On the description of Brownian particles in confinement on a non-Cartesian coordinates basis.

We developed a theoretical framework to study the diffusion of Brownian point-like particles in bounded geometries in two and three dimensions. We use the Frenet-Serret moving frame as the coordinate system. For narrow tubes and channels, we use an effective one-dimensional description reducing the diffusion equation to a Fick-Jacobs-like equation.

On the covariant description of diffusion in two-dimensional confined environments.

A covariant description of diffusion of point-size Brownian particles in bounded geometries is presented. To this end, we provide a formal theoretical framework using differential geometry. We propose a coordinate transformation to map the boundaries of a general two-dimensional channel into a straight channel in a non-Cartesian geometry.