Viscous attractor for the Galton board.
We analyze the Galton Board [or periodic "Lorentz Gas"] with a point mass scattered by elastic disks of diameter sigma, using a constant driving field g and a constant-viscosity linear drag force -p/tau, where p is the point-mass momentum. This combination leads to a nonequilibrium steady state which depends only upon the dimensionless ratio gtau(2)/sigma. The long-time-averaged trajectory leads to multifractal phase-space structures closely resembling those we found earlier using isokinetic equations of motion derived from Gauss' Principle of Least Constraint. A highly damped [small tau] creeping-flow limit describes our results for gtau(2)/sigma less than about 0.2. The lightly damped Green-Kubo linear-response limit for the model provides an accurate description of the dissipative dynamics for gtau(2)/sigma greater than about 2.0.
Hoover
W. G.
WG
Department of Applied Science, University of California at Davis/Livermore and Lawrence Livermore National Laboratory, Livermore, California 94550.
Moran
B.
B