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This work focuses on the dynamics of particles in a confined geometry with position-dependent diffusivity, where the confinement is modelled by a periodic channel consisting of unit cells connected by narrow passage ways. We consider three functional forms for the diffusivity, corresponding to the scenarios of a constant (D0), as well as a low (Dm) and a high (Dd) mobility diffusion in cell centre of the longitudinally symmetric cells. Due to the interaction among the diffusivity, channel shape and external force, the system exhibits complex and interesting phenomena. By calculating the probability density function, mean velocity and mean first exit time with the Itô calculus form, we find that in the absence of external forces the diffusivity Dd will redistribute particles near the channel wall, while the diffusivity Dm will trap them near the cell centre. The superposition of external forces will break their static distributions. Besides, our results demonstrate that for the diffusivity Dd, a high dependence on the x coordinate (parallel with the central channel line) will improve the mean velocity of the particles. In contrast, for the diffusivity Dm, a weak dependence on the x coordinate will dramatically accelerate the moving speed. In addition, it shows that a large external force can weaken the influences of different diffusivities; inversely, for a small external force, the types of diffusivity affect significantly the particle dynamics. In practice, one can apply these results to achieve a prominent enhancement of the particle transport in two- or three-dimensional channels by modulating the local tracer diffusivity via an engineered gel of varying porosity or by adding a cold tube to cool down the diffusivity along the central line, which may be a relevant effect in engineering applications. Effects of different stochastic calculi in the evaluation of the underlying multiplicative stochastic equation for different physical scenarios are discussed.

The mechanical-diffusion coupling behavior between molar concentration and strain fields have aroused great interest in biosensors, artificial muscles and actuators of adaptive structures and so on. In such nonuniform concentration environment, the space-dependent diffusivity verified in experimental observation is still not considered. Present work aims to establish the non-Fick mechanical-diffusion model with space-dependent diffusivity. To numerically solve the nonlinear governing equations, the time-domain finite element method is developed based on the principle of virtual work. The newly established model and numerical approach are applied to investigate impact responses of a thick circular plate with space-dependent diffusivity under transient chemical shock loadings. With the increase in the space-dependent diffusivity parameter, the dimensionless results reveal that the diffusive wave propagation is proportionally accelerated. And the nonlinear mechanical/chemical responses are maximally enhanced.

While inhomogeneous diffusivity has been identified as a ubiquitous feature of the cellular interior, its implications for particle mobility and concentration at different length scales remain largely unexplored. In this work, we use agent-based simulations of diffusion to investigate how heterogeneous diffusivity affects the movement and concentration of diffusing particles. We propose that a nonequilibrium mode of membrane-less compartmentalization arising from the convergence of diffusive trajectories into low-diffusive sinks, which we call ‘diffusive lensing,’ is relevant for living systems. Our work highlights the phenomenon of diffusive lensing as a potentially key driver of mesoscale dynamics in the cytoplasm, with possible far-reaching implications for biochemical processes.