| In nature,many particles move irregularly in non-static media,and in recent years,Brownian non-Gaussian diffusion has been observed in biological systems.This paper focuses on the non-Gaussian diffusion of polymer in non-static media and investigates the effect of polymer size fluctuations on the Brownian non-Gaussian diffusion behavior for the center of mass.Firstly,we mainly establish a diffusing diffusivity model for polymer size fluctuations,linking the polymer size variation to the birth and death process,and introduce co-moving and physical coordinate systems to characterize the position for the center of mass in non-static media.Next,the important statistical quantities for the center of mass diffusing diffusivity model in non-static media,such as mean square displacement and kurtosis,are obtained by adopting the subordinate process approach,and the long-time asymptotic behavior of the mean square displacement in different types media is specifically analyzed.Finally,we derive in detail the bivariate Fokker-Planck equation and the FeynmanKac equation which correspond to the diffusing diffusivity model.It is found that when the initial size of the polymer satisfies the steady-state distribution,the center of mass shows non-Gaussian diffusion in the short time,but the probability density function for the center of mass returns to a Gaussian distribution after a long enough time.The common non-static media includes power-law media and exponential media.In power-law strongly expanding media,the center of mass shows superdiffusion,while in exponential contraction media,the mean square displacement for the center of mass asymptotically becomes a constant after sufficiently long time. |
