An effective phase shift diffusion equation method for analysis of PFG normal and fractional diffusions

Analysis of PFG Anomalous Diffusion via Real-Space and Phase-Space Approaches

“…The PFG signal attenuation can be obtained based on Equation (2) or (3), but the phase evolution process based on the phase path integral Equation (1) is complicated. Nevertheless, the recently developed EPSDE method provides a simple way to describe the phase evolution based on an effective phase diffusion process [18]. In the following, the effective phase diffusion equation method [18] will be briefly reintroduced.…”

“…Nevertheless, the recently developed EPSDE method provides a simple way to describe the phase evolution based on an effective phase diffusion process [18]. In the following, the effective phase diffusion equation method [18] will be briefly reintroduced. Additionally, a general solution including the FGPW effect will be given that has not been reported in [18].…”

“…In the following, the effective phase diffusion equation method [18] will be briefly reintroduced. Additionally, a general solution including the FGPW effect will be given that has not been reported in [18]. For simplicity, only diffusion with a symmetric probability distribution is studied here.…”

“…In most PFG experiments, K(t tot ) = 0 where t tot is the time at the end of the rephasing gradient pulse, so Equation (4) can be further simplified to [18] …”

“…PFG anomalous diffusion [17][18][19][20][21][22][23] is different from PFG normal diffusion. Unlike normal diffusion, anomalous diffusion has a non-Gaussian probability distribution [2,24], and its mean square …”