Dresden 2020 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 26: Brownian Motion, Transport and Anomalous Diffusion
DY 26.10: Talk
Tuesday, March 17, 2020, 12:30–12:45, HÜL 186
Infinite-densities and the Moses, Noah and Joseph effects in Levy walks — •Erez Aghion1, Vidushi Adlakha2, Kevin Bassler2, Holger Kantz1, and Philipp Meyer1 — 1mpiPKS, Dresden, Germany — 2U. Huston, Dep. of Physics, USA
When one is presented with an ensemble of data sets, each obtained as a time series, for example in an experiment, which anomalous diffusion, it is often not possible to know exactly the details of the underlying dynamics that produced it. The braking of the CLT can be decomposed into three root causes: temporal correlations in the process, statistical aging, and power-law distributions, known respectivley as the Joseph, Moses and Noah effects. These effects, are quantified individually, and measured individually from the time series.
We study this decomposition using numerical simulations, which are compared with analytical results, for a coupled Levy walk model, where the particle's velocity v at each step is decays nonlinearly with the step-duration Tau. The step durations are independent, identically distributed random variables, taken from the fat tailed distribution where the mean <Tau> is divergent. Here, recently it was shown [Akimoto et al., 2019] that the velocity distribution of the particles converges to a non-normalizable infinite-invariant density, when t approaches infinity. This scenario is tantamount to a sort-of ``temporal equilibrium", when we rescale the probability density properly with time. We study how this leads to a different manifestation of the three effects, depending on whether infinite-ergodic theory describes the time-average of |v| or v^2.