Hybrid or multiphysics algorithms provide an efficient computational tool for combining microand macroscale descriptions of physical phenomena. Their use becomes imperative when microscale descriptions are too computationally expensive to be conducted in the whole domain, while macroscale descriptions fail in a small portion of the computation domain. We present a hybrid algorithm to model a ge...

The macaque brain serves as a model for the human brain, but its suitability is challenged by unique human features, including connectivity reconfigurations, which emerged during primate evolution. We perform a quantitative comparative analysis of the whole brain macroscale structural connectivity of the two species. Our findings suggest that the human and macaque brain as a whole are similarly...

Stochastic chemical systems with diffusion are modeled with a reactiondiffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic level, the master equation for a well stirred chemical system is combined with Brownian motion in space to obtain the reactiondiffusion master equation. The space...

One of the key goals of macromolecular modeling is to elucidate how macroscale physical properties arise from the microscale behavior of the polymer constituents. For many biological and industrial applications, a direct simulation approach is impractical due to to the wide range of length scales that must be spanned by the model, necessitating physically sound and practically relevant procedur...

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...