We study stochastic processes of ultraslow diffusion in the presence of instantaneous Poissonian stochastic resetting (SR). We present the analytical results which are in close agreement with the findings from computer simulations for the main standard characteristics of this SR-process, such as the mean-squared displacement (MSD), the time-averaged MSD (TAMSD), the probability-density function (PDF), and the mean first-passage time (MFPT) of the tracers. In particular, we demonstrate the nonergodicity of the ultraslow SR-process featuring MSD ≠ TAMSD, the non-Gaussianity of the resulting long-time PDF in the realized nonequilibrium stationary state, as well as the existence of an optimal reset rate minimizing the MPFT to a target. Via comparing the current results for logarithmically slow processes under SR to the main characteristics of Poissonian-reset (i) power-law fractional Brownian motion, (ii) heterogeneous-diffusion processes, and (iii) exponentially fast geometric Brownian motion, we demonstrate the universality of many key statements regarding the MSD, TAMSD, PDF, and MFPT behaviors for these mathematically very different stochastic processes under the conditions of SR.

We consider the fractional Langevin equation far from equilibrium (FLEFE) to describe stochastic dynamics which do not obey the fluctuation-dissipation theorem, unlike the conventional fractional Langevin equation (FLE). The solution of this equation is Riemann-Liouville fractional Brownian motion (RL-FBM), also known in the literature as FBM II. Spurious nonergodicity, stationarity, and aging properties of the solution are explored for all admissible values α>1/2 of the order α of the time-fractional Caputo derivative in the FLEFE. The increments of the process are asymptotically stationary. However when 1/2<α<3/2, the time-averaged mean-squared displacement (TAMSD) does not converge to the mean-squared displacement (MSD). Instead, it converges to the mean-squared increment (MSI) or structure function, leading to the phenomenon of spurious nonergodicity. When α≥3/2, the increments of FLEFE motion are nonergodic, however the higher order increments are asymptotically ergodic. We also discuss the aging effect in the FLEFE by investigating the influence of an aging time t_{a} on the MSD, TAMSD and autocovariance function of the increments. We find that under strong aging conditions the process becomes ergodic, and the increments become stationary in the domain 1/2<α<3/2.

Dense oxygen ion conducting ceramic membranes with CO₂ resistance can promote many advanced applications like membrane reactors for green chemical synthesis and oxy‐fuel combustion for clean energy delivery. In article number 1800701, a hybrid dual‐phase membrane is developed, which displays high CO₂ resistance but still maintaining good oxygen fluxes at high operation temperatures. This cover is showcasing research arising from the collaboration between the laboratories of Prof. Shuguang Zhang, Shandong University of Technology, China, and Prof. Shaomin Liu, Curtin University, Australia. More details can be found in article number 1800701 by Shuguang Zhang, Shaomin Liu, and co‐workers.

The effects of "diffusing diffusivity” (DD), a stochastically time-varying diffusion coefficient, are explored within the frameworks of three different forms of fractional Brownian motion (FBM): (i) the Langevin equation driven by fractional Gaussian noise (LE-FBM), (ii) the Weyl integral representation introduced by Mandelbrot and van Ness (MN-FBM), and (iii) the Riemann-Liouville fractional integral representation (RL-FBM) introduced by Lévy. The statistical properties of the three FBM-generalized DD models are examined, including the mean-squared displacement (MSD), mean-squared increment (MSI), autocovariance function (ACVF) of increments, and the probability density function (PDF). Despite the long-believed equivalence of MN-FBM and LE-FBM, their corresponding FBM-DD models exhibit distinct behavior in terms of MSD and MSI. In the MN-FBM-DD model, the statistical characteristics directly reflect an effective diffusivity equal to its mean value. In contrast, in LE-FBM-DD, correlations in the random diffusivity give rise to an unexpected crossover behavior in both MSD and MSI. We also find that the MSI and ACVF are nonstationary in RL-FBM-DD but stationary in the other two DD models. All DD models display a crossover from a short-time non-Gaussian PDF to a long-time Gaussian PDF. Our findings offer guidance for experimentalists in selecting appropriate FBM-generalized models to describe viscoelastic yet non-Gaussian dynamics in bio- and soft-matter systems with heterogeneous environments.

Based on the multiple barriers concept of deep geological disposal of high-level waste, fractional advection diffusion equations for radionuclide migration in multiple layers low-permeability porous media are proposed in this work. The presented fractional advection diffusion models in terms of different definitions of fractional derivative are analytically addressed via the Laplace integral transform method. This work provides a theoretical foundation for further simulations of radionuclide migration in the multiple barriers system of the high-level waste repository.