Multiscale Patterning from Competing Interactions and Length Scales.

We live in a research era marked by impressive new tools powering the scientific method to accelerate the discovery, prediction, and control of increasingly complex systems. In common with many disciplines and societal challenges and opportunities, materials and condensed matter sciences are beneficiaries. The volume and fidelity of experimental, computational, and visualization data available, and tools to rapidly interpret them, are remarkable. Conceptual frameworks, including multiscale, multiphysics modeling of this complexity, are fueled by the data and, in turn, guide directions for future experimental and computational strategies. In this spirit, I discuss the importance of competing interactions, length scales, and constraints as pervasive sources of spatiotemporal complexity. I use representative examples drawn from materials and condensed matter, including the important role of elasticity in some technologically important quantum materials. Expected final online publication date for the Annual Review of Materials Research, Volume 50 is July 1, 2020. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.