Crossover in rescaled-range analysis and power spectra: Measurements and simulations

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Abstract
We have measured and simulated particle flow through a single pore and made comparisons with theory. The simulations are based on an experimental system where particles suspended in an electrolyte are caused to flow by pressure difference through a pore. Each particle in the pore gives rise to a pulse in the measured pore resistance. The pulse height is proportional to the particle volume and the pulse width is given by the particle velocity. In dilute solutions individual particle pulses can be detected and analyzed, but at higher concentrations the pulses start to overlap and the signal looks like noise. Measured and simulated signals are analyzed in terms of Hurst’s rescaled-range (the R/S analysis, where R is the range and S the standard deviation) and the power spectrum. The signal is sampled and we find a clear crossover from persistent behavior (Hurst exponent H≃1) for short times corresponding to the fact that particles reside a finite time in the pore to an independent process (H≃0.5) corresponding to the uncorrelated entry of particles into the pore. The calculated effective Hurst exponent depends on the time resolution (sampling interval) used, but R/S curves for different sampling intervals scale when reduced time (sampling interval divided by pulse width) is included in the analysis and yields a nice data collapse for experiments on different types of particles, flow rates, and pore sizes.

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