How do waves spread, stall, or pile up in materials that are both messy and “open”—leaking energy to their surroundings? Researchers at the Institute of Physics, Chinese Academy of Sciences have derived a compact mathematical rule, the universal Thouless relations (UTRs), that links two seemingly separate things: how densely energy levels populate the spectrum, and how strongly waves grow or decay across the system. The relations work for a broad family of one-dimensional disordered, non-Hermitian models, predict the boundary between two kinds of wave trapping without heavy computation, and uncover a new type of “half-localized, half-fractal” critical state with no counterpart in ordinary closed systems.

POSTECH Professor Sunmin Ryu’s team analyzes structural inhomogeneity in large-area thin films using interferometric SHG imaging.

Future math teachers may be the key to bringing data science into high‑school classrooms, and curriculum designed by researchers from Iowa State University and the University of Northern Iowa is helping pre-service teachers build their data‑science skills by tapping into the math they already know. 

In International Journal of Extreme Manufacturing, researchers have created a wearable sensor that reads the chemical signature of human breath to translate silent mouth movements into text. Built on standard silicon wafers, the device uses a microscopic, tree-like structure to capture the rapid water vapor changes that occur when a person mouths words.

researchers at Virginia Tech have developed an “acoustic atom” — a chip-scale device that traps and controls sound waves in ways that mimic the behavior of real atoms. Long term, these advances could influence technologies connected to quantum artificial intelligence (AI), telecommunication, medical imaging, GPS, and more.