Universal spectral features of different classes of random diffusivity processes

Abstract

.Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments and the displacement probability density function. Here we develop the complementary power spectral description for a broad class of random diffusivity processes. In our approach we cater for typical single particle tracking data in which a small number of trajectories with finite duration are garnered. Apart from the diffusing-diffusivity model we study a range of previously unconsidered random diffusivity processes, for which we obtain exact forms of the probability density function. These new processes are different versions of jump processes as well as functionals of Brownian motion. The resulting behaviour subtly depends on the specific model details. Thus, the central part of the probability density function may be Gaussian or non-Gaussian, and the tails may assume Gaussian, exponential, log-normal or even power-law forms. For all these models we derive analytically the moment-generating function for the single-trajectory power spectral density. We establish the generic $1/f^2$-scaling of the power spectral density as function of frequency in all cases. Moreover, we establish the probability density for the amplitudes of the random power spectral density of individual trajectories. The latter functions reflect the very specific properties of the different random diffusivity models considered here. Our exact results are in excellent agreement with extensive numerical simulations.

39 pages, 11 figures, IOP LaTeX

References in corpus (21)

• Anomalous transport in the crowded world of biological cells
• "Diffusing diffusivity": A model for anomalous and "anomalous yet Brownian" diffusion
• Weak ergodicity breaking of receptor motion in living cells stemming from random diffusivity
• Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
• Diffusion-limited reactions in dynamic heterogeneous media
• First passages for a search by a swarm of independent random searchers
• Spectral content of a single non-Brownian trajectory
• Strong defocusing of molecular reaction times results from an interplay of geometry and reaction control
• Statistics of 3-dimensional Lagrangian turbulence
• Non-ergodicity, fluctuations, and criticality in heterogeneous diffusion processes
• Measurement of Anomalous Diffusion Using Recurrent Neural Networks
• Characterizations and simulations of a class of stochastic processes to model anomalous diffusion
• Non-Markovian diffusion equations and processes: analysis and simulations
• Ergodicity breaking in geometric Brownian motion
• Brownian motion and beyond: first-passage, power spectrum, non-Gaussianity, and anomalous diffusion
• Heterogeneities Shape Passive Intracellular Transport
• Anomalous fluctuations of currents in Sinai-type random chains with strongly correlated disorder
• Helix or Coil? Fate of a Melting Heteropolymer
• Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems
• Codifference can detect ergodicity breaking and non-Gaussianity
• Anomalous Dynamical Responses in a Driven System

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