摘要We find that there are two time scales t and ε ln t in the asymptotic behaviour of diffusion process in the porous medium, which give us a new insight to the anomalous dimension in this problem. Further we construct an iterative method to calculate the anomalous dimension and obtain an improved result.
Abstract:We find that there are two time scales t and ε ln t in the asymptotic behaviour of diffusion process in the porous medium, which give us a new insight to the anomalous dimension in this problem. Further we construct an iterative method to calculate the anomalous dimension and obtain an improved result.
TU Tao;HAO Xiao-Jie;GUO Guo-Ping;GUO Guang-Can. Two-Time Diffusion Process in the Porous Medium[J]. 中国物理快报, 2007, 24(8): 2293-2296.
TU Tao, HAO Xiao-Jie, GUO Guo-Ping, GUO Guang-Can. Two-Time Diffusion Process in the Porous Medium. Chin. Phys. Lett., 2007, 24(8): 2293-2296.
[1] Kath W L 1984 Physica D 12 375 [2] Aronson D G 1986 Nonlinear Diffusion Problemsed Fasano A and Primicerio M (Berlin: Springer) [3] Barenblatt G I 1996 Scaling, Self-Similarity,and Intermediate Asymptotics (Cambridge: Cambridge University) [4] Veysey J and Goldenfled N 2007 Rev. Mod. Phys. (to bepublished) (physics/0609138) [5] Chen L Y Goldenfeld N and Oono Y 1994 Phys. Rev.Lett. 73 1311 [6] Goldenfeld N, Martin O, Oono Y and Liu F 1990 Phys. Rev. Lett. 64 1361 [7] Chen L Y, Goldenfeld N and Oono Y 1996 Phys. Rev. E 54 376 [8] Yoshida S and Fukui T 2005 Phys. Rev. E 72 046136 [9] Graham R 1996 Phys. Rev. Lett. 76 2185 [10] Nozaki K and Oono Y 2001 Phys. Rev. E 63 046101 [11] Shiwa Y 2001 Phys. Rev. E 63 016119 [12] Athreya B P, Goldenfeld N and Dantzig J A 2006 Phys.Rev. E 74 011601 [13] Paquette G C, Chen L Y, Goldenfeld N and Oono Y 1994 Phys. Rev. Lett. 72 76 [14] Tu T and Cheng G 2002 Phys. Rev. E 64046625 [15] Kunihiro T 1998 Phys. Rev. D 57 R2035 [16] Boyanovsky D, de Vega H J and Wang S Y 2000 Phys.Rev. D 61 065006 [17] Frasca M 1997 Phys. Rev. A 56 1548 [18] Dalvit D A R and Mazzitelli F D 1998 Phys. Rev. A 57 2113 [19] Bender C M and Orszag S A 1978 AdvancedMathematical Methods for Scientists and Engineers (New York:McGraw-Hill) [20] Tu T et al 2007 (in prepration)