210Pb-Derived Bioturbation Rates in Sediments Around Seamounts in the Tropical Northwest Pacific

To evaluate bioturbation coefficients (DB) and mixing depths (L), 210Pb and 226Ra activity was measured in two sediments cores (from water depths of 5,398 m and 4,428 m), which were collected from seamount areas in the Northwest Pacific. Using a steady-state diffusion mode, we estimated DB values of 16.8 and 24.1 cm2/a, higher than those in abyssal sediments and those predicted by traditional empirical equations. Corresponding L values varied between 19.3 and 23.1 cm. These high values indicate that seamounts are the area of active bioturbation. A one-dimensional model for the transport of total organic carbon (TOC) from the surface layer of sediments to the deep layer was developed using the distribution pattern of the specific activity of excess 210Pb (210Pbex) and its relationship with TOC. The model showed that the TOC flux transmitted downward by bioturbation was 0.09 mmol/(cm2⋅a) and 0.12 mmol/(cm2⋅a).

Exponential ergodicity and steady-state approximations for a class of markov processes under fast regime switching

We study ergodic properties of a class of Markov-modulated general birth–death processes under fast regime switching. The first set of results concerns the ergodic properties of the properly scaled joint Markov process with a parameter that is taken to be large. Under very weak hypotheses, we show that if the averaged process is exponentially ergodic for large values of the parameter, then the same applies to the original joint Markov process. The second set of results concerns steady-state diffusion approximations, under the assumption that the ‘averaged’ fluid limit exists. Here, we establish convergence rates for the moments of the approximating diffusion process to those of the Markov-modulated birth–death process. This is accomplished by comparing the generator of the approximating diffusion and that of the joint Markov process. We also provide several examples which demonstrate how the theory can be applied.

Gas Steady-state Diffusion in Fractal Porous Media

Gas diffusion in fractal pores does not follow the classic Fick’s and Knudsen’s laws, so more research on gas diffusion in fractal porous media is needed. Fractal pore models are generated using the random walk method. The gas diffusion governing equations for the fractal pores are derived from the classic kineti theory of gases. The gas diffusion model is used to study the gas diffusion in fractal porous meida and to determine steady-state diffusion coefficient formulas. The results show that the diffusion coefficient is proportional to the mean proe diameter, porosity, and the exponetial function of the fractal dimension in the Knudsen diffusion regime. The diffusion coefficient is not only related to the three pore parameters but is also related to the molecular mean free path in the configurational diffusion regime.