Analytical solution for restricted diffusion in circular and spherical layers under inhomogeneous magnetic fields.

摘要: We propose an analytical solution for restricted diffusion of spin-bearing particles in circular and spherical layers inhomogeneous magnetic fields. More precisely, we derive exact explicit formulas the matrix representing applied field Laplacian eigenbasis governing magnetization evolution. For thin layers, a significant difference between two geometrical length scales (thickness overall size) allows accurate perturbative calculations. In these two-scale geometries, apparent coefficient (ADC) as function time exhibits new region with reduced but constant value. The emergence this intermediate regime, which is analogous to tortuosity regime porous media, explained terms underlying Laplace operator eigenvalues. general, regions ADCs would be reminiscent multiscale their observation can potentially used experiments detect by varying time.