Continuous time random walk (CTRW) subdiffusion along with the associated fractional Fokker-Planck equation (FFPE) is traditionally based on the premise of random clock with divergent mean period. This work considers an alternative CTRW and FFPE description which is featured by finite mean residence times (MRTs) in any spatial domain of finite size. Transient subdiffusive transport can occur on...

We consider weak solutions of hyperbolic conservation laws as singular limits of solutions for associated complex regularized problems. We are interested in situations such that undercompressive (Non-Laxian) shock waves occur in the limit. In this setting one can view the conservation law as a macroscale formulation while the regularization can be understood as the microscale model. With this p...

Knowledge of location and magnitude of charge density, together with the pore morphology allows one to calculate the Donnan potential, characterizing ion exclusion in charged porous materials. Use of the electro-chemical potential together with Gauss’ electrostatic theorem allows the computation of the ion and voltage distribution at the microscale. On the other hand, commonly used macroscopic ...

In many problems of multiscale modeling, we are interested in capturing the macroscale behavior of the system with the help of some accurate microscale models, bypassing the need of using empirical macroscale models. This paper gives an overview of the recent efforts on establishing general strategies for designing such algorithms. After reviewing some important classical examples, the Car-Parr...

Maps serve as a ubiquitous organizing principle in the mammalian brain. In several sensory systems, such as audition, vision, and somatosensation, topographic maps are evident throughout multiple levels of brain pathways. Topographic maps, like retinotopy and tonotopy, persist from the receptor surface up to the cortex. Other maps, such as those of orientation preference in the visual cortex, a...

Prokaryotic flagellum is considered as the only known example of a biological “wheel,” system capable converting action rotatory actuator into continuous propulsive force. For this reason, flagella are an interesting case study in soft robotics and they represent appealing source inspiration for design underwater robots. A great number flagellum-inspired devices exists, but these ...