Lett., 58(10): 1038
196. Savage SB (1979) Gravity flow of cohesionless granular materials in chutes and channels. J. Fluid Mech., 92:53
197. Savage SB (1992) Instability of unbounded uniform granular shear flow. J. Fluid Mech., 241:109
198. Savage SB (1993) Disoder, diffusion, and structure formation in granular flows. In Bideau D, editor, Disorder and granular media, page 264, Amsterdam. North Holland
199. Savage SB (1997) Problems in the statics and dynamics of granular materials. In Behringer RP, Jenkins JT editors Powders & Grains 97, pages 185-194. Balkema, Rotterdam
200. Schäfer J, Dippel S, Wolf DE (1996) Force schemes in simulations of granular materials. J. Phys. I France, 6:5-20
201. Schick K, Verveen A (1974) I// noise with a low frequency white noise limit. Nature, 251:599
202. Shattuck MD, Bizon C, Umbanhowar PB, Swift JB, Swinney HL (1997) 2d vertically vibrated granular media-Experiment and simulation. In Powders & Grains 97, Rotterdam. Balkema
203. Shinbrot T (1997) Competition between randomizing impacts and inelastic collisions in granular pattern formation. Nature 389-574-576
204. Smid J, Novosad J (1981) Pressure distribution under heaped bulk solids. I. Chem. E. Symposium Series, 63 D3/V/1-12
205. Sornette A, Davy P, Sornette D (1991) Growth of fractal fault patterns. Phys. Rev. Lett., 65:2266
206. Taguchi Y (1992) New origin of a convective motion: Elastically induced convection in granular materials. Phys. Rev. Lett.,
207. Taguchi Y, Takayasu H (1995) A set of hard spheres with tangential inelastic collision as a model of granular matter: 1/f fluctuation, non-gaussian distribution, and convective motion, preprint
208. Tanaka T, Yonemura S, Yashi KK, Tsuji Y (1996) Cluster formation and particle-induced instability in gas-solid flows predicted by the dsmc method. JSME Int. Journal B, 39(21):239-245
209. Thompson PA, Grest GS (1991) Granular flow: Friction and the dilatancy transition. Phys. Rev. Lett., 67(13): 1751
210. Thornton C, editor (1993) Powders & Grains 93. Balkema, Rotterdam
211. Thornton C, Randall CW (1988) Applications of theoretical contact mechanics to solid particle system simulation. In Micromechanics of granular media, Amsterdam. Elsevier
212. Tillemans HJ, Herrmann HJ (1995) Simulating deformations of granular solids under shear. Physica A, 217-261-288
213. Ting JM, Corkum BT, Kauffman CR, Greco C (1989) Discrete numerical-model for soil mechanics. J. of Geotech. Eng., 115:379
214. Trollope DH, Burman BC (1980) Physical and numerical experiments with granular wedges. Géotechnique, 30(2):137-157
215. Umbanhowar PB, Melo F, Swinney HL (1996) Localized excitations in a vertically vibrated granular layer. Nature, 382-793-796
216. Vermeer PA (1990) The orientation of shear bands in biaxial tests. Géotechnique, 40:223
217. Vermeer PA, de Borst R (1984) Non-associated plasticity for soil, concrete and rock. Heron, 29:1
218. Vollmar S, Herrmann HJ (1995) Settling of particles studied by a hydrodynamic cellular automaton for granular media. Physica
219. Walker J (1982) When different powders are shaken, they seem to have lives of their own. Sc. American, 247(3)-166
220. Wallon OR (I993a) Numerical simulation of inclined chute flows of monodisperse, inelastic, frictional spheres Mechanics of Materials, 16:239-247
221. Walton OR (1993b) Numerical simulation of inelastic, frictional particle-particle interactions. In Roco MC, editor Paniculate two-phase flow, page 884, Boston. Butterworth-Heinemann
222. Walton OR (1994) Effects of interparticle friction and particle shape on dynamic angles of repose via particle-dynamics simulation In Workshop: Mechanics and Statistical Physics of Paniculate Materials
223. Walton OR, Braun R (1986) Viscosity, granular-temperature, and stress calculations for shearing assemblies of inelastic frictional disks. Journal of Rheology, 30(5):949-980
224. Walton OR, Braun R (1993) Simulation of rotary-drum and repose tests for frictional spheres and rigid sphere clusters In DOE/NSF Workshop on Flow of Particulates and Fluids, pages 1-17
225. Warr S, Hansen JP (1996) Relaxation of local density fluctuations in a fluidized granular medium. Europhys. Lett., 36(8):589-594
226. Warr S, Huntley JM, Jacques G. TH (1995) Fluidization of a two-dimensional granular system: Experimental study and scaling behavior. Phys. Rev. E, 52(5):5583-5595
227. Warr S, Jacques G. TH, Huntley JM (1994) Tracking the translational and rotational motion of granular particles: use of high-speed photography and image processing. Powder Technol., 81:41-56
228. Wassgren CR, Hunt ML, Brennen CE (1997) Investigation f /2 and f /4 waves in granular beds subject to vertical sinusoidal oscillations. In Powders & Grains 97, Rotterdam. Balkema
229. Williams JC (1976) The segregation of paniculate materials: A review. Powder Technol., 15:245
230. Wittmer JP, Gates ME, Claudin P (1997) Stress propagation and arching in static sandpiles J Phys I 7-39-80
231. Wmmer JP, Claudin P, Cates M, Bouchaud JP (1996) An explanation for the central stress minimum in sand piles. Nature, 382:336-338
232. Wolf DE, (1996) Modeling and computer simulation of granular media. In Hoffmann KH, Schreiber M, editors Computational Physics. Springer, Heidelberg
233. Wolf DE, Grassberger P, editors (1997) Friction, Arching and Contact Dynamics. World Scientific, Singapore
234. Zik O, Stavans J, Rabin Y (1992) Mobility of a sphere in vibrated granular media. Europhys. Lett., 17(4)315-319