메뉴 건너뛰기




Volumn 17, Issue 10, 2005, Pages

A driven two-dimensional granular gas with Coulomb friction

Author keywords

Flow simulation; Friction; Granular flow

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; DEGREES OF FREEDOM (MECHANICS); FLOW OF FLUIDS; FRICTION; MATHEMATICAL MODELS;

EID: 33645741245     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2049277     Document Type: Article
Times cited : (39)

References (55)
  • 1
    • 0003765549 scopus 로고    scopus 로고
    • H.J. Herrmann, J.-P. Hovi, and S. Luding edited by (Kluwer Academic, Dordrecht)
    • Physics of Dry Granular Media - NATO ASI Series E350, edited by H. J. Herrmann, J.-P. Hovi, and S. Luding (Kluwer Academic, Dordrecht, 1998).
    • (1998) Physics of Dry Granular Media - NATO ASI Series E350
  • 2
    • 0003847914 scopus 로고    scopus 로고
    • P.A. Vermeer, S. Diebels, W. Ehlers, H.J. Herrmann, S. Luding, and E. Ramm Lecture notes in Physics 568, edited by (Springer, Berlin)
    • Continuous and Discontinuous Modelling of Cohesive Frictional Materials, Lecture notes in Physics 568, edited by P. A. Vermeer, S. Diebels, W. Ehlers, H. J. Herrmann, S. Luding, and E. Ramm (Springer, Berlin, 2001).
    • (2001) Continuous and Discontinuous Modelling of Cohesive Frictional Materials
  • 3
    • 2542495103 scopus 로고    scopus 로고
    • edited by Y. Kishino (Balkema, Rotterdam)
    • Powders & Grains 2001, edited by Y. Kishino (Balkema, Rotterdam, 2001).
    • (2001) Powders & Grains 2001
  • 4
    • 12144281707 scopus 로고    scopus 로고
    • T. Pöschel, and N.V. Brilliantov edited by (Springer, Berlin)
    • Granular Gas Dynamics, edited by T. Pöschel and N. V. Brilliantov (Springer, Berlin, 2003).
    • (2003) Granular Gas Dynamics
  • 5
    • 0001142863 scopus 로고
    • "Kinetic theory for plane shear flows of a dense gas of identical, rough, inelastic, circular disks"
    • pfl PFLDAS 0031-9171 10.1063/1.865302
    • J. T. Jenkins and M. W. Richman, "Kinetic theory for plane shear flows of a dense gas of identical, rough, inelastic, circular disks," Phys. Fluids 28, 3485 (1985). pfl PFLDAS 0031-9171 10.1063/ 1.865302
    • (1985) Phys. Fluids , vol.28 , pp. 3485
    • Jenkins, J.T.1    Richman, M.W.2
  • 6
    • 84983709074 scopus 로고
    • "A simple kinetic theory for granular flow of rough, inelastic, spherical particles"
    • jah JAMCAV 0021-8936
    • C. K. K. Lun and S. B. Savage, "A simple kinetic theory for granular flow of rough, inelastic, spherical particles," J. Appl. Mech. 54, 47 (1987). jah JAMCAV 0021-8936
    • (1987) J. Appl. Mech. , vol.54 , pp. 47
    • Lun, C.K.K.1    Savage, S.B.2
  • 7
    • 0026392047 scopus 로고
    • "Kinetic theory for granular flow of dense, slightly inelastic, slightly rough spheres"
    • jfl JFLSA7 0022-1120
    • C. K. K. Lun, "Kinetic theory for granular flow of dense, slightly inelastic, slightly rough spheres," J. Fluid Mech. 233, 539 (1991). jfl JFLSA7 0022-1120
    • (1991) J. Fluid Mech. , vol.233 , pp. 539
    • Lun, C.K.K.1
  • 8
    • 0028992020 scopus 로고
    • "Mechanics of collisional motion of granular materials. Part 1. General hydrodynamic equations"
    • jfl JFLSA7 0022-1120
    • A. Goldshtein and M. Shapiro, "Mechanics of collisional motion of granular materials. Part 1. General hydrodynamic equations," J. Fluid Mech. 282, 75 (1995). jfl JFLSA7 0022-1120
    • (1995) J. Fluid Mech. , vol.282 , pp. 75
    • Goldshtein, A.1    Shapiro, M.2
  • 9
    • 0001382425 scopus 로고    scopus 로고
    • "On the flux of fluctuation energy in a collisional grain flow at a flat, frictional wall"
    • phf PHFLE6 1070-6631 10.1063/1.869396
    • J. T. Jenkins and M. Y. Louge, "On the flux of fluctuation energy in a collisional grain flow at a flat, frictional wall," Phys. Fluids 9, 2835 (1997). phf PHFLE6 1070-6631 10.1063/1.869396
    • (1997) Phys. Fluids , vol.9 , pp. 2835
    • Jenkins, J.T.1    Louge, M.Y.2
  • 10
    • 0000365265 scopus 로고    scopus 로고
    • "Dynamics of inelastically colliding rough spheres: Relaxation of translational and rotational energy"
    • pre PLEEE8 1063-651X 10.1103/PhysRevE.56.R6275
    • M. Huthmann and A. Zippelius, "Dynamics of inelastically colliding rough spheres: Relaxation of translational and rotational energy," Phys. Rev. E 56, R6275 (1997). pre PLEEE8 1063-651X 10.1103/ PhysRevE.56.R6275
    • (1997) Phys. Rev. E , vol.56
    • Huthmann, M.1    Zippelius, A.2
  • 11
    • 0032340997 scopus 로고    scopus 로고
    • "Velocity distributions in homogeneous granular fluids: The free and the heated case"
    • 8wa GRMAFE 1434-5021 10.1007/s100350050009
    • T. P. C. van Noije and M. H. Ernst, "Velocity distributions in homogeneous granular fluids: The free and the heated case," Granular Matter 1, 57 (1998). 8wa GRMAFE 1434-5021 10.1007/s100350050009
    • (1998) Granular Matter , vol.1 , pp. 57
    • van Noije, T.P.C.1    Ernst, M.H.2
  • 12
    • 0001398820 scopus 로고    scopus 로고
    • "Randomly driven granular fluids: Large scale structure"
    • pre PLEEE8 1063-651X 10.1103/PhysRevE.59.4326
    • T. P. C. van Noije, M. H. Ernst, E. Trizac, and I. Pagonabarraga, "Randomly driven granular fluids: Large scale structure," Phys. Rev. E 59, 4326 (1999). pre PLEEE8 1063-651X 10.1103/ PhysRevE.59.4326
    • (1999) Phys. Rev. E , vol.59 , pp. 4326
    • van Noije, T.P.C.1    Ernst, M.H.2    Trizac, E.3    Pagonabarraga, I.4
  • 13
    • 0034366837 scopus 로고    scopus 로고
    • "Dynamics of inelastically colliding spheres with Coulomb friction: Relaxation of translational and rotational energy"
    • 8wa GRMAFE 1434-5021
    • O. Herbst, M. Huthmann, and A. Zippelius, "Dynamics of inelastically colliding spheres with Coulomb friction: Relaxation of translational and rotational energy," Granular Matter 2, 211 (2000). 8wa GRMAFE 1434-5021
    • (2000) Granular Matter , vol.2 , pp. 211
    • Herbst, O.1    Huthmann, M.2    Zippelius, A.3
  • 14
    • 0036504172 scopus 로고    scopus 로고
    • "Kinetic theory for identical, frictional, nearly elastic spheres"
    • phf PHFLE6 1070-6631 10.1063/1.1449466
    • J. T. Jenkins and C. Zhang, "Kinetic theory for identical, frictional, nearly elastic spheres," Phys. Fluids 14, 1228 (2002). phf PHFLE6 1070-6631 10.1063/1.1449466
    • (2002) Phys. Fluids , vol.14 , pp. 1228
    • Jenkins, J.T.1    Zhang, C.2
  • 15
    • 12144281707 scopus 로고    scopus 로고
    • "Driven granular gases"
    • edited by T. Pöschel and N. V. Brilliantov (Springer, Berlin)
    • S. Luding, "Driven granular gases," in Granular Gas Dynamics, edited by T. Pöschel and N. V. Brilliantov (Springer, Berlin, 2003), pp. 293-316.
    • (2003) Granular Gas Dynamics , pp. 293-316
    • Luding, S.1
  • 16
    • 33645732648 scopus 로고    scopus 로고
    • "Weakly frictional granular gases"
    • edited by S. P. Hoogendoom, S. Luding, P. H. L. Bovy, M. Schreckenberg and D. E. Wolf (Springer, Berlin Heidelberg) I. Goldhirsch, S. H. Noskowicz, and O. Bar-Lev, "Nearly smooth granular gases," Phys. Rev. Lett. 95, 068002 (2005)
    • Goldhirsch, S. H. Noskowicz, and O. Bar-Lev "Weakly frictional granular gases", in Traffic and Granular Flow '03, edited by S. P. Hoogendoom, S. Luding, P. H. L. Bovy, M. Schreckenberg and D. E. Wolf (Springer, Berlin Heidelberg 2005), pp. 459-473; I. Goldhirsch, S. H. Noskowicz, and O. Bar-Lev, "Nearly smooth granular gases," Phys. Rev. Lett. 95, 068002 (2005)
    • (2005) Traffic and Granular Flow '03 , pp. 459-473
    • Goldhirsch, I.1    Noskowicz, S.H.2    Bar-Lev, O.3
  • 17
    • 0022138225 scopus 로고
    • "Viscosity, granular-temperature, and stress calculations for shearing assemblies of inelastic, frictional disks"
    • jor JORHD2 0148-6055 10.1122/1.549893
    • O. R. Walton and R. L. Braun, "Viscosity, granular-temperature, and stress calculations for shearing assemblies of inelastic, frictional disks," J. Rheol. 30, 949 (1986). jor JORHD2 0148-6055 10.1122/ 1.549893
    • (1986) J. Rheol. , vol.30 , pp. 949
    • Walton, O.R.1    Braun, R.L.2
  • 18
    • 0025000507 scopus 로고
    • "Rapid granular flows"
    • arf ARVFA3 0066-4189 10.1146/annurev.fluid.22.1.57
    • C. S. Campbell, "Rapid granular flows," Annu. Rev. Fluid Mech. 22, 57 (1990). arf ARVFA3 0066-4189 10.1146/annurev.fluid.22.1.57
    • (1990) Annu. Rev. Fluid Mech. , vol.22 , pp. 57
    • Campbell, C.S.1
  • 19
    • 0028056058 scopus 로고
    • "Computer simulations of rapid granular flows of spheres interacting with a flat, frictional boundary"
    • phf PHFLE6 1070-6631 10.1063/1.868178
    • M. Y. Louge, "Computer simulations of rapid granular flows of spheres interacting with a flat, frictional boundary," Phys. Fluids 6, 2253 (1994). phf PHFLE6 1070-6631 10.1063/1.868178
    • (1994) Phys. Fluids , vol.6 , pp. 2253
    • Louge, M.Y.1
  • 20
    • 0000209370 scopus 로고
    • "Granular materials under vibration: Simulations of rotating spheres"
    • pre PLEEE8 1063-651X 10.1103/PhysRevE.52.4442
    • S. Luding, "Granular materials under vibration: Simulations of rotating spheres," Phys. Rev. E 52, 4442 (1995). pre PLEEE8 1063-651X 10.1103/PhysRevE.52.4442
    • (1995) Phys. Rev. E , vol.52 , pp. 4442
    • Luding, S.1
  • 21
    • 0001386809 scopus 로고    scopus 로고
    • "Homogeneous cooling of rough dissipative particles: Theory and simulations"
    • pre PLEEE8 1063-651X 10.1103/PhysRevE.58.3416
    • S. Luding, M. Huthmann, S. McNamara, and A. Zippelius, "Homogeneous cooling of rough dissipative particles: Theory and simulations," Phys. Rev. E 58, 3416 (1998). pre PLEEE8 1063-651X 10.1103/ PhysRevE.58.3416
    • (1998) Phys. Rev. E , vol.58 , pp. 3416
    • Luding, S.1    Huthmann, M.2    McNamara, S.3    Zippelius, A.4
  • 22
    • 0001122756 scopus 로고    scopus 로고
    • "Energy nonequipartition in systems of inelastic, rough spheres"
    • pre PLEEE8 1063-651X 10.1103/PhysRevE.58.2247
    • S. McNamara and S. Luding, "Energy nonequipartition in systems of inelastic, rough spheres," Phys. Rev. E 58, 2247 (1998). pre PLEEE8 1063-651X 10.1103/PhysRevE.58.2247
    • (1998) Phys. Rev. E , vol.58 , pp. 2247
    • McNamara, S.1    Luding, S.2
  • 23
    • 42749108338 scopus 로고    scopus 로고
    • "Role of friction in pattern formation in oscillated granular layers"
    • pre PLEEE8 1063-651X 10.1103/PhysRevE.69.031301
    • S. J. Moon, J. B. Swift, and H. L. Swinney, "Role of friction in pattern formation in oscillated granular layers," Phys. Rev. E 69, 031301 (2004). pre PLEEE8 1063-651X 10.1103/PhysRevE.69.031301
    • (2004) Phys. Rev. E , vol.69 , pp. 031301
    • Moon, S.J.1    Swift, J.B.2    Swinney, H.L.3
  • 24
    • 4344600693 scopus 로고    scopus 로고
    • "Clustering, order and collapse in a driven granular monolayer"
    • prl PRLTAO 0031-9007 10.1103/PhysRevLett.81.4369
    • J. S. Olafsen and J. S. Urbach, "Clustering, order and collapse in a driven granular monolayer," Phys. Rev. Lett. 81, 4369 (1998). prl PRLTAO 0031-9007 10.1103/PhysRevLett.81.4369
    • (1998) Phys. Rev. Lett. , vol.81 , pp. 4369
    • Olafsen, J.S.1    Urbach, J.S.2
  • 25
    • 17944369302 scopus 로고    scopus 로고
    • "Velocity distributions and density fluctuations in a 2d granular gas"
    • pre PLEEE8 1063-651X 10.1103/PhysRevE.60.R2468
    • J. S. Olafsen and J. S. Urbach, "Velocity distributions and density fluctuations in a 2d granular gas," Phys. Rev. E 60, R2468 (1999). pre PLEEE8 1063-651X 10.1103/PhysRevE.60.R2468
    • (1999) Phys. Rev. E , vol.60
    • Olafsen, J.S.1    Urbach, J.S.2
  • 26
    • 0001110212 scopus 로고    scopus 로고
    • "Propagating front in an excited granular layer"
    • pre PLEEE8 1063-651X 10.1103/PhysRevE.59.5855
    • W. Losert, D. G. W. Cooper, and J. P. Gollub, "Propagating front in an excited granular layer," Phys. Rev. E 59, 5855 (1999). pre PLEEE8 1063-651X 10.1103/PhysRevE.59.5855
    • (1999) Phys. Rev. E , vol.59 , pp. 5855
    • Losert, W.1    Cooper, D.G.W.2    Gollub, J.P.3
  • 27
    • 0142153261 scopus 로고    scopus 로고
    • "Kinetics - Gaussian statistics in granular gases"
    • bnh NATUAS 0028-0836 10.1038/425680a
    • G. W. Baxter and J. S. Olafsen, "Kinetics - Gaussian statistics in granular gases," Nature 425, 680 (2003). bnh NATUAS 0028-0836 10.1038/425680a
    • (2003) Nature , vol.425 , pp. 680
    • Baxter, G.W.1    Olafsen, J.S.2
  • 28
    • 42749108991 scopus 로고    scopus 로고
    • "Pressure measurement in two-dimensional horizontal granular gases"
    • pre PLEEE8 1063-651X 10.1103/PhysRevE.70.021301
    • J.-C. Géminard and C. Laroche, "Pressure measurement in two-dimensional horizontal granular gases," Phys. Rev. E 70, 021301 (2004). pre PLEEE8 1063-651X 10.1103/PhysRevE.70.021301
    • (2004) Phys. Rev. E , vol.70 , pp. 021301
    • Géminard, J.-C.1    Laroche, C.2
  • 29
    • 0343390515 scopus 로고    scopus 로고
    • "Two-dimensional granular gas of inelastic spheres with multiplicative driving"
    • prl PRLTAO 0031-9007 10.1103/PhysRevLett.84.6014
    • R. Cafiero, S. Luding, and H. J. Herrmann, "Two-dimensional granular gas of inelastic spheres with multiplicative driving," Phys. Rev. Lett. 84, 6014 (2000). prl PRLTAO 0031-9007 10.1103/ PhysRevLett.84.6014
    • (2000) Phys. Rev. Lett. , vol.84 , pp. 6014
    • Cafiero, R.1    Luding, S.2    Herrmann, H.J.3
  • 30
    • 0027962992 scopus 로고
    • "Measurements of the collision properties of small spheres"
    • phf PHFLE6 1070-6631 10.1063/1.868075
    • S. F. Foerster, M. Y. Louge, H. Chang, and K. Allia, "Measurements of the collision properties of small spheres," Phys. Fluids 6, 108 (1994). phf PHFLE6 1070-6631 10.1063/1.868075
    • (1994) Phys. Fluids , vol.6 , pp. 108
    • Foerster, S.F.1    Louge, M.Y.2    Chang, H.3    Allia, K.4
  • 32
    • 0012067474 scopus 로고    scopus 로고
    • "Collisions & contacts between two particles"
    • edited by H. J. Herrmann, J.-P. Hovi, and S. Luding (Kluwer Academic, Dordrecht)
    • S. Luding, "Collisions & contacts between two particles," in Physics of Dry Granular Media - NATO ASI Series E350, edited by H. J. Herrmann, J.-P. Hovi, and S. Luding (Kluwer Academic, Dordrecht, 1998), p. 285.
    • (1998) Physics of Dry Granular Media - NATO ASI Series E350 , pp. 285
    • Luding, S.1
  • 33
    • 0000071792 scopus 로고
    • "How to simulate billards and similar systems"
    • jct JCTPAH 0021-9991 10.1016/0021-9991(91)90222-7
    • B. D. Lubachevsky, "How to simulate billards and similar systems," J. Comput. Phys. 94, 255 (1991). jct JCTPAH 0021-9991 10.1016/0021-9991(91)90222-7
    • (1991) J. Comput. Phys. , vol.94 , pp. 255
    • Lubachevsky, B.D.1
  • 34
    • 0001170114 scopus 로고
    • "Numerical simulation of inelastic, frictional particle-particle interactions"
    • edited by M. C. Roco (Butterworth-Heinemann, Boston)
    • O.R. Walton, "Numerical simulation of inelastic, frictional particle-particle interactions," in Particulate Two-phase Flow, edited by M. C. Roco (Butterworth-Heinemann, Boston, 1993), p. 884.
    • (1993) Particulate Two-phase Flow , pp. 884
    • Walton, O.R.1
  • 35
    • 30444450152 scopus 로고    scopus 로고
    • "Measurements of collision properties of spheres using high-speed video analysis"
    • pre PLEEE8 1063-651X 10.1103/PhysRevE.56.5717
    • L. Labous, A. D. Rosato, and R. Dave, "Measurements of collision properties of spheres using high-speed video analysis," Phys. Rev. E 56, 5715 (1997). pre PLEEE8 1063-651X 10.1103/PhysRevE.56.5717
    • (1997) Phys. Rev. E , vol.56 , pp. 5715
    • Labous, L.1    Rosato, A.D.2    Dave, R.3
  • 36
    • 0012965399 scopus 로고    scopus 로고
    • "Segregation of polydisperse granular media in the presence of a temperature gradient"
    • edited by T. Rosato (Kluwer Academic, Dordrecht)
    • S. Luding, O. Strauß, and S. McNamara, "Segregation of polydisperse granular media in the presence of a temperature gradient," in IUTAM Symposium on Segregation in Granular Flows, edited by T. Rosato (Kluwer Academic, Dordrecht, 1999), pp. 297-304.
    • (1999) IUTAM Symposium on Segregation in Granular Flows , pp. 297-304
    • Luding, S.1    Strauß, O.2    McNamara, S.3
  • 37
    • 0000872238 scopus 로고    scopus 로고
    • "Departure from Fourier's law for fluidized granular media"
    • prl PRLTAO 0031-9007 10.1103/PhysRevLett.83.5003
    • R. Soto, M. Mareschal, and D. Risso, "Departure from Fourier's law for fluidized granular media," Phys. Rev. Lett. 83, 5003 (1999). prl PRLTAO 0031-9007 10.1103/PhysRevLett.83.5003
    • (1999) Phys. Rev. Lett. , vol.83 , pp. 5003
    • Soto, R.1    Mareschal, M.2    Risso, D.3
  • 38
    • 0035306308 scopus 로고    scopus 로고
    • "Statistical mechanics of fluidized granular media: Short range velocity correlations"
    • pre PLEEE8 1063-651X 10.1103/PhysRevE.63.041303
    • R. Soto and M. Mareschal, "Statistical mechanics of fluidized granular media: Short range velocity correlations," Phys. Rev. E 63, 041303 (2001). pre PLEEE8 1063-651X 10.1103/PhysRevE.63.041303
    • (2001) Phys. Rev. E , vol.63 , pp. 041303
    • Soto, R.1    Mareschal, M.2
  • 39
    • 37649028920 scopus 로고    scopus 로고
    • "Local equation of state and velocity distributions of a driven granular gas,"
    • pre PLEEE8 1063-651X 10.1103/PhysRevE.70.051313
    • O. Herbst, P. Müller M. Otto, and A. Zippelius, "Local equation of state and velocity distributions of a driven granular gas," Phys. Rev. E 70, 051313 (2004). pre PLEEE8 1063-651X 10.1103/ PhysRevE.70.051313
    • (2004) Phys. Rev. E , vol.70 , pp. 051313
    • Herbst, O.1    Müller, P.2    Otto, M.3    Zippelius, A.4
  • 40
    • 0032476441 scopus 로고    scopus 로고
    • "Clustering and non-Gaussian behavior in granular matter"
    • prl PRLTAO 0031-9007 10.1103/PhysRevLett.81.3848
    • A. Puglisi, V. Loreto, U. M. B. Marconi, and A. Vulpiani, "Clustering and non-Gaussian behavior in granular matter," Phys. Rev. Lett. 81, 3848 (1998). prl PRLTAO 0031-9007 10.1103/ PhysRevLett.81.3848
    • (1998) Phys. Rev. Lett. , vol.81 , pp. 3848
    • Puglisi, A.1    Loreto, V.2    Marconi, U.M.B.3    Vulpiani, A.4
  • 41
    • 0000640163 scopus 로고    scopus 로고
    • "Linear stability analysis of a vertically oscillated granular layer"
    • pre PLEEE8 1063-651X 10.1103/PhysRevE.60.7210
    • C. Bizon, M. D. Shattuck, and J. B. Swift, "Linear stability analysis of a vertically oscillated granular layer," Phys. Rev. E 60, 7210 (1999). pre PLEEE8 1063-651X 10.1103/PhysRevE.60.7210
    • (1999) Phys. Rev. E , vol.60 , pp. 7210
    • Bizon, C.1    Shattuck, M.D.2    Swift, J.B.3
  • 42
    • 18744399894 scopus 로고    scopus 로고
    • "Rotationally driven gas of inelastic rough spheres"
    • eul EULEEJ 0295-5075 10.1209/epl/i2002-00295-7
    • R. Cafiero, S. Luding, and H. J. Herrmann, "Rotationally driven gas of inelastic rough spheres," Europhys. Lett. 60, 854 (2002). eul EULEEJ 0295-5075 10.1209/epl/i2002-00295-7
    • (2002) Europhys. Lett. , vol.60 , pp. 854
    • Cafiero, R.1    Luding, S.2    Herrmann, H.J.3
  • 43
    • 0000995930 scopus 로고
    • "Disks vs. spheres: Contrasting properties of random packings"
    • jst JSTPBS 0022-4715 10.1007/BF01048304
    • B. D. Lubachevsky, F. H. Stillinger, and E. N. Pinson, "Disks vs. spheres: Contrasting properties of random packings," J. Stat. Phys. 64, 501 (1991). jst JSTPBS 0022-4715 10.1007/BF01048304
    • (1991) J. Stat. Phys. , vol.64 , pp. 501
    • Lubachevsky, B.D.1    Stillinger, F.H.2    Pinson, E.N.3
  • 44
    • 7444236945 scopus 로고
    • "Steady state of a column of shaked inelastic spheres"
    • pre PLEEE8 1063-651X 10.1103/PhysRevE.50.4551
    • R. Mazighi, B. Bernu, and F. Delyon, "Steady state of a column of shaked inelastic spheres," Phys. Rev. E 50, 4551 (1994). pre PLEEE8 1063-651X 10.1103/PhysRevE.50.4551
    • (1994) Phys. Rev. E , vol.50 , pp. 4551
    • Mazighi, R.1    Bernu, B.2    Delyon, F.3
  • 45
    • 0002843730 scopus 로고
    • "Inelastic collapse in two dimensions"
    • pre PLEEE8 1063-651X 10.1103/PhysRevLett.70.1619
    • S. McNamara and W. R. Young, "Inelastic collapse in two dimensions," Phys. Rev. E 50, R28 (1994). pre PLEEE8 1063-651X 10.1103/PhysRevLett.70.1619
    • (1994) Phys. Rev. E , vol.50
    • McNamara, S.1    Young, W.R.2
  • 46
    • 0039648118 scopus 로고    scopus 로고
    • "Simulations of pattern formation in vibrated granular media"
    • eul EULEEJ 0295-5075 10.1209/epl/i1996-00217-9
    • S. Luding, E. Clément, J. Rajchenbach, and J. Duran, "Simulations of pattern formation in vibrated granular media," Europhys. Lett. 36, 247 (1996). eul EULEEJ 0295-5075 10.1209/epl/ i1996-00217-9
    • (1996) Europhys. Lett. , vol.36 , pp. 247
    • Luding, S.1    Clément, E.2    Rajchenbach, J.3    Duran, J.4
  • 47
    • 0032278755 scopus 로고    scopus 로고
    • "How to handle the inelastic collapse of a dissipative hard-sphere gas with the TC model"
    • 8wa GRMAFE 1434-5021 10.1007/s100350050017
    • S. Luding and S. McNamara, "How to handle the inelastic collapse of a dissipative hard-sphere gas with the TC model,"Granular Matter, 1, 113 (1998). 8wa GRMAFE 1434-5021 10.1007/s100350050017
    • (1998) Granular Matter , vol.1 , pp. 113
    • Luding, S.1    McNamara, S.2
  • 48
    • 0348225000 scopus 로고    scopus 로고
    • "Collisional cooling with multi-particle interactions"
    • 8wa GRMAFE 1434-5021 10.1007/s10035-003-0136-8
    • S. Luding and A. Goldshtein, "Collisional cooling with multi-particle interactions," Granular Matter 5, 159 (2003). 8wa GRMAFE 1434-5021 10.1007/s10035-003-0136-8
    • (2003) Granular Matter , vol.5 , pp. 159
    • Luding, S.1    Goldshtein, A.2
  • 49
    • 0001120321 scopus 로고
    • "A simple equation of state for hard discs"
    • mop MOPHAM 0026-8976
    • D. Henderson, "A simple equation of state for hard discs," Mol. Phys. 30, 971 (1975). mop MOPHAM 0026-8976
    • (1975) Mol. Phys. , vol.30 , pp. 971
    • Henderson, D.1
  • 50
    • 29444440462 scopus 로고
    • "Monte Carlo and perturbation theory studies of the equation of state of the two-dimensional Lennard-Jones fluid"
    • mop MOPHAM 0026-8976
    • D. Henderson, "Monte Carlo and perturbation theory studies of the equation of state of the two-dimensional Lennard-Jones fluid," Mol. Phys. 34, 301 (1977). mop MOPHAM 0026-8976
    • (1977) Mol. Phys. , vol.34 , pp. 301
    • Henderson, D.1
  • 51
    • 0000934434 scopus 로고
    • "Integral equations for classical fluids. III. The hard disks system"
    • mop MOPHAM 0026-8976
    • L. Verlet and D. Levesque, "Integral equations for classical fluids. III. The hard disks system," Mol. Phys. 46, 969 (1982). mop MOPHAM 0026-8976
    • (1982) Mol. Phys. , vol.46 , pp. 969
    • Verlet, L.1    Levesque, D.2
  • 52
    • 0001084109 scopus 로고    scopus 로고
    • "Temperature scaling in a dense vibrofluidized granular material"
    • pre PLEEE8 1063-651X 10.1103/PhysRevE.60.1951
    • P. Sunthar and V. Kumaran, "Temperature scaling in a dense vibrofluidized granular material," Phys. Rev. E 60, 1951 (1999). pre PLEEE8 1063-651X 10.1103/PhysRevE.60.1951
    • (1999) Phys. Rev. E , vol.60 , pp. 1951
    • Sunthar, P.1    Kumaran, V.2
  • 53
    • 24144453176 scopus 로고    scopus 로고
    • "Kinetic theory for identical, frictional, nearly elastic disks"
    • phf PHFLE6 1070-6631 10.1063/1.2000768
    • D. K. Yoon and J. T. Jenkins, "Kinetic theory for identical, frictional, nearly elastic disks," Phys. Fluids 17, 083301 (2005). phf PHFLE6 1070-6631 10.1063/1.2000768
    • (2005) Phys. Fluids , vol.17 , pp. 083301
    • Yoon, D.K.1    Jenkins, J.T.2
  • 55
    • 0001117617 scopus 로고
    • "Equation of state for nonattracting rigid spheres"
    • jcp JCPSA6 0021-9606 10.1063/1.1672048
    • W. F. Carnahan and K. E. Starling, "Equation of state for nonattracting rigid spheres," J. Chem. Phys. 51, 635 (1969). jcp JCPSA6 0021-9606 10.1063/1.1672048
    • (1969) J. Chem. Phys. , vol.51 , pp. 635
    • Carnahan, W.F.1    Starling, K.E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.