Energy fluctuations in one dimensional Zhang sandpile model

We consider the Zhang sandpile model in one-dimension (1D) with locally conservative (or dissipative) dynamics and examine its total energy fluctuations at external drive time scale. The bulk-driven system leads to Lorentzian spectra, a cutoff $T$ growing linearly size $L$. show $1/f^{\alpha}$ behavior $\alpha \sim 1$ for boundary drive, varies non-linearly. For local dynamics, shows power-law growth $T L^{\lambda}$ that differs from an exponential form $ \exp(\mu L)$ observed nonconservative case. suggest dissipation is not necessary ingredient of 1D get $1/f$ noise, can reveal distinct nature dynamics. also discuss random dissipation.