arXiv subjects

Sławomir Wąsik

Publications and source records attributed to Sławomir Wąsik.

2 recordsLinked to original sources

arXiv2022

Subdiffusion equation with Caputo fractional derivative with respect to another function in modelling diffusion in a complex system consisting of matrix and channels

Diffusion equation with a fractional Caputo time derivative with respect to another function $g$, which defines new time scale of the process, is applied to describe anomalous diffusion of antibiotic (colistin) in a system consisting of packed gel (alginate) beads immersed in water and impregnated with the antibiotic. We show that ultraslow diffusion of colistin in the system occurs. The equation, which is more general than the "ordinary" fractional subdiffusion equation, can be widely used in various fields of science to model diffusion in a matrix with channels system when subdiffusion parameters and even a type of diffusion evolves over time.

cond-mat.stat-mech↗

arXiv2017

How to determine a boundary condition at a thin membrane for diffusion from experimental data

We present a new method of deriving a boundary condition at a thin membrane for diffusion from experimental data. Based on experimental results obtained for normal diffusion of ethanol in water, we show that the derived boundary condition at a membrane contains a term with the Riemann--Liouville fractional time derivative of the $1/2$ order. Such a form of the boundary condition shows that a transfer of particles through a thin membrane is a `long memory process'. Presented method is an example that an important part of mathematical model of physical process may be derived directly from experimental data.

cond-mat.stat-mech↗