Free Access
Math. Model. Nat. Phenom.
Volume 6, Number 4, 2011
Granular hydrodynamics
Page(s) 118 - 150
Published online 18 July 2011
  1. M. P. Allen, D. J. Tildesley. Computer Simulation of Liquids. Oxford University Press, Oxford, 1987.
  2. J. C. Almekinders, C. Jones. Multiple jet electrohydrodynamic spraying and applications. J. Aerosol Sci., 30 (1999), 969–971. [CrossRef]
  3. J. Barnes, P. Hut. A hierarchical O(NlogN) force calculation algorithm. Nature, 324 (1986), 446–449. [NASA ADS] [CrossRef]
  4. D. L. Blair, A. Kudrolli. Magnetized granular materials. In H. Hinrichsen and D. Wolf, editors, The Physics of Granular Media., pages 281–296, Weinheim, 2004. Wiley-VCH.
  5. J. Blum, S. Bruns, D. Rademacher, A. Voss, B. Willenberg, M. Krause. Measurement of the translational and rotational Brownian motion of individual particles in a rarefied gas. Phys. Rev. Lett., 97 (2006), 230601. [NASA ADS] [CrossRef] [PubMed]
  6. J. Blum, G. Wurm, S. Kempf, T. Poppe, H. Klahr, T. Kozasa, M. Rott, T. Henning, J. Dorschner, R. Schräpler, H.U. Keller, W.J. Markiewicz, I. Mann, B.A.S. Gustafson, F. Giovane, D. Neuhaus, H. Fechtig, E. Grün, B. Feuerbacher, H. Kochan, L. Ratke, A. El Goresy, G. Morfill, S.J. Weidenschilling, G. Schwehm, K. Metzler, W.-H. Ip. Growth and form of planetary seedlings: Results from a microgravity aggregation experiment. Phys. Rev. Lett., 85 (2000), 2426–2429. [NASA ADS] [CrossRef] [PubMed]
  7. P. Bode, J. P. Ostriker. Tree particle-mesh: An adaptive, efficient, and parallel code of collisionless cosmological simulation. Astrophys. J. Supplem. Series, 145 (2003), No. 1, 1–13. [NASA ADS] [CrossRef]
  8. A. Brahic. Systems of colliding bodies in a gravitational field: I - numerical simulation of the standard model. Astronomy and Astrophysics, 54 (1977), 895–907.
  9. F. G. Bridges, A. Hatzes, D. N. C. Lin. Structure, stability and evolution of Saturn’s rings. Nature, 309 (1984), 333–335. [NASA ADS] [CrossRef]
  10. N. V. Brilliantov, T. Pöschel. Deviation from maxwell distribution in granular gases with constant restitution coefficient. Phys. Rev. E, 61 (2000), 2809–2814. [CrossRef]
  11. N. V. Brilliantov, T. Pöschel. Kinetic Theory of Granular Gases. Oxford University Press, Oxford, 2004.
  12. N. V. Brilliantov, C. Saluena, T. Schwager, T. Pöschel. Transient structures in a granular gas. Phys. Rev. Let., 93 (2004), No. 13, 134301. [CrossRef] [PubMed]
  13. N. V. Brilliantov, F. Spahn, J.-M. Hertzsch, T. Pöschel. A model for collisions in granular gases. Phys. Rev. E, 53 (1996), 5382–5392. [NASA ADS] [CrossRef]
  14. N. F. Carnahan, K. E. Starling. Equation of state for nonattractive rigid spheres. J. Chem. Phys., 51 (1969), No. 2, 635–636. [NASA ADS] [CrossRef]
  15. J. A. Cross. Electrostatics: Principles, Problems and Applications. Adam Hilger, Bristol, 1987.
  16. S. M. Dammer, J. Werth, H. Hinrichsen. Electrostatically charged granular matter. In H. Hinrichsen D. Wolf, editors, The Physics of Granular Media., pages 255–280, Wiley-VCH, Weinheim, 2004.
  17. S. M. Dammer, D. E. Wolf. Self-focusing dynamics in monopolarly charged suspensions. Phys. Rev. E, 93 (2004), No. 15, 150602.
  18. J. Du. Hydrostatic equilibrium and Tsallis’ equilibrium for self-gravitating systems. Central European Journal of Physics, 3 (2005), No. 3, 376–381. [CrossRef]
  19. J. Duran. Sands, Powders and Grains. Springer-Verlag, New York, 2000.
  20. J. W. Eastwood, R. W. Hockney, D. Lawrence. P3M3DP - the 3-dimensional periodic particle-particle-particle-mesh program. Comp. Phys. Commun., 19 (1980), 215–261. [CrossRef]
  21. M. H. Ernst. Nonlinear model-Boltzmann equations and exact solutions. Physics Reports, 78 (1981), No. 1, 1–171. [CrossRef] [MathSciNet]
  22. M. H. Ernst, J. R. Dorfman, W. R. Hoegy, J. M. J. van Leeuwen. Hard-sphere dynamics and binary-collision operators. Physica, 45 (1969), No. 1, 127–146. [CrossRef]
  23. M. H. Ernst, E. Trizac, A. Barrat. The Boltzmann equation for driven systems of inelastic soft spheres. J. Stat. Phys., 124 (2006), No. 2–4, 549–586. [CrossRef] [MathSciNet]
  24. P. Eshuis, K. van der Weele, D. van der Meer, D. Lohse. The granular Leidenfrost effect: Experiment and theory of floating particle clusters. Phys. Rev. E, 95 (2005), 258001.
  25. S. E. Esipov, T. Pöschel.. The granular phase diagram. J. Stat. Phys., 86 (1997), No. 5/6, 1385–1395. [CrossRef]
  26. L. W. Esposito, J. N. Cuzzi, J. B. Holberg, E. A. Marouf, G. L. Tyler, C. C. Porco. Saturn’s rings, structure, dynamics and particle properties. In Saturn, pages 463–545, Tucson, AZ, Univ. of Arizona Press, 1984.
  27. P. P. Ewald. The calculation of optical and electrostatic grid potential. Ann. d. Physik, 64 (1921), 253–287. [CrossRef]
  28. K. B. Geerse. Application of Electrospray: from people to plants. Ph.D. thesis, Technische Universiteit Delft, 2003.
  29. I. Goldhirsch, G. Zanetti. Clustering instability in dissipative gases. Phys. Rev. Lett., 70 (1993), No. 11, 1619–1622. [NASA ADS] [CrossRef] [PubMed]
  30. P. Goldreich. The dynamics of planetary rings. Ann. Rev. Astron. Astrophys., 20 (1982), 249–283. [NASA ADS] [CrossRef]
  31. R. Greenberg, A. Brahic. Planetary Rings. Arizona University Press, Tucson, AZ, 1984.
  32. L. Greengard, V. Rokhlin. A fast algorithm for particle simulations. J. of Comp. Phys., 73 (1987), 325–348. [NASA ADS] [CrossRef] [MathSciNet] [PubMed]
  33. P. K. Haff. Grain flow as a fluid-mechanical phenomenon. J. Fluid Mech., 134 (1983), 401–430. [NASA ADS] [CrossRef]
  34. J.-P. Hansen, I. R. McDonald. Theory of Simple Liquids. Academic Press Ltd., London, San Diego, 1990.
  35. D. Henderson. A simple equation of state for hard discs. Molec. Phys., 30 (1975), No. 3, 971–972. [CrossRef]
  36. O. Herbst, R. Cafiero, A. Zippelius, H. J. Herrmann, S. Luding. A driven two-dimensional granular gas with coulomb friction. Phys. of Fluids, 17 (2005), No. 10, 107102. [CrossRef] [MathSciNet]
  37. O. Herbst, P. Müller, A. Zippelius. Local heat flux and energy loss in a two-dimensional vibrated granular gas. Phys. Rev. E, 72 (2005) No. 4, 041303. [CrossRef]
  38. L. Hernquist. Hierarchical N-body methods. Comp. Phys. Commun., 48 (1988), 107–115. [CrossRef]
  39. R. Hoffmann. Modeling and Simulation of an Electrostatic Image Transfer. (Ph.D. thesis) Shaker Verlag, Aachen, 2004.
  40. J. S. Høye. Dynamical pair correlations of classical and quantum fluids perturbed with long-range forces. Physica A, 389 (2010), 1380–1390. [CrossRef]
  41. M. Huthmann, A. Zippelius. Dynamics of inelastically colliding rough spheres: Relaxation of translational and rotational energy. Phys. Rev. E, 56 (1997), No. 6, R6275–R6278. [CrossRef]
  42. W. Kleber,. A. Lang. Triboelectrically charged powder coatings generated by running through holes and slits. J. of Electrostatics, 40&41 (1997), 237–240. [CrossRef]
  43. M. Krause, J. Blum. Growth and form of planetary seedlings: Results from a sounding rocket microgravity aggregation experiment. Phys. Rev. Lett., 93 (2004), 021103. [NASA ADS] [CrossRef] [MathSciNet] [PubMed]
  44. C. W. J. Lemmens. An Investigation, Implementation and Comparison of 3 important Particle Simulation Techniques: PP: Particle-Particle PM: Particle-Mesh TC: Tree-Code. Report 97-46, Faculty of Technical Mathematics and Informatics, Delft, 1997.
  45. M. Linsenbühler, J. H. Werth, S. M. Dammer, H. A. Knudsen, H. Hinrichsen, K.-E. Wirth, D. E. Wolf. Cluster size distribution of charged nanopowders in suspensions. Powder Technology, 167 (2006), No. 3, 124–133. [CrossRef]
  46. D. Lohse, R. Bergmann, R. Mikkelsen, C. Zeilstra, D. van der Meer, M. Versluis, K. van der Weele, M. van der Hoef, H. Kuipers. Impact on soft sand: Void collapse and jet formation. Phys. Rev. Let., 93 (2004), No. 19, 198003. [NASA ADS] [CrossRef]
  47. J. Lowell, A. C. Rose-Innes. Contact electrification. Adv. in Phys., 29 (1980), No. 6, 947–1023. [NASA ADS] [CrossRef]
  48. S. Luding. Clustering instabilities, arching, and anomalous interaction probabilities as examples for cooperative phenomena in dry granular media. T.A.S.K. Quarterly, Scientific Bulletin of Academic Computer Centre of the Technical University of Gdansk., 2 (1998), No. 3, 417–443.
  49. S. Luding. Collisions & contacts between two particles. In H. J. Herrmann, J.-P. Hovi, S. Luding, editors, Physics of dry granular media - NATO ASI Series E350, page 285, Dordrecht, 1998. Kluwer Academic Publishers.
  50. S. Luding. Structure and cluster formation in granular media. Pranama-J. Phys., 64 (2005), No. 6, 893–902. [CrossRef]
  51. S. Luding. Cohesive frictional powders: Contact models for tension. Granular Matter, 10 (2008), No. 4, 235–246. [CrossRef]
  52. S. Luding. Towards dense, realistic granular media in 2d. Nonlinearity, 22 (2009), R101–R146. [CrossRef]
  53. S. Luding, A. Goldshtein. Collisional cooling with multi-particle interactions. Granular Matter, 5 (2003), No. 3, 159–163. [CrossRef]
  54. S. Luding, H. J. Herrmann. Cluster growth in freely cooling granular media. Chaos, 9 (1999), No. 3, 673–681. [NASA ADS] [CrossRef] [PubMed]
  55. S. Luding, M. Huthmann, S. McNamara, A. Zippelius. Homogeneous cooling of rough, dissipative particles: Theory and simulations. Phys. Rev. E, 58 (1998), 3416–3425. [CrossRef]
  56. S. Luding, S. McNamara. How to handle the inelastic collapse of a dissipative hard-sphere gas with the TC model. Granular Matter, 1 (1998), No. 3, 113–128. [CrossRef]
  57. S. McNamara. Hydrodynamic modes of a uniform granular medium. Phys. of Fluids A, 5 (1993), 3056–3070. [NASA ADS] [CrossRef] [MathSciNet]
  58. S. McNamara W. R. Young. Dynamics of a freely evolving, two-dimensional granular medium. Phys. Rev. E, 53 (1996), 5089–5100. [CrossRef]
  59. S. Miller. Clusterbildung in Granularen Gasen. (in German). Ph.D. thesis, Universität Stuttgart, 2003.
  60. S. Miller, S. Luding. Cluster growth in two- and three-dimensional granular gases. Phys. Rev. E, 69 (2004), No. 3, 031305. [CrossRef]
  61. J. M. Montanero, V. Garzò, M. Alam, S. Luding. Rheology of 2d and 3d granular mixtures under uniform shear flow: Enskog kinetic theory versus molecular dynamics simulations. Granular Matter, 8 (2006), No. 2, 103–115. [CrossRef]
  62. M.-K. Müller. Untersuchung von Akkretionsscheiben mit Hilfe der Molekulardynamik. (in German). Diploma thesis, Universität Stuttgart, 2001.
  63. M.-K. Müller. Long-Range Interactions In Dilute Granular Systems. Ph.D. thesis, Universiteit Twente/Enschede, 2007.
  64. M.-K. Müller, S. Luding. Long-range interactions in ring-shaped particle aggregates. In R. García-Rojo, H.J. Herrmann, S. McNamara, editors, Powders & Grains, pages 1119–1122, Balkema, Leiden, 2005.
  65. M.-K. Müller, S. Luding. Homogeneous cooling with repulsive and attractive long-range interactions. In M. Nakagawa S. Luding, editors, Powders & Grains, pages 697–700, AIP Conf. Procs. #1145, 2009.
  66. M.-K. Müller, T. Winkels, K.B. Geerse, J.C.M. Marijnissen, A. Schmidt-Ott, S. Luding. Experiment and simulation of charged particle sprays. In Proceedings PARTEC 2004, Nuremberg, 2004.
  67. B. Muth, M.-K. Müller, P. Eberhard, S. Luding. Contacts between many bodies. In W. Kurnik, editor, Machine Dynamics Problems, pages 101–114, Warsaw, 2004.
  68. E. Németh. Triboelektrische Aufladung von Kunststoffen. (in German). Ph.D. thesis, Technische Universität Bergakademie Freiberg, 2003.
  69. F. Niermöller. Ladungsverteilung in Mineralgemischen und elektrostatische Sortierung nach Triboaufladung. (in German). Ph.D. thesis, Technische Universität Clausthal, 1988.
  70. J. S. Olafsen, J. S. Urbach. Clustering, order, and collapse in a driven granular monolayer. Phys. Rev. Lett., 81 (1998), 4369. [CrossRef]
  71. J. A. G. Orza, R. Brito, T. P. C. van Noije, M. H. Ernst. Patterns and long range correlations in idealized granular flows. Int. J. of Mod. Phys. C, 8 (1997), No. 4, 953–965. [CrossRef]
  72. T. Pöschel S. Luding, editors. Granular Gases, Lecture Notes in Physics 564. Springer, Berlin, 2001.
  73. R. Ramírez, T. Pöschel, N. V. Brilliantov, T. Schwager. Coefficient of restitution of colliding viscoelastic spheres. Phys. Rev. E, 60 (1999), 4465–4472. [CrossRef]
  74. F. H. Ree, W. G. Hoover. Fifth and sixth virial coefficients for hard spheres and hard disks. J. Chem. Phys., 40 (1964), No. 4, 939–950. [CrossRef] [MathSciNet]
  75. T. N. Scheffler. Kollisionskühlung in elektrisch geladener granularer Materie. (in German). Ph.D. thesis, Gerhard-Mercator-Universität Duisburg, 2000.
  76. T. N. Scheffler, D. E. Wolf. Collision rates in charged granular gases. Granular Matter, 4 (2002), No. 3, 103–113. [CrossRef]
  77. T. Schwager, T. Pëoschel. Coefficient of restitution of viscous particles and cooling rate of granular gases. Phys. Rev. E, 57 (1998), 650–654. [CrossRef]
  78. F. Spahn, J. Schmidt. Saturn’s bared mini-moons. Nature, 440 (2006), 614–615. [CrossRef] [PubMed]
  79. V. Springel, S. D. M. White, A. Jenkins, C. S. Frenk, N. Yoshida, L. Gao, J. Navarro, R. Thacker, D. Croton, J. Helly, J. A. Peacock, S. Cole, P. Thomas, H. Couchman, A. Evrard, J. Colberg, F. Pearce. Simulating the joint evolution of quasars, galaxies and their large-scale distribution. Nature, 435 (2005), 629–636. [NASA ADS] [CrossRef] [PubMed]
  80. U. Trottenberg, C. W. Oosterlee, A. Schüller. Multigrid. Academic Press, San Diego, 2001.
  81. T. P. C. van Noije, M. H. Ernst, R. Brito. Ring kinetic theory for an idealized granular gas. Physica A, 251 (1998), 266–283. [NASA ADS] [CrossRef]
  82. J. H. Werth, S. M. Dammer, Z. Farkas, H. Hinrichsen, D. E. Wolf. Agglomeration in charged suspensions. Computer Physics Communications, 147 (2002), 259–262. [CrossRef]
  83. J. H. Werth, H. Knudsen, H. Hinrichsen. Agglomeration of oppositely charged particles in nonpolar liquids. Phys. Rev. E, 73 (2006), 021402. [CrossRef]
  84. J. H. Werth, M. Linsenbuhler, S. M. Dammer, Z. Farkas, H. Hinrichsen, K.-E. Wirth, D. E. Wolf. Agglomeration of charged nanopowders in suspensions. Powder Technology, 133 (2003), 106–112. [CrossRef]
  85. D. E. Wolf, T. N. Scheffler, J. Schäfer. Granular flow, collisional cooling and charged grains. Physica A, 274 (1999), 171–181. [CrossRef]

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