Spectral design of anomalous diffusion

Iddo Eliazar

Physica A: Statistical Mechanics and its Applications, 2023, vol. 626, issue C

Abstract: This paper poses and addresses the following goal: design a random motion that displays one type of anomalous diffusion in real space, and another type of anomalous diffusion in Fourier space. The two prominent Gaussian and selfsimilar anomalous-diffusion models – scaled Brownian motion (SBM), and fractional Brownian motion (FBM) – are not up to the task. This paper establishes a class of random motions that are up to the task. As a ‘bonus’, the random-motions’ velocities are also up to an additional task: generating flicker noise (1/f noise) behaviors. In general, the random motions are neither Gaussian nor selfsimilar. When both Gaussian and selfsimilar then the resulting random motion is a ‘hybrid’ Brownian model: it generalizes SBM on the one hand, and it generalizes the Riemann–Liouville FBM on the other hand.

Keywords: Mean square displacement; Spectral density; Anomalous diffusion; Flicker noise (1/f noise); Selfsimilarity (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:626:y:2023:i:c:s0378437123006210

DOI: 10.1016/j.physa.2023.129066

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