Correlation dimension of the sheared hard-disk Lorentz gas

The correlation dimension for the isokinetic Lorentz gas is calculated for hard disks using nonequilibrium molecular dynamics simulation. The trajectories are confined to a strange attractor embedded in a four-dimensional phase space - the additional degree of freedom having not been included properly until this work. This degree of freedom accounts for the explicit time dependence of the system (as quantified by the moving periodic cells under shear) and is significant because the collisions tend to synchronize with the periodic change of symmetry of the lattice at high shear rates