Power spectrum of rare events in a two-dimensional BTW model. (29th August 2018) - Moghadam, Z; Najafi, M N; Saber, A; Ebadi, Z
Abstract: One of the primary aims of the two-dimensional BTW model had been to explain the 1/ f α noise which is widely seen in the natural systems. In this paper we study some time signals, namely the activity inside an avalanche ( x ( t )), the avalanches sizes ( s ( T )) and the rare events waiting time ( τ ( n ) as a new type of noise). The latter is expected to be important in predicting the period and also the vastness of the upcoming large scale events in a sequence of self-organized natural events. Especially we report some exponential anti-correlation behaviors for s ( T ) and τ ( n ) which are finite size effects. Two characteristic time scales δT s and δT τ emerge in our analysis, and the power spectrum of s ( T ) and τ ( n ) behave like ( b s, τ ( L ) 2 + ω 2 ) − 1, in which b s and b τ are some L -dependent parameters and ω is the angular frequency. The 1/ f 2 noise is therefore obtained in the limit ω ≫ b s, τ . b s and b τ decrease also in a power-law fashion with the system size L, which signals the fact that in the thermodynamic limit the power spectrum tends to the Dirac delta function.