Diffusion behaviors of heterogeneous materials are paramount importance in many engineering problems. Numerical models that take into account the internal structure such robust but computationally very expensive. This burden can be partially decreased by using discrete models, however even then practical application is limited to relatively small material volumes. paper formulates a homogenizat...

We consider diffusion-controlled release of particles from d-dimensional radially-symmetric geometries. A quantity commonly used to characterise such diffusive processes is the proportion remaining within geometry over time, denoted as P(t). The stochastic approach for computing P(t) time-consuming and lacks analytical insight into key parameters while continuum yields complicated expressions t...

An overview of the edge detection techniques based on partial differential equations (PDE) is presented in this work. Nonlinear anisotropic diffusion-based boundary extraction approaches, like influential Perona- Malik model and some improved variants it, are described first. Anisotropic schemes using mean curvature motion nonlinear PDE-based approaches combining diffusion to bilateral filter t...