Numerical study of the force network ensemble

Molecular Simulation

Volumn 35, Issue 14, 2009, Pages 1168-1184

  Van Eerd, A R T ^a   Tighe, B P ^b   Vlugt, T J H ^c  

^a UTRECHT UNIVERSITY   (Netherlands)

^b UNIVERSITEIT LEIDEN   (Netherlands)

^c DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Force network ensemble; Granular materials; Monte Carlo simulation

Indexed keywords

CONTACT FORCE DISTRIBUTION; CONTACT FORCES; FINITE SIZE EFFECT; FORCE NETWORK ENSEMBLE; FORCE NETWORKS; GRANULAR MATTER; GRANULAR SOLIDS; MONTE CARLO SIMULATION; NEW APPROACHES; NUMERICAL STUDIES; STATIC GRANULAR MATERIALS;

GRANULAR MATERIALS; MONTE CARLO METHODS; PRESSURE DISTRIBUTION; RAILROAD ROLLING STOCK; SIMULATORS;

PROBABILITY DISTRIBUTIONS;

EID: 70449096471     PISSN: 08927022     EISSN: 10290435     Source Type: Journal    
DOI: 10.1080/08927020903015361     Document Type: Article

References (55)

1. L.K.A. Dorren, A review of rockfall mechanics and modelling approaches, Prog. Phys. Geogr. 27 (2003), pp. 69-87.
2. S. De Toni and P. Scotton, Two-dimensional mathematical and numerical model for the dynamics of granular avalanches, Cold Regions Sci. Technol. 43 (2005), pp. 36-48.
3. W.R. Ketterhagen, J.S. Curtis, C.R. Wassgren, and B.C. Hancock, Modeling granular segregation in flow from quasi-three-dimensional, wedge-shaped hoppers, Powder Technol. 179 (2008), pp. 126-143.
4. F.Y. Fraige, P.A. Langston, and G.Z. Chen, Distinct element modelling of cubic particle packing and flow, Powder Technol. 186 (2008), pp. 224-240.
5. E. DesRosiers Lachiver, N. Abatzoglou, L. Cartilier, and J.S. Simard, Agglomeration tendency in dry pharmaceutical granular systems, Eur. J. Pharm. Biopharm. 64 (2006), pp. 193-199.
6. K. Lee, T. Kim, P. Rajniak, and T. Matsoukas, Compositional distributions in multicomponent aggregation, Chem. Eng. Sci. 63 (2008), pp. 1293-1303.
7. M. van Hecke, Shape matters, Science 317 (2007), pp. 49-50.
8. M. van Hecke, Granular matter: a tale of tails, Science 435 (2005), pp. 1041-1042.
9. H.P. Zhu, Z.Y. Zhou, R.Y. Yang, and A.B. Yu, Discrete particle simulation of particulate systems: theoretical developments, Chem. Eng. Sci. 62 (2007), pp. 3378-3396.
10. H.M. Jaeger, S.R. Nagel, and R.P. Behringer, Granular solids, liquids, and gases, Rev. Mod. Phys. 68 (1996), pp. 1259-1273.
11. C.-h. Liu, A.R. Nagel, D.A. Schecter, S.N. Coppersmith, S. Majumdar, O. Narayan, and T.A. Witten, Force fluctuations in bead packs, Science 269 (1995), pp. 513-515.
12. D.M. Mueth, H.M. Jaeger, and S.R. Nagel, Force distribution in a granular medium, Phys. Rev. E 57 (1998), pp. 3164-3169.
13. D.L. Blair, N.W. Mueggenburg, A.H. Marshall, H.M. Jaeger, and S.R. Nagel, Force distributions in three-dimensional granular assemblies: effects of packing order and interparticle friction, Phys. Rev. E 63 (2001), 041304.
14. J.M. Erikson, N.W. Mueggenburg, H.M. Jaeger, and S.R. Nagel, Force distributions in three-dimensional compressible granular packs, Phys. Rev. E 66 (2002), 040301.
15. G. Løvoll, K.J. Maløy, and E.G. Flekkøy, Force measurements on static granular materials, Phys. Rev. E 60 (1999), pp. 5872-5878.
16. T.S. Majmudar and R.P. Behringer, Contact force measurements and stress-induced anisotropy in granular materials, Nature 435 (2005), pp. 1079-1082.
17. N.P. Kruyt and L. Rothenburg, Probability density functions of contact forces for cohesionless frictional granular materials, Int. J. Solids Struct. 39 (2002), pp. 571-583.
18. P.T. Metzger, Granular contact force density of states and entropy in a modified Edwards ensemble, Phys. Rev. E 70 (2004), 051303.
19. P.T. Metzger, H theorem for contact forces in granular materials, Phys. Rev. E 77 (2008), 011307.
20. P.T. Metzger and C.M. Donahue, Elegance of disordered granular packings: a validation of Edward's hypothesis, Phys. Rev. Lett. 94 (2005), 148001.
21. A.H.W. Ngan, Mechanical analog of temperature for the description of force distribution in static granular packings, Phys. Rev. E 68 (2003), 011301.
22. S. Henkes, C.S. O'Hern, and B. Chakraborty, Entropy and temperature of a static granular assembly: an ab initio approach, Phys. Rev. Lett. 99 (2007), 038002.
23. H.A. Makse, D.L. Johnson, and L.M. Schwartz, Packing of compressible granular materials, Phys. Rev. Lett. 84 (2000), pp. 4160-4163.
24. F. Radjai, M. Jean, J.J. Moreau, and S. Roux, Force distributions in dense two-dimensional granular systems, Phys. Rev. Lett. 77 (1996), pp. 274-277.
25. C.S. O'Hern, S.A. Langer, A.J. Liu, and S.R. Nagel, Force distributions near jamming and glass transitions, Phys. Rev. Lett. 86 (2001), pp. 111-114.
26. C.S. O'Hern, L.E. Silbert, A.J. Liu, and S.R. Nagel, Jamming at zero temperature and zero applied stress: the epitome of disorder, Phys. Rev. E 68 (2003), 011306.
27. L.E. Silbert, G.S. Grest, and J.W. Landry, Statistics of the contact network in frictional and frictionless granular matter, Phys. Rev. E 66 (2002), 061303.
28. J.H. Snoeijer, T.J.H. Vlugt, M. van Hecke, and W. van Saarloos, Force network ensemble: a new approach to static granular matter, Phys. Rev. Lett. 92 (2004), 054302.
29. J.H. Snoeijer, T.J.H. Vlugt, W.G. Ellenbroek, M. van Hecke, and J.M.J. van Leeuwen, Ensemble theory for force networks in hyperstatic granular matter, Phys. Rev. E 70 (2004), 061306.
30. S.F. Edwards and R.B.S. Oakeshott, Theory of powders, Physica A 157 (1989), pp. 1080-1090.
31. T. Unger, J. Kertész, and D.E. Wolf, Force indeterminacy in the jammed state of hard disks, Phys. Rev. Lett. 94 (2005), 178001.
32. B.P. Tighe, J.E.S. Socolar, D.G. Schaeffer, W.G. Mitchener, and M.L. Huber, Force distributions in a triangular lattice of rigid bars, Phys. Rev. E 72 (2005), 031306.
33. S. Ostojic and D. Panja, Elasticity from the force network ensemble in granular media, Phys. Rev. Lett. 97 (2006), 208001.
34. S. McNamara and H. Herrmann, Measurement of indeterminacy in packings of perfectly rigid disks, Phys. Rev. E 70 (2004), 061303.
35. J.H. Snoeijer, W.G. Ellenbroek, T.J.H. Vlugt, and M. van Hecke, Sheared force-networks: anisotropies, yielding and geometry, Phys. Rev. Lett. 96 (2006), 098001.
36. S. Ostojic, E. Somfai, and B. Nienhuis, Scale invariance and universality of force networks in static granular matter, Nature 439 (2006), pp. 828-830.
37. S.Ostojic, Statisticalmechanics of static granularmatter, Ph.D. thesis, University of Amsterdam, Amsterdam, The Netherlands, 2006.
38. T.J.H. Vlugt and A.R.T. van Eerd, Krachtenbalans op zandkorrels, Vakidioot, Studievereniging A-Eskwadraat 1 (2005), pp. 19-23.
39. A.R.T. van Eerd, W.G. Ellenbroek, M. van Hecke, J.H. Snoeijer, and T.J.H. Vlugt, The tail of the contact force distribution in static granular materials, Phys. Rev. E 75 (2007), 060302 (R).
40. B.P. Tighe, A.R.T. van Eerd, and T.J.H. Vlugt, Entropy maximization in the force network ensemble for granular solids, Phys. Rev. Lett. 100 (2008), 238001.
41. J.H. Snoeijer, Statistics of force networks in granular media, Ph.D. thesis, Leiden University, Leiden, The Netherlands, 2003.
42. W.H. Press, S.A. Teukolsky, W.T. Vertterling, and B.P. Flannery, Numerical Recipes in Fortran 77: The Art of Scientific Computing, 2nd ed., Cambridge University Press, Cambridge, 1992.
43. M.P. Allen and D.J. Tildesley, Computer Simulations of Liquids, Oxford University Press, Oxford, 1987.
44. S. Ostojic, T.J.H. Vlugt, and B. Nienhuis, Universal anisotropy in force networks under shear, Phys. Rev. E 45 (2007), 030301 (R).
45. D. Frenkel and B. Smit, Understanding Molecular Simulation: From Algorithms to Applications, 2nd ed., Academic Press, San Diego, 2002.
46. G.M. Torrie and J.P. Valleau, Nonphysical sampling distributions in Monte Carlo free-energy estimation: umbrella sampling, J. Comp. Phys. 23 (1977), pp. 187-199.
47. A.R.T. van Eerd, Statistics of large contact forces in granular matter, Ph.D. thesis, Utrecht University, Utrecht, The Netherlands, 2008.
48. W.G. Ellenbroek and J.H. Snoeijer, Bounds on the yield stress of cohesionless granular matter, J. Stat. Mech. (2007), P01023.
49. F. Wang and D.P. Landau, Efficient, multiple-range random walk algorithm to calculate the density of states, Phys. Rev. Lett. 86 (2001), pp. 2050-2053.
50. F. Wang and D.P. Landau, Determining the density of states for classical statistical models; A random walk algorithm to produce a flat histogram, Phys. Rev. E 64 (2001), p. 56101.
51. E.I. Corwin, H.M. Jaeger, and S.R. Nagel, Structural signature of jamming in granular media, Nature 435 (2005), pp. 1075-1078.
52. J. Brujić, S.F. Edwards, I. Hopkinson, and H.A. Makse, Measuring the distribution of interdroplet forces in a compressed emulsion system, Physica A 327 (2003), p. 201.
53. J. Zhou, S. Long, Q. Wang, and A.D. Dinsmore, Measurement of forces inside a three-dimensional pile of frictionless droplets, Science 312 (2006), pp. 1631-1633.
54. J.D. Weeks, D. Chandler, and H.C. Andersen, Role of repulsive forces in determining the equilibrium structure of simple liquids, J. Chem. Phys. 54 (1971), pp. 5237-5247.
55. C.S. O'Hern, S.A. Langer, A.J. Liu, and S.R. Nagel, Random packings of frictionless particles, Phys. Rev. Lett. 88 (2002), 075507.