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All issues Volume 6 / No 4 (2011) Math. Model. Nat. Phenom., 6 4 (2011) 118-150 References
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Issue
Math. Model. Nat. Phenom.
Volume 6, Number 4, 2011
Granular hydrodynamics
Page(s) 118 - 150
DOI https://doi.org/10.1051/mmnp/20116406
Published online 18 July 2011
  1. M. P. Allen, D. J. Tildesley. Computer Simulation of Liquids. Oxford University Press, Oxford, 1987. [Google Scholar]
  2. J. C. Almekinders, C. Jones. Multiple jet electrohydrodynamic spraying and applications. J. Aerosol Sci., 30 (1999), 969–971. [CrossRef] [Google Scholar]
  3. J. Barnes, P. Hut. A hierarchical O(NlogN) force calculation algorithm. Nature, 324 (1986), 446–449. [NASA ADS] [CrossRef] [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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. [CrossRef] [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  11. N. V. Brilliantov, T. Pöschel. Kinetic Theory of Granular Gases. Oxford University Press, Oxford, 2004. [Google Scholar]
  12. N. V. Brilliantov, C. Saluena, T. Schwager, T. Pöschel. Transient structures in a granular gas. Phys. Rev. Let., 93 (2004), No. 13, 134301. [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  15. J. A. Cross. Electrostatics: Principles, Problems and Applications. Adam Hilger, Bristol, 1987. [Google Scholar]
  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. [Google Scholar]
  17. S. M. Dammer, D. E. Wolf. Self-focusing dynamics in monopolarly charged suspensions. Phys. Rev. E, 93 (2004), No. 15, 150602. [Google Scholar]
  18. J. Du. Hydrostatic equilibrium and Tsallis’ equilibrium for self-gravitating systems. Central European Journal of Physics, 3 (2005), No. 3, 376–381. [CrossRef] [Google Scholar]
  19. J. Duran. Sands, Powders and Grains. Springer-Verlag, New York, 2000. [Google Scholar]
  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. [Google Scholar]
  21. M. H. Ernst. Nonlinear model-Boltzmann equations and exact solutions. Physics Reports, 78 (1981), No. 1, 1–171. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  25. S. E. Esipov, T. Pöschel.. The granular phase diagram. J. Stat. Phys., 86 (1997), No. 5/6, 1385–1395. [CrossRef] [Google Scholar]
  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. [Google Scholar]
  27. P. P. Ewald. The calculation of optical and electrostatic grid potential. Ann. d. Physik, 64 (1921), 253–287. [Google Scholar]
  28. K. B. Geerse. Application of Electrospray: from people to plants. Ph.D. thesis, Technische Universiteit Delft, 2003. [Google Scholar]
  29. I. Goldhirsch, G. Zanetti. Clustering instability in dissipative gases. Phys. Rev. Lett., 70 (1993), No. 11, 1619–1622. [NASA ADS] [CrossRef] [PubMed] [Google Scholar]
  30. P. Goldreich. The dynamics of planetary rings. Ann. Rev. Astron. Astrophys., 20 (1982), 249–283. [CrossRef] [Google Scholar]
  31. R. Greenberg, A. Brahic. Planetary Rings. Arizona University Press, Tucson, AZ, 1984. [Google Scholar]
  32. L. Greengard, V. Rokhlin. A fast algorithm for particle simulations. J. of Comp. Phys., 73 (1987), 325–348. [Google Scholar]
  33. P. K. Haff. Grain flow as a fluid-mechanical phenomenon. J. Fluid Mech., 134 (1983), 401–430. [NASA ADS] [CrossRef] [Google Scholar]
  34. J.-P. Hansen, I. R. McDonald. Theory of Simple Liquids. Academic Press Ltd., London, San Diego, 1990. [Google Scholar]
  35. D. Henderson. A simple equation of state for hard discs. Molec. Phys., 30 (1975), No. 3, 971–972. [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  38. L. Hernquist. Hierarchical N-body methods. Comp. Phys. Commun., 48 (1988), 107–115. [Google Scholar]
  39. R. Hoffmann. Modeling and Simulation of an Electrostatic Image Transfer. (Ph.D. thesis) Shaker Verlag, Aachen, 2004. [Google Scholar]
  40. J. S. Høye. Dynamical pair correlations of classical and quantum fluids perturbed with long-range forces. Physica A, 389 (2010), 1380–1390. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  47. J. Lowell, A. C. Rose-Innes. Contact electrification. Adv. in Phys., 29 (1980), No. 6, 947–1023. [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  50. S. Luding. Structure and cluster formation in granular media. Pranama-J. Phys., 64 (2005), No. 6, 893–902. [Google Scholar]
  51. S. Luding. Cohesive frictional powders: Contact models for tension. Granular Matter, 10 (2008), No. 4, 235–246. [Google Scholar]
  52. S. Luding. Towards dense, realistic granular media in 2d. Nonlinearity, 22 (2009), R101–R146. [CrossRef] [Google Scholar]
  53. S. Luding, A. Goldshtein. Collisional cooling with multi-particle interactions. Granular Matter, 5 (2003), No. 3, 159–163. [CrossRef] [Google Scholar]
  54. S. Luding, H. J. Herrmann. Cluster growth in freely cooling granular media. Chaos, 9 (1999), No. 3, 673–681. [NASA ADS] [CrossRef] [PubMed] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  57. S. McNamara. Hydrodynamic modes of a uniform granular medium. Phys. of Fluids A, 5 (1993), 3056–3070. [Google Scholar]
  58. S. McNamara W. R. Young. Dynamics of a freely evolving, two-dimensional granular medium. Phys. Rev. E, 53 (1996), 5089–5100. [CrossRef] [Google Scholar]
  59. S. Miller. Clusterbildung in Granularen Gasen. (in German). Ph.D. thesis, Universität Stuttgart, 2003. [Google Scholar]
  60. S. Miller, S. Luding. Cluster growth in two- and three-dimensional granular gases. Phys. Rev. E, 69 (2004), No. 3, 031305. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  62. M.-K. Müller. Untersuchung von Akkretionsscheiben mit Hilfe der Molekulardynamik. (in German). Diploma thesis, Universität Stuttgart, 2001. [Google Scholar]
  63. M.-K. Müller. Long-Range Interactions In Dilute Granular Systems. Ph.D. thesis, Universiteit Twente/Enschede, 2007. [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  68. E. Németh. Triboelektrische Aufladung von Kunststoffen. (in German). Ph.D. thesis, Technische Universität Bergakademie Freiberg, 2003. [Google Scholar]
  69. F. Niermöller. Ladungsverteilung in Mineralgemischen und elektrostatische Sortierung nach Triboaufladung. (in German). Ph.D. thesis, Technische Universität Clausthal, 1988. [Google Scholar]
  70. J. S. Olafsen, J. S. Urbach. Clustering, order, and collapse in a driven granular monolayer. Phys. Rev. Lett., 81 (1998), 4369. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  72. T. Pöschel S. Luding, editors. Granular Gases, Lecture Notes in Physics 564. Springer, Berlin, 2001. [Google Scholar]
  73. R. Ramírez, T. Pöschel, N. V. Brilliantov, T. Schwager. Coefficient of restitution of colliding viscoelastic spheres. Phys. Rev. E, 60 (1999), 4465–4472. [Google Scholar]
  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] [Google Scholar]
  75. T. N. Scheffler. Kollisionskühlung in elektrisch geladener granularer Materie. (in German). Ph.D. thesis, Gerhard-Mercator-Universität Duisburg, 2000. [Google Scholar]
  76. T. N. Scheffler, D. E. Wolf. Collision rates in charged granular gases. Granular Matter, 4 (2002), No. 3, 103–113. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  78. F. Spahn, J. Schmidt. Saturn’s bared mini-moons. Nature, 440 (2006), 614–615. [CrossRef] [PubMed] [Google Scholar]
  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] [Google Scholar]
  80. U. Trottenberg, C. W. Oosterlee, A. Schüller. Multigrid. Academic Press, San Diego, 2001. [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  83. J. H. Werth, H. Knudsen, H. Hinrichsen. Agglomeration of oppositely charged particles in nonpolar liquids. Phys. Rev. E, 73 (2006), 021402. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  85. D. E. Wolf, T. N. Scheffler, J. Schäfer. Granular flow, collisional cooling and charged grains. Physica A, 274 (1999), 171–181. [CrossRef] [Google Scholar]

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