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Solutions Derived for 140-Year-Old Boltzmann Equation

May 26, 2010

University of Pennsylvania mathematicians Philip T. Gressman and Robert M. Strain III have found solutions to the 140-year-old, 7-dimensional Boltzmann equation.

The equation maintains a significant place in history because it modeled gaseous behavior; its predictions have been backed up by experimentation. The solutions of this equation describe the location of gas molecules probabilistically, along with the likelihood that a molecule will reside at a particular location and have a particular momentum at a given time.

Derived by James Clerk Maxwell in 1867 and Ludwig Boltzmann in 1872, the equation, according to Strain, "grants a fundamental example where a range of geometric fractional derivatives occur in a physical model of the natural world.” The mathematical techniques that lead to the breakthrough had only been developed in the modern era.

The mathematicians reported their findings in "Global Classical Solutions of the Boltzmann Equation with Long-Range interactions," which appeared in Proceedings of the National Academy of Sciences (March 15, 2010).

Source: University of Pennsylvania (May 12, 2010)

Start Date: 
Wednesday, May 26, 2010