The central objective, as in Taylor's approach, is to predict the turbulent diffusion (mean square displacement and/or concentration distribution) given certain statistical information about the turbulent velocity field.
In Gaussian diffusion approximation, the mean square displacement (MSD) of diffusing molecules is linearly proportional to the diffusion coefficient D and the time t during which the diffusion process is observed [ 56]: (1) MSD = 2 N D t, where N is the "dimensionality" of the space over which diffusion distances are measured.
A Lévy walk leads to anomalous diffusion, meaning that the mean squared displacement from the starting point increases faster than linearly with time t, while Brownian walks is a normal diffusion where the increase is linear.
The motion is analyzed in terms of a mean-squared displacement, diffusion coefficient, and radius of gyration.
Their trajectories were analyzed quantitatively to determine their mean square displacement (MSD), diffusion coefficient (D), confinement index (L), and confinement area L2 (see Materials and Methods).
These parameters include mean squared displacement (MSD), diffusion coefficient (D ), and radius of confinement (rconf).
The anomalous diffusion is characterized by a scaling parameter γ as well as the diffusion constant D and the mean square displacement of diffusing species 〈 r 2 ( t ) 〉 scales as a nonlinear power law in time, i.e., 〈 r 2 ( t ) 〉 ∼ t γ [7 9].
The lithium ion diffusion was studied by mean square displacement calculations and it was found that the self-diffusion coefficient just depends on the Li content.
In the limit q→ 0, i.e., in the absence of the external AC electric field, Equation 8 is reduced to the mean square displacement (MSD) relation for diffusion in the long-time limit, σxx = 2Dt, where D is diffusion coefficient given as Einstein's relation D = k B T ξ [30].
