Complex Systems and Biological Physics Seminars
Lattice points on circles and the discrete velocity model for the Boltzmann equation
by
→
Europe/Stockholm
Description
In the context of the Discrete Velocity Model (DVM) for the Boltzmann equation in the plane, it is interesting to know whether lattice points on circles are angularly equidistributed. Using results from analytic number theory, namely certain bounds on mean values of multiplicative functions, we can show that lattice points on circles are angularly equidistributed on average, and from this it follows that the DVM is consistent. (Joint with L. Fainsilber and B. Wennberg.) Time permitting we will discuss which probability measures on the unit circle that ``comes from'' lattice points on circles.