-
1
-
-
34447250290
-
-
BIOJAU 0006-3495 10.1529/biophysj.106.096966
-
C. Brangwynne, G. H. Koenderink, E. Barry, Z. Dogic, F. C. MacKintosh, and D. A. Weitz, Biophys. J. BIOJAU 0006-3495 10.1529/biophysj.106.096966 93, 346 (2007).
-
(2007)
Biophys. J.
, vol.93
, pp. 346
-
-
Brangwynne, C.1
Koenderink, G.H.2
Barry, E.3
Dogic, Z.4
MacKintosh, F.C.5
Weitz, D.A.6
-
2
-
-
0033345114
-
-
SSREDI 0167-5729 10.1016/S0167-5729(98)00010-7
-
H.-C. Jeong and E. D. Williams, Surf. Sci. Rep. SSREDI 0167-5729 10.1016/S0167-5729(98)00010-7 34, 171 (1999).
-
(1999)
Surf. Sci. Rep.
, vol.34
, pp. 171
-
-
Jeong, H.-C.1
Williams, E.D.2
-
3
-
-
0041422282
-
-
1431-9276
-
A. K. Schmid, K. L. Man, N. C. Bartelt, H. Poppa, and M. S. Altman, Microsc. Microanal. 9, 134 (2003). 1431-9276
-
(2003)
Microsc. Microanal.
, vol.9
, pp. 134
-
-
Schmid, A.K.1
Man, K.L.2
Bartelt, N.C.3
Poppa, H.4
Altman, M.S.5
-
4
-
-
35748944560
-
-
NJOPFM 1367-2630 10.1088/1367-2630/9/10/387
-
E. D. Williams, A. Bondarchuk, C. G. Tao, W. Yan, W. G. Cullen, P. J. Rous, and T. Bole, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/9/10/387 9, 387 (2007).
-
(2007)
New J. Phys.
, vol.9
, pp. 387
-
-
Williams, E.D.1
Bondarchuk, A.2
Tao, C.G.3
Yan, W.4
Cullen, W.G.5
Rous, P.J.6
Bole, T.7
-
5
-
-
0030245149
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.77.2581
-
J. Wilhelm and E. Frey, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.2581 77, 2581 (1996).
-
(1996)
Phys. Rev. Lett.
, vol.77
, pp. 2581
-
-
Wilhelm, J.1
Frey, E.2
-
6
-
-
0031386328
-
-
JPAHER 1155-4312 10.1051/jp2:1997214
-
R. Granek, J. Phys. II JPAHER 1155-4312 10.1051/jp2:1997214 7, 1761 (1997).
-
(1997)
J. Phys. II
, vol.7
, pp. 1761
-
-
Granek, R.1
-
7
-
-
36749050069
-
-
Since dynamics is linear and stable, the evolution from an arbitrary initial condition will be the sum of the decay of this initial condition and the evolution from a flat initial condition.
-
Since dynamics is linear and stable, the evolution from an arbitrary initial condition will be the sum of the decay of this initial condition and the evolution from a flat initial condition.
-
-
-
-
8
-
-
36149027699
-
-
RMPHAT 0034-6861 10.1103/RevModPhys.17.323
-
M. C. Wang and G. E. Uhlenbeck, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.17.323 17, 323 (1945).
-
(1945)
Rev. Mod. Phys.
, vol.17
, pp. 323
-
-
Wang, M.C.1
Uhlenbeck, G.E.2
-
9
-
-
36749089781
-
-
note
-
For arbitrary times, using the Schwarz inequality, for any t, and t′: Gδ Qp (t, t′) 8 π2 La [G xp ζ (t, t′)] 2, where a is a microscopic cutoff.
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10
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36749014780
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note
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Formally, m=1/2 corresponds to the case where G eq xm ζ (0) diverges logarithmically, in an extended definition of G eq xm ζ (τ) based on Eq. 6.
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-
-
-
11
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36749017776
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note
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In order to obtain explicit analytic formulas, we approximate the sum over k with a continuous integration, and the size L is here simply introduced by considering a cutoff at k=2π/L. While this approach gives the correct scaling behavior, the numerical prefactors may not be accurate.
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12
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36749065276
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note
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Nevertheless, the diffusive behavior of the TCFs must be distinguished from the diffusion of the center of mass of the system. The position of the center of mass is hk=0 (t) /L. Its diffusion results from the fact that i ωk=0 =0, so that t hk=0 = ηk=0. Solving this equation, one finds [hk=0 (t+τ) - hk=0 (t)] 2 = Bk=0 τ, so that Bk=0 is the diffusion constant of the center of mass. Using Eq. 14, Bk=0 = (4πA kB T/σ) for n=0, and Bk=0 =0 for n>1. Taking the example of atomic steps, we recover the fact that the center of mass of a straight step should diffuse for n=0 (nonconserved, or Glauber dynamics), and cannot move due to mass conservation for n=2 (conserved, or Kawasaki dynamics). Since ζ -defined in Eq. (4)-does not contain the mode k=0, the quantities Qp, which are functionals of ζ, also do not account for this mode. (In order to be more explicit, we may define R0 = dx h2 by analogy with Q0. We then find Fδ R0 (τ) = Fδ Q0 (τ) + B k=0 2 (2t+τ) τ. Hence, we see explicitly the consequences of the diffusion of the center of mass in the term B k=0 2 (2t+τ) τ.)
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-
-
-
13
-
-
0001232154
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.57.4782
-
S. V. Khare and T. L. Einstein, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.57.4782 57, 4782 (1998).
-
(1998)
Phys. Rev. B
, vol.57
, pp. 4782
-
-
Khare, S.V.1
Einstein, T.L.2
-
14
-
-
39249083669
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.87.106104
-
O. Pierre-Louis, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 87.106104 87, 106104 (2001).
-
(2001)
Phys. Rev. Lett.
, vol.87
, pp. 106104
-
-
Pierre-Louis, O.1
-
15
-
-
0001046333
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.58.2289
-
T. Ihle, C. Misbah, and O. Pierre-Louis, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.58.2289 58, 2289 (1998).
-
(1998)
Phys. Rev. B
, vol.58
, pp. 2289
-
-
Ihle, T.1
Misbah, C.2
Pierre-Louis, O.3
-
16
-
-
0000967138
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.54.11752
-
S. V. Khare and T. L. Einstein, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.54.11752 54, 11752 (1996)
-
(1996)
Phys. Rev. B
, vol.54
, pp. 11752
-
-
Khare, S.V.1
Einstein, T.L.2
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