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Finite-size scaling of one-dimensional reaction-diffusion systems. Part II. Numerical methods
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H. Hinrichsen, K. Krebs, and M. P. Pfannmüller, "Finite-size scaling of one-dimensional reaction-diffusion systems. Part I. Analytic results," J. Stat. Phys. 78, 1429 (1995); B. Wehefritz, K. Krebs, and M. P. Pfannmüller, "Finite-size scaling of one-dimensional reaction-diffusion systems. Part II. Numerical methods," ibid. 78, 1471 (1995); H. Hinrichsen, K. Krebs, and I. Peschel, "Solution of a one-dimensional reaction- diffusion model with spatial asymmetry," Z. Phys. B: Condens. Matter 100, 105 (1996).
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Solution of a one-dimensional reaction-diffusion model with spatial asymmetry
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H. Hinrichsen, K. Krebs, and M. P. Pfannmüller, "Finite-size scaling of one-dimensional reaction-diffusion systems. Part I. Analytic results," J. Stat. Phys. 78, 1429 (1995); B. Wehefritz, K. Krebs, and M. P. Pfannmüller, "Finite-size scaling of one-dimensional reaction-diffusion systems. Part II. Numerical methods," ibid. 78, 1471 (1995); H. Hinrichsen, K. Krebs, and I. Peschel, "Solution of a one-dimensional reaction-diffusion model with spatial asymmetry," Z. Phys. B: Condens. Matter 100, 105 (1996).
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Exact results for diffusion-limited reactions with synchronous dynamics
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V. Privman, "Exact results for diffusion-limited reactions with synchronous dynamics," Phys. Rev. E 50, 50 (1994); "Exact results for ID conserved order parameter model," Mod. Phys. Lett. B 143, 1994 (1994); V. Privman, A. M. R. Cadilhe, and M. L. Glasser, "Exact solutions of anisotropic diffusion-limited reactions with coagulation and annihilation," J. Stat. Phys. 81, 881 (1995); "Anisotropic diffusion-limited reactions with coagulation and annihilation," Phys. Rev. E 53, 739 (996).
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Diffusion-limited exciton kinetics in one-dimensional systems
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Exciton percolation in molecular alloys and aggregates
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edited by F. K. Fang Springer-Verlag, Heidelberg
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Diffusion-limited annihilation in inhomogeneous environments
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A general treatment of annihilation in disordered environments has been presented in: G. M. Schütz, "Diffusion-limited annihilation in inhomogeneous environments," Z. Phys. B: Condens. Matter 104, 583 (1998); G. M. Schütz and K. Mussawisade, "Annihilating random walks in one- dimensional media," Phys. Rev. E 57, 2563 (1998).
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Annihilating random walks in one-dimensional media
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A general treatment of annihilation in disordered environments has been presented in: G. M. Schütz, "Diffusion-limited annihilation in inhomogeneous environments," Z. Phys. B: Condens. Matter 104, 583 (1998); G. M. Schütz and K. Mussawisade, "Annihilating random walks in one-dimensional media," Phys. Rev. E 57, 2563 (1998).
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85037496850
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note
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In reality, the distribution of the largest clusters at the percolation threshold is discrete. Also, physical samples are finite in extent and so the largest cluster is only as large as the system. Neither of these effects has much impact on the scaling of Eq. (31).
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41
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85037498928
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note
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Our results are quite different from Ref. 14. We note that their numerical simulations for two-dimensional percolation were for τ≲20, not long enough to study the long-time asymptotic behavior.
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