Applied mathematics articles from across Nature Portfolio

From monitoring sea-level changes at the millimetre-level to navigating through the streets of Gothenburg, Karine Le Bail discusses the need for precise positioning within well-defined 3D terrestrial and celestial reference frames.

Inspired by the morphologies of xeric plant leaves, we have developed biomimetic liquid crystal elastomer bilayers that can bend, spiral and twist. These adaptive shape morphing structures can twist to improve water collection efficiency and wind resistance, suggesting their potential application in adaptive water collection and directional transportation.

We introduce free-energy machine (FEM), an efficient and general method for solving combinatorial optimization problems. FEM combines free-energy minimization from statistical physics with gradient-based optimization techniques in machine learning and utilizes parallel computation, outperforming state-of-the-art algorithms and showcasing the synergy of merging statistical physics with machine learning.

We present Morpho, an extensible programmable environment that uses finite elements for shape optimization in soft matter. Given an energy functional that incorporates physical boundaries and effects such as elasticity and electromagnetism, together with additional constraints to be satisfied, Morpho predicts the optimized shape and structure adopted by the material.