The relation between the Lyapunov modes (delocalized Lyapunov vectors) and the momentum autocorrelation function is discussed in two-dimensional hard-disk systems. We show numerical evidence that the smallest time-oscillating period of the Lyapunov modes is twice as long as the time-oscillating...

Originating with the Newark foot patrol experiment, research has found police foot patrols improve community perception of the police and reduce fear of crime, but are generally unable to reduce the incidence of crime. Previous tests of foot patrol have, however, suffered from statistical and...