Slowly varying, macroscale models emerge from microscale dynamics over multiscale domains

Patch Dynamics for Multiscale Problems Bridging the Macroscale and Microscale

There are important systems—those that couple molecular dynamics with a material’s macroscale behavior or use a Boltzmann particle model to predict large-scale patterns in a fluid flow, for example—that must be modeled on relatively long time or space scales, but the dynamics can be advanced only on short time or space scales. First developed by Yannis Kevrekidis and his collaborators,1–5 patch...

Simulating macroscale brain circuits with microscale resolution

Building macroscale models from microscale probabilistic models: a general probabilistic approach for nonlinear diffusion and multispecies phenomena.

A discrete agent-based model on a periodic lattice of arbitrary dimension is considered. Agents move to nearest-neighbor sites by a motility mechanism accounting for general interactions, which may include volume exclusion. The partial differential equation describing the average occupancy of the agent population is derived systematically. A diffusion equation arises for all types of interactio...

Resolving macroscale and microscale heterogeneity in virus filtration

In this paper, we characterize the filtration and deposition profiles of a recombinant analog of Norwalk virus, an important waterborne pathogen, in packed beds of saturated quartz sand under both ‘clean-bed’ and ‘dirty-bed’ conditions. Under clean-bed conditions with NaCl as the electrolyte, the retained Norwalk virus particles decline like a power-law with depth. The power-law decay in retain...

A Spotlight on Bridging Microscale and Macroscale Human Brain Architecture

We place a spotlight on the emerging trend of jointly studying the micro- and macroscale organization of nervous systems. We discuss the pioneering studies of Ding et al. (2016) and Glasser et al. (2016) in the context of growing efforts to combine and integrate multiple features of brain organization into a multi-modal and multi-scale examination of the human brain.