"Diffusing diffusivity": A model of "anomalous yet Brownian" diffusion


Chubynsky, M. (2013). "Diffusing diffusivity": A model of "anomalous yet Brownian" diffusion. Perimeter Institute. https://pirsa.org/13120024


Chubynsky, Mykyta. "Diffusing diffusivity": A model of "anomalous yet Brownian" diffusion. Perimeter Institute, Dec. 05, 2013, https://pirsa.org/13120024


          @misc{ pirsa_PIRSA:13120024,
            doi = {10.48660/13120024},
            url = {https://pirsa.org/13120024},
            author = {Chubynsky, Mykyta},
            keywords = {},
            language = {en},
            title = {"Diffusing diffusivity": A model of "anomalous yet Brownian" diffusion},
            publisher = {Perimeter Institute},
            year = {2013},
            month = {dec},
            note = {PIRSA:13120024 see, \url{https://pirsa.org}}

Mykyta Chubynsky University of Ottawa


Wang et al. [PNAS 106 (2009) 15160] have found that in several systems, the linear time dependence of mean-square displacement (MSD) of diffusing colloidal particles, typical of normal diffusion, is accompanied by a non-Gaussian displacement distribution (DD), with roughly exponential tails at short times, a situation termed “anomalous yet Brownian” diffusion. We point out that lack of “direction memory” in the particle trajectory (a jump in a particular direction does not change the probability of subsequent jumps in that direction) is sufficient for a strictly linear MSD (assuming that the system is pre-equilibrated), but if at the same time there is “diffusivity memory” (a particle diffusing faster than average is likely to keep diffusing faster for some time), the DD will be non-Gaussian at short times. A gradual change in diffusivity can be due to the environment of the particle changing slowly on its own, the particle moving between different environments, or both. In our model, this is represented by the particle diffusivity itself undergoing a (perhaps biased) random walk (“diffusing diffusivity”). Roughly exponential tails of the DD, as in experiment, are observed in several variants of the model.