There is a growing recognition of diffusion in nonstatic media across a spectrum of scientific fields, from cosmology to biology. This paper focuses on more complex practical scenarios of center-of-mass (c.m.) motion of polymers, which is not only determined by the basic motion of time-changed Brownian motion but also regulated by the fluctuations of polymer size and the nonstatic medium. A diffusing diffusivity (DD) model describing the motion of the c.m. is established. By introducing comoving coordinates and the physical coordinate system, based on the DD model, the important statistical quantities of the c.m. are calculated, and the dynamic behavior of the c.m. is further systematically analyzed. Specifically, the motion characteristics of the c.m. in exponential and power-law media are investigated, leading to several interesting conclusions: in exponential media, the c.m. motion is primarily dominated by the medium; while in power-law media, classification is performed with $\alpha /2$ as the critical value, and the c.m. is dominated by the medium and time-changed Brownian motion, respectively. In particular, the kurtosis reveals that DD-induced non-Gaussianity persists in exponentially expanding media and in strongly expanding power-law media. Finally, we derive thoroughly the Feynman-Kac equation corresponding to the DD model under time-changed Brownian motion in nonstatic media and verify its correctness.

Close

PrevNext

View figure in article

• Brownian motion
• Chemical reactions
• Diffusion
• Polymers