Long-range anticorrelations and non-Gaussian behavior of a leaky faucet.

We nd that intervals between successive drops from a leaky faucet display scale-invariant, long-range anticorrelations characterized by the same exponents of heart beat-to-beat intervals of healthy subjects. This behavior is also connrmed by numerical simulations on lattice and it is faucet-width-and ow-rate-independent. The histogram for the drop intervals is also well described by a L evy distribution with the same index for both histograms of healthy and diseased subjects. This additional result corroborates the evidence for similarities between leaky faucets and healthy hearts underlying dynamics. Very recently, long-range power-law correlations have been reported in a wide variety of systems as DNA sequences 1], stock market uctuations 2], literary pieces 3] and heart beat intervals 4,5]. Due to this power-law behavior it is possible to characterize these diverse phenomena by critical exponents and, through the latter, to identify similarities between the systems, which have not been noticed before. In this Letter, we present a novel example of this connection. We measured experimentally the exponents from time series of drops in leaky faucets and we found the same values as obtained by Peng et al. 4] for heartbeat time series. Furthermore, we nd that the statistics of this process is also described by L evy distribution. Scale invariance and non-Gaussian behaviors were connrmed by a theoretical model for two-dimensional drops. Leaky faucets are dynamical systems presenting complex behavior in drop-to-drop interval time series. It has been connrmed by experimental data 6{9] and through numerical simulations 10]. The most relevant parameter in this case is the ow rate. In g. 1(a,b) we present two experimental time series and the return maps constructed plotting the time interval B(n) between drop n and drop n + 1 (we adopt the same notation as ref. 4]). The experimental setup is described in ref. 9]. Each set of experimental data consists of 8192 drops (8 Kdrops, hereafter). We measured fourteen sets at diierent ow rates. Recently, a numerical procedure to simulate dripping faucets was introduced 10]. This model is based on the near and next-nearest neighbor Ising model on a square lattice, where a spin up (down) represents the uid (air). The earth gravitation is imposed as a magnetic eld varying uniformly in the vertical direction, and the dynamics is mass-conservative. The return maps obtained from this model are quite similar to those measured on thin faucets 8,9] (inner diameter<1mm). From numerical simulations we have obtained time …