Diffusion

ans it i g ec lida three-dimensional examples.) nucle comm rials [ tion. However, for large scale models of porous systems, finding even a moderate number of Laplacian eigenfunctions is in itself a challenging problem. The commonly used numerical techniques involve a discretization of the domain that results in a large size matrix representation of the Laplace operator. The eigenvalues and eigenfunctions of this matrix are then obtained by iterative where D denotes the Laplace operator, D the self-diffusion coeffi-cient, c the gyromagnetic ratio, g the gradient strength and BðrÞ the normalized spatial gradient profile which is assumed to be lin-ear and directed in the x-direction: BðrÞ ðex rÞ x. For simplicity the relaxation of the spins is not taken into account. Formally one can integrate Eq. (1) in time: mðr; tÞ exptðDDþ icgBðrÞÞm0ðrÞ: ð2Þ Here m0ðrÞ denotes the initial magnetization which is transformed by the above evolution operator. Barzykin [9] represented Eq. (2