BLAST AND SPLASH IN A COLD GAS

Pavel Krapivsky (Personal webpage)

We study the response of a cold gas (all particles are initially at rest) to a sudden kick when one particle suddenly starts moving. The outcome is a spherical shock wave advancing as \(t^\frac{2}{d+2}\). The density, velocity, and temperature behind the shock are described by Euler equations. Deviations from the predictions of non-dissipative hydrodynamics arise in the central region that grows as \(t^\frac{38}{93}, ~t^\frac{2}{5}, ~t^\frac{62}{175}\) when \(d=1,2,3\). In a one-dimensional semi-infinite setting, when the left-most particle suddenly starts moving to the right, a growing number of "splatter" particles penetrate the initially empty half-line. The total energy and momentum of the splatter particles exhibit counterintuitive behaviors.