FRACTIONAL DIFFUSION EQUATION FOR TRANSPORT PHENOMENA IN RANDOM-MEDIA

被引:184
作者
GIONA, M [1 ]
ROMAN, HE [1 ]
机构
[1] UNIV HAMBURG,INST THEORET PHYS 1,W-2000 HAMBURG 36,GERMANY
来源
PHYSICA A | 1992年 / 185卷 / 1-4期
关键词
D O I
10.1016/0378-4371(92)90441-R
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
A differential equation for diffusion in isotropic and homogeneous fractal structures is derived within the context of fractional calculus, It generalizes the fractional diffusion equation valid in Euclidean systems. The asymptotic behavior of the probability density function is obtained exactly and coincides with the accepted asymptotic form obtained using scaling argument and exact enumeration calculations on large percolation clusters at criticalitY. The asymptotic frequency dependence of the scattering function is derived exactly from the present approach, which can be studied by X-ray and neutron scattering experiments on fractals.
引用
收藏
页码:87 / 97
页数:11
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