-
7
-
-
21744440694
-
-
Note that [Formula Presented]
-
J. Stat. Phys.B. P. LeeJ. Cardy87, 951 (1997). Note that lrz∼lAB.
-
(1997)
J. Stat. Phys.
, vol.87
, pp. 951
-
-
Lee, B.P.1
Cardy, J.2
-
10
-
-
36149030823
-
-
Note that their coarse-grained approach is only valid for [Formula Presented] JPHAC5
-
E. Ben-Naim and S. Redner, J. Phys. A 25, L575 (1992). Note that their coarse-grained approach is only valid for d>2.JPHAC5
-
(1992)
J. Phys. A
, vol.25
-
-
Ben-Naim, E.1
Redner, S.2
-
13
-
-
6444223959
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-
They impose [Formula Presented] For reaction-diffusive systems this is correct only for [Formula Presented] JSTPBS
-
S. Redner and F. Leyvraz, J. Stat. Phys. 65, 1043 (1991). They impose W∼lAB. For reaction-diffusive systems this is correct only for d<2.JSTPBS
-
(1991)
J. Stat. Phys.
, vol.65
, pp. 1043
-
-
Redner, S.1
Leyvraz, F.2
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15
-
-
85036323887
-
-
No diagrams dress the particle propagators of formal approaches when the only interaction is annihilation (see Ref. c3). This is not true when long-range interactions are included
-
No diagrams dress the particle propagators of formal approaches when the only interaction is annihilation (see Ref. 3). This is not true when long-range interactions are included.
-
-
-
-
16
-
-
0003764420
-
-
S. Komura, H. Furukawa, Plenum, New York
-
H. Toyoki, in Dynamics of Ordering Processes in Condensed Matter, edited by S. Komura and H. Furukawa (Plenum, New York, 1988), p. 173
-
(1988)
Dynamics of Ordering Processes in Condensed Matter
, pp. 173
-
-
Toyoki, H.1
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17
-
-
11744370100
-
-
Phys. Rev. A 42, 911 (1990).
-
(1990)
Phys. Rev. A
, vol.42
, pp. 911
-
-
-
18
-
-
0000748209
-
-
Note that their [Formula Presented] PLEEE8
-
I. Ispolatov and P. L. Krapivsky, Phys. Rev. E 53, 3154 (1996). Note that their λ≡n.PLEEE8
-
(1996)
Phys. Rev. E
, vol.53
, pp. 3154
-
-
Ispolatov, I.1
Krapivsky, P.L.2
-
21
-
-
5344247381
-
-
This paper applies to the generalized Coulombic model [Formula Presented] rather than [Formula Presented] as stated. PYLAAG
-
T. Ohtsuki, Phys. Lett. 106A, 224 (1984). This paper applies to the generalized Coulombic model n=d-1, rather than n=2 as stated.PYLAAG
-
(1984)
Phys. Lett.
, vol.106A
, pp. 224
-
-
Ohtsuki, T.1
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23
-
-
0039890730
-
-
W. G. Jang, V. V. Ginzburg, C. D. Muzny, and N. A. Clark, Phys. Rev. E 51, 411 (1995).PLEEE8
-
(1995)
Phys. Rev. E
, vol.51
, pp. 411
-
-
Jang, W.G.1
Ginzburg, V.V.2
Muzny, C.D.3
Clark, N.A.4
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25
-
-
85036270323
-
-
J.-M. Park and M. W. Deem, Phys. Rev. E (to be published)
-
J.-M. Park and M. W. Deem, Phys. Rev. E (to be published).
-
-
-
-
27
-
-
85036321930
-
-
When one species is immobile correlations can become important c7, particularly for the domain structure of the immobile species. For purely diffusive systems, this is a singular limit c3
-
When one species is immobile correlations can become important 7, particularly for the domain structure of the immobile species. For purely diffusive systems, this is a singular limit 3.
-
-
-
-
28
-
-
85036348287
-
-
There is no pair creation, [Formula Presented] in our dynamics. This corresponds to being at a temperature far below the chemical potential of pairs
-
There is no pair creation, ∅→A+B, in our dynamics. This corresponds to being at a temperature far below the chemical potential of pairs.
-
-
-
-
29
-
-
85036332195
-
-
The initial particle density is tuned by a chemical potential. It does not affect the asymptotic exponents of the subsequent evolution
-
The initial particle density is tuned by a chemical potential. It does not affect the asymptotic exponents of the subsequent evolution.
-
-
-
-
34
-
-
11744365503
-
-
D. Dhar, Phys. Lett. 81A, 19 (1981).PYLAAG
-
(1981)
Phys. Lett.
, vol.81A
, pp. 19
-
-
Dhar, D.1
-
35
-
-
85036417964
-
-
A quenched [Formula Presented] model can be approximated by a system of charged-vortices interacting logarithmically, with [Formula Presented] (see Sec. V). Coarse-grained charge fluctuations with μ=2, as described by Eq. (4), lead to the correct mixed morphology with [Formula Presented] (up to logarithms; see, e.g., Refs. c19 c38). In contrast, characterizing the initial fluctuations by the excess number of vortices within a sharply defined box of size L, i.e., [Formula Presented] leads to a segregated morphology with [Formula Presented] but [Formula Presented] c25, which is not observed c19 c38
-
A quenched 2D XY model can be approximated by a system of charged-vortices interacting logarithmically, with n=1 (see Sec. V). Coarse-grained charge fluctuations with μ=2, as described by Eq. (4), lead to the correct mixed morphology with L∼lAA∼t1/2 (up to logarithms; see, e.g., Refs. 1938). In contrast, characterizing the initial fluctuations by the excess number of vortices within a sharply defined box of size L, i.e., μ=32, leads to a segregated morphology with L∼t1/2 but lAA∼t3/8 25, which is not observed 1938.
-
-
-
-
36
-
-
85036224477
-
-
We coarse grain the charge density to a small but finite fraction of L, and we assume a smooth domain structure at that scale. Alternatively, we could build in a fractal domain structure (see Ref. c7), but we cannot a priori determine if a fractal structure evolves from the dynamics
-
We coarse grain the charge density to a small but finite fraction of L, and we assume a smooth domain structure at that scale. Alternatively, we could build in a fractal domain structure (see Ref. 7), but we cannot a priori determine if a fractal structure evolves from the dynamics.
-
-
-
-
38
-
-
85036223361
-
-
We self-consistently determine the shortest applicable annihilation time [Formula Presented] the largest relevant reaction-zone width [Formula Presented] and the corresponding particle spacing in the reaction zone [Formula Presented] in terms of their time exponents. The results are given in Tables II and III
-
We self-consistently determine the shortest applicable annihilation time τ(lAB), the largest relevant reaction-zone width W(τ), and the corresponding particle spacing in the reaction zone lAB, in terms of their time exponents. The results are given in Tables II and III.
-
-
-
-
39
-
-
85036350386
-
-
Other morphologies are possible in principle, though they have not been observed in reaction-diffusion systems. They would introduce new length scales
-
Other morphologies are possible in principle, though they have not been observed in reaction-diffusion systems. They would introduce new length scales.
-
-
-
-
40
-
-
85036385689
-
-
general, reaction zones are inhomogeneous, with profiles scaled by the reaction-zone width W and particle spacing [Formula Presented] c4 c6, and with dilute multiscaling tails c8. Our analysis is unchanged by these refinements
-
In general, reaction zones are inhomogeneous, with profiles scaled by the reaction-zone width W and particle spacing lAB 46, and with dilute multiscaling tails 8. Our analysis is unchanged by these refinements.
-
-
-
-
41
-
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85036154095
-
-
This linear transition zone is precisely the “boundary layer” in the coarse-grained treatment of Ben-Naim and Redner c6. Note that force-driven and ballistic annihilation mechanisms, not contained in their approach, stabilize the reaction zone when [Formula Presented]
-
This linear transition zone is precisely the “boundary layer” in the coarse-grained treatment of Ben-Naim and Redner 6. Note that force-driven and ballistic annihilation mechanisms, not contained in their approach, stabilize the reaction zone when LX≪W.
-
-
-
-
44
-
-
0000165998
-
-
The ordering kinetics of scalar systems in d=1 with long-range interactions reduces to alternatingly charged domain walls (particles) with long-range interactions when the domain walls are initially randomly distributed. See A. D. Rutenberg and A. J. Bray, Phys. Rev. E 50, 1900 (1994).PLEEE8
-
(1994)
Phys. Rev. E
, vol.50
, pp. 1900
-
-
Rutenberg, A.D.1
Bray, A.J.2
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47
-
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0001404506
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-
B. Yurke, A. N. Pargellis, T. Kovacs, and D. A. Huse, Phys. Rev. E 47, 1525 (1993).PLEEE8
-
(1993)
Phys. Rev. E
, vol.47
, pp. 1525
-
-
Yurke, B.1
Pargellis, A.N.2
Kovacs, T.3
Huse, D.A.4
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