New Answer to 80-Year-Old Question Makes Computer Modeling 100,000 Times Faster | Popular Science: "A new formula allows computers to simulate how new materials behave up to 100,000 times faster than previously possible, and could drastically speed up innovation relating to electronic devices and energy-efficient cars. Princeton engineers came up with the model based on an 80-year-old quantum physics puzzle.
Llewellyn Hilleth Thomas and Nobel laureate Enrico Fermi first theorized in 1927 that they could calculate the energy of electrons in motion based on how electrons are distributed in a material. Knowing that kinetic energy of electrons in a material helps researchers understand the structure and properties of new materials, as well as how they might respond to physical stress.
But the Thomas-Fermi equation was based on a theoretical gas with electrons distributed evenly, and so it could not work for imperfect real materials. Pierre Hohenberg and Walter Kohn, another Nobel laureate, managed to prove that the Thomas-Fermi equation could apply to real materials in 1964. But they only established the groundwork to prove the equation's existence.
Researchers have tried calculating each atom's energy from scratch to simulate how a material might behave, but simulations beyond just a few hundred atoms bogged down even the most powerful computers. That put a severe limit on the types of materials that researchers could simulate.
By contrast, the Princeton team stuck it out with the Thomas-Fermi equation. They eventually came up with a working model that could predict the kinetic energy of electrons in simple metals. A slight modification also allowed the model to also work for semiconductors, which find use in a wide variety of electronic devices."
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