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Volumn 58, Issue 3, 1998, Pages 2918-2930

Reaction zones and quenched charged-particle systems with long-range interactions

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Indexed keywords


EID: 11744258246     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.58.2918     Document Type: Article
Times cited : (1)

References (55)
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    • Note that [Formula Presented]
    • J. Stat. Phys.B. P. LeeJ. Cardy87, 951 (1997). Note that lrz∼lAB.
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    • 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
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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
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    • Redner, S.1    Leyvraz, F.2
  • 15
    • 85036323887 scopus 로고    scopus 로고
    • 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.
  • 17
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    • Phys. Rev. A 42, 911 (1990).
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    • Note that their [Formula Presented] PLEEE8
    • I. Ispolatov and P. L. Krapivsky, Phys. Rev. E 53, 3154 (1996). Note that their λ≡n.PLEEE8
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    • 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
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    • J.-M. Park and M. W. Deem, Phys. Rev. E (to be published).
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    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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
  • 35
    • 85036417964 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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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    • 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.
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    • 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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    • references therein. PRPLCM
    • J.-P. Bouchaud and A. Georges, Phys. Rep. 195, 127 (1990), and references therein.
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    • Bouchaud, J.-P.1    Georges, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.