MATH-BASED MANAGEMENT “Battleship”-Style Math Can Improve Sustainable Design, Groundwater Management, Nuclear Waste Storage and More
Scientists can now accurately determine where randomly distributed components appear in concrete, soil, and other common materials using a statistical model. The findings could enable the design of better, stronger, cheaper materials.
In an approach reminiscent of the classic board game Battleship, Stanford researchers have discovered a way to characterize the microscopic structure of everyday materials such as sand and concrete with high precision.
Heterogeneous, or mixed, materials have components in random locations. For example, concrete – the most abundant human-made material – is composed of cement, water, sand, and coarse stone. Predicting where a particular component appears in a jumbled mosaic of concrete or in Earth’s subsurface can help researchers understand how to design stronger materials, evaluate the long-term viability of potential sites for underground storage of carbon dioxide or nuclear waste, and answer other critical questions about the behavior of complex systems. But previous modeling efforts have fallen short.
In an Oct. 9 study in Physical Review Letters, researchers show a new mathematical approach to unlocking information about the composition of a material based on knowledge of any other random point – like taking a shot in Battleship. The approach is based on a common statistical method known as a Poisson model.
“With this study, we’ve solved the famous Poisson model for heterogenous materials,” said lead study author Alec Shelley, a PhD student in applied physics in Daniel Tartakovsky’s lab at the Stanford Doerr School of Sustainability. “Our result could have a broad impact on several areas of science, because heterogenous materials are common and their models almost never have exact solutions.”
Because a vast range of useful properties stem from microstructural arrangements like those in concrete, the new findings could enable the design of better, stronger, cheaper materials.
“What Alec has succeeded in doing in this study is quite remarkable,” said Tartakovsky, a professor of energy science and engineering. “Using his approach, you could design a composite material to your specifications and obtain certain properties based on the proper mixture of components.”
Abundant applications
Looking ahead, Shelley and Tartakovsky are interested in applying the mathematical solution to predict the compositions of several materials. The model reveals “a huge list” of properties tied to microstructure, Shelley said, including hardness, elasticity, tensile strength, electrical and heat conductivity, how quickly a substance moves through another substance, magnetic susceptibility, light transmittance, and more.
