-
1
-
-
4243664116
-
-
M. E. Cates, J. P. Wittmer, J.-P. Bouchaud, and P. Claudin, Phys. Rev. Lett. 81, 1841 (1998).
-
(1998)
Phys. Rev. Lett.
, vol.81
, pp. 1841
-
-
Cates, M.E.1
Wittmer, J.P.2
Bouchaud, J.-P.3
Claudin, P.4
-
3
-
-
0013549443
-
-
C.-H. Liu, S. R. Nagel, D. A. Schecter, S. N. Coppersmith, S. Majumdar, O. Narayan, and T. A. Witten, Science 269, 513 (1995).
-
(1995)
Science
, vol.269
, pp. 513
-
-
Liu, C.-H.1
Nagel, S.R.2
Schecter, D.A.3
Coppersmith, S.N.4
Majumdar, S.5
Narayan, O.6
Witten, T.A.7
-
8
-
-
85036294454
-
-
G. Ahmadi (private communication)
-
G. Ahmadi (private communication);
-
-
-
-
13
-
-
0001455852
-
-
K. Yamne, M. Nakagawa, S. A. Altobelli, T. Tanaka, and Y. Tsuji, Phys. Fluids 10, 1419 (1998);
-
(1998)
Phys. Fluids
, vol.10
, pp. 1419
-
-
Yamne, K.1
Nakagawa, M.2
Altobelli, S.A.3
Tanaka, T.4
Tsuji, Y.5
-
15
-
-
85036410027
-
-
P. K. Haff, in Granular Matter, edited by Anita Mehta (Springer-Verlag, New York, 1994)
-
P. K. Haff, in Granular Matter, edited by Anita Mehta (Springer-Verlag, New York, 1994).
-
-
-
-
18
-
-
0031246549
-
-
J. Fluid Mech.C. S. Campbell, 348, 85 (1997);
-
(1997)
, vol.348
, pp. 85
-
-
Campbell, C.S.1
-
19
-
-
0001211434
-
-
P. Zamankhan, T. Tynjälä, W. Polashenski, Jr., P. Zamankhan, and P. Sarkomaa, Phys. Rev. E 60, 7149 (1999).
-
(1999)
Phys. Rev. E
, vol.60
, pp. 7149
-
-
Zamankhan, P.1
Tynjälä, T.2
Polashenski, W.3
Zamankhan, P.4
Sarkomaa, P.5
-
20
-
-
0032484448
-
-
C. Bizon, M. D. Shattuck, J. B. Swift, W. D. McCormick, and H. L. Swinney, Phys. Rev. Lett. 80, 57 (1998).
-
(1998)
Phys. Rev. Lett.
, vol.80
, pp. 57
-
-
Bizon, C.1
Shattuck, M.D.2
Swift, J.B.3
McCormick, W.D.4
Swinney, H.L.5
-
22
-
-
0001049132
-
-
J. Chem. Phys.P. Zamankhan, H. Vahedi Tafreshi, W. Polashenski, Jr., P. Sarkomaa, and C. L. Hyndman, 109, 4487 (1998).
-
(1998)
, vol.109
, pp. 4487
-
-
Zamankhan, P.1
Vahedi Tafreshi, H.2
Polashenski, W.3
Sarkomaa, P.4
Hyndman, C.L.5
-
24
-
-
85036230675
-
-
At short times, namely, before collisions occur, a particle diffuses as a free particle and (Formula presented) grows as (Formula presented) At long times, after many collisions, (Formula presented) grows as t, where the Einstein relation, namely, (Formula presented) is obeyed. Here, D represents the coefficient of self-diffusion that characterizes, on average, the dissipation of spontaneous density fluctuations produced by local aggregation and redispersion of particles. The dynamics of density fluctuations may be monitored by calculating of the self-space-time correlation function (Formula presented) which involves features of the radial distribution function combined with features of time correlation functions
-
At short times, namely, before collisions occur, a particle diffuses as a free particle and (Formula presented) grows as (Formula presented) At long times, after many collisions, (Formula presented) grows as t, where the Einstein relation, namely, (Formula presented) is obeyed. Here, D represents the coefficient of self-diffusion that characterizes, on average, the dissipation of spontaneous density fluctuations produced by local aggregation and redispersion of particles. The dynamics of density fluctuations may be monitored by calculating of the self-space-time correlation function (Formula presented) which involves features of the radial distribution function combined with features of time correlation functions.
-
-
-
-
25
-
-
0032209225
-
-
P. Zamankhan, W. Polashenski, Jr., H. Vahedi Tafreshi, A. Shakib Manesh, and P. Sarkomaa, Phys. Rev. E 58, R5237 (1998).
-
(1998)
Phys. Rev. E
, vol.58
-
-
Zamankhan, P.1
Polashenski, W.2
Vahedi Tafreshi, H.3
Shakib Manesh, A.4
Sarkomaa, P.5
-
26
-
-
85036412558
-
-
J. Bridgwater, in Granular Matter (Ref. 10
-
J. Bridgwater, in Granular Matter (Ref. 10).
-
-
-
-
28
-
-
85036391890
-
-
N. Menon (private communication)
-
N. Menon (private communication).
-
-
-
-
32
-
-
85036139226
-
-
J.-P. Hansen and I. R. McDonald, Theory of Simple Liquids (Academic, New York, 1986)
-
J.-P. Hansen and I. R. McDonald, Theory of Simple Liquids (Academic, New York, 1986).
-
-
-
-
38
-
-
0001033766
-
-
G. Boffetta, V. Carbone, P. Dgiuliani, P. Veltri, and A. Vulpiani, Phys. Rev. Lett. 83, 4662 (1999).
-
(1999)
Phys. Rev. Lett.
, vol.83
, pp. 4662
-
-
Boffetta, G.1
Carbone, V.2
Dgiuliani, P.3
Veltri, P.4
Vulpiani, A.5
-
41
-
-
36549104812
-
-
J. Chem. Phys.D. Y. C. Chan and R. G. Horn, 83, 5311 (1985);
-
(1985)
, vol.83
, pp. 5311
-
-
Chan, D.Y.C.1
Horn, R.G.2
-
44
-
-
36549105034
-
-
R. G. Horn, S. J. Hirz, G. Hadziioannou, C. W. Frank, and J. M. Catala, J. Chem. Phys. 90, 6767 (1989);
-
(1989)
J. Chem. Phys.
, vol.90
, pp. 6767
-
-
Horn, R.G.1
Hirz, S.J.2
Hadziioannou, G.3
Frank, C.W.4
Catala, J.M.5
-
45
-
-
0642371520
-
-
J. Chem. Phys.M. L. Gee, P. M. McGuiggan, J. N. Israelachvili, and A. M. Nomola, 93, 1895 (1990);
-
(1990)
, vol.93
, pp. 1895
-
-
Gee, M.L.1
McGuiggan, P.M.2
Israelachvili, J.N.3
Nomola, A.M.4
-
48
-
-
0000486160
-
-
N. V. Brilliantov, F. Spahn, J. M. Hertzsch, and T. Pöschel, Phys. Rev. E 53, 5382 (1996).
-
(1996)
Phys. Rev. E
, vol.53
, pp. 5382
-
-
Brilliantov, N.V.1
Spahn, F.2
Hertzsch, J.M.3
Pöschel, T.4
-
49
-
-
85036289875
-
-
W. Goldsmith, Impact: The Theory and Physical Behaviour of Colliding Solids (Arnold, London, 1960)
-
W. Goldsmith, Impact: The Theory and Physical Behaviour of Colliding Solids (Arnold, London, 1960).
-
-
-
-
51
-
-
85052507481
-
-
M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Clarendon, Oxford, 1997)
-
M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Clarendon, Oxford, 1997).
-
-
-
-
56
-
-
85036247089
-
-
A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity (Dover, New York, 1944)
-
A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity (Dover, New York, 1944).
-
-
-
-
57
-
-
85040956871
-
-
K. J. Johnson, Contact Mechanics (Cambridge University Press, Cambridge, 1987)
-
K. J. Johnson, Contact Mechanics (Cambridge University Press, Cambridge, 1987).
-
-
-
-
63
-
-
85036325241
-
-
H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids (Clarendon, Oxford, 1976)
-
H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids (Clarendon, Oxford, 1976).
-
-
-
-
66
-
-
85036340317
-
-
J. W. Dally and W. F. Riley, Experimental Stress Analysis (McGraw-Hill, Tokyo, 1978)
-
J. W. Dally and W. F. Riley, Experimental Stress Analysis (McGraw-Hill, Tokyo, 1978).
-
-
-
-
67
-
-
85036243655
-
-
J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954)
-
J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954).
-
-
-
-
69
-
-
85036271209
-
-
B. Miller, Ph.D. thesis, Duke University, 1997, p. 54
-
B. Miller, Ph.D. thesis, Duke University, 1997, p. 54.
-
-
-
-
71
-
-
0013549443
-
-
C. H. Liu, S. R. Nagel, D. A. Schecter, S. N. Coppersmith, S. Majumdar, O. Narayan, and T. A. Witten, Science 269, 513 (1995).
-
(1995)
Science
, vol.269
, pp. 513
-
-
Liu, C.H.1
Nagel, S.R.2
Schecter, D.A.3
Coppersmith, S.N.4
Majumdar, S.5
Narayan, O.6
Witten, T.A.7
-
72
-
-
0026809031
-
-
I. Daubechies, Ten Lectures on Wavelets (SIAM, Montpelier, Vermont, 1992)
-
M. Farge, Annu. Rev. Fluid Mech. 24, 395 (1992);I. Daubechies, Ten Lectures on Wavelets (SIAM, Montpelier, Vermont, 1992).
-
(1992)
Annu. Rev. Fluid Mech.
, vol.24
, pp. 395
-
-
Farge, M.1
-
74
-
-
85036318171
-
-
S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge University Press, Cambridge, 1970)
-
S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge University Press, Cambridge, 1970).
-
-
-
|