The characteristics of solute transport within log-conductivity fields represented by power-law semi-variograms are investigated by an analytical Lagrangian approach that accounts for the automatic frequency cut-off induced by the initial contaminant plume size. The transport process anomaly is critically controlled by the magnitude of the Péclet number. Interestingly enough, unlike the case of...

We present a general derivation of the non-Fickian behavior for the self-diffusion of identically interacting particle systems with excluded mutual passage. We show that the conditional probability distribution of finding a particle at position x(t) after time t, when the particle was located at x(0) at t=0, follows a Gaussian distribution in the long-time limit, with variance 2W(t) approximate...

Accumulated experimental information is used to assess the possible significance of thermal diffusion to mass transport in living matter. Possible thermal gradients across membranes, a single living cell, and an ensemble of such cells (e.g. an organ, tumor, etc.) are estimated. The corresponding model calculations, although not describing the biological process in detail, lead to conclusions ab...

The motion of nanoparticles (NPs) in entangled melts of linear polymers and nonconcatenated ring polymers are compared by large-scale molecular dynamics simulations. The comparison provides a paradigm for the effects of polymer architecture on the dynamical coupling between NPs and polymers in nanocomposites. Strongly suppressed motion of NPs with diameter d larger than the entanglement spacing...

Mathematical analysis is presented of the water transport and drug release from hydrophilic tablets coated with impermeable coatings. Numerical solutions are provided for a number of cases of partial coating. It is shown that depending on the restriction provided to the tablets by the coating, Fickian or non-Fickian transport can be

We consider discrete schemes for a nonlinear model of non-Fickian diffusion in viscoelastic polymers. The model is motivated by, but not the same as, that proposed by Cohen et al. in SIAM J. Appl. Math., 55, pp. 348–368, 1995. The spatial discretisation is effected with both the symmetric and non-symmetric interior penalty discontinuous Galerkin finite element method, and the time discretisatio...

The classical wave-of-advance model of the neolithic transition (i.e., the shift from hunter-gatherer to agricultural economies) is based on Fisher’s reaction-diffusion equation. Here we present an extension of Einstein’s approach to Fickian diffusion, incorporating reaction terms. On this basis we show that second-order terms in the reaction-diffusion equation, which have been neglected up to ...

A new model was developed for drug release from microspheres. Drug dissolution, diffusion, moving front, and size distribution were considered as main release mechanisms. The proposed dissolution-diffusion model was solved numerically for analysis of dissolved drug concentration profiles. In comparison with Fickian diffusion model and Koizumi model, the proposed model is characteristic of the w...