Seeing stable relationships in a new light with a little help from advanced mathematics
When Joseph Louis Lagrange in 1762 derived the equation of minimal surfaces, he could not possibly suspect its deep connections with the theory of phase transitions, which would only be developed two centuries later. We are all familiar with some phase transitions such as ice melting in water. But there are dozens of them which are critical to daily activity and human innovation: metals in an alloy, superconductivity, decision boundaries in finance, liquid crystals, combustion, optimal design of insulators, and many more. Despite the ubiquitous nature and significance of phase transitions, our ability to analyse their stable behaviours mathematically is astoundingly limited. The EU-funded StableIF project combines recent advances with classical tools from the theory of minimal surfaces to develop the mathematical analysis that will enhance our understanding of stable phase transitions.
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