TY - JOUR A1 - Guggenberger, Tobias A1 - Chechkin, Aleksei A1 - Metzler, Ralf T1 - Absence of stationary states and non-Boltzmann distributions of fractional Brownian motion in shallow external potentials JF - New journal of physics : the open-access journal for physics N2 - We study the diffusive motion of a particle in a subharmonic potential of the form U(x) = |x|( c ) (0 < c < 2) driven by long-range correlated, stationary fractional Gaussian noise xi ( alpha )(t) with 0 < alpha <= 2. In the absence of the potential the particle exhibits free fractional Brownian motion with anomalous diffusion exponent alpha. While for an harmonic external potential the dynamics converges to a Gaussian stationary state, from extensive numerical analysis we here demonstrate that stationary states for shallower than harmonic potentials exist only as long as the relation c > 2(1 - 1/alpha) holds. We analyse the motion in terms of the mean squared displacement and (when it exists) the stationary probability density function. Moreover we discuss analogies of non-stationarity of Levy flights in shallow external potentials. KW - diffusion KW - Boltzmann distribution KW - fractional Brownian motion Y1 - 2022 U6 - https://doi.org/10.1088/1367-2630/ac7b3c SN - 1367-2630 VL - 24 IS - 7 PB - Dt. Physikalische Ges. CY - [Bad Honnef] ER - TY - JOUR A1 - Sandev, Trifce A1 - Domazetoski, Viktor A1 - Kocarev, Ljupco A1 - Metzler, Ralf A1 - Chechkin, Aleksei T1 - Heterogeneous diffusion with stochastic resetting JF - Journal of physics : A, Mathematical and theoretical N2 - We study a heterogeneous diffusion process (HDP) with position-dependent diffusion coefficient and Poissonian stochastic resetting. We find exact results for the mean squared displacement and the probability density function. The nonequilibrium steady state reached in the long time limit is studied. We also analyse the transition to the non-equilibrium steady state by finding the large deviation function. We found that similarly to the case of the normal diffusion process where the diffusion length grows like t (1/2) while the length scale xi(t) of the inner core region of the nonequilibrium steady state grows linearly with time t, in the HDP with diffusion length increasing like t ( p/2) the length scale xi(t) grows like t ( p ). The obtained results are verified by numerical solutions of the corresponding Langevin equation. KW - heterogeneous diffusion KW - Fokker-Planck equation KW - Langevin equation KW - stochastic resetting KW - nonequilibrium stationary state KW - large deviation function Y1 - 2022 U6 - https://doi.org/10.1088/1751-8121/ac491c SN - 1751-8113 SN - 1751-8121 VL - 55 IS - 7 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Doerries, Timo J. A1 - Chechkin, Aleksei A1 - Schumer, Rina A1 - Metzler, Ralf T1 - Rate equations, spatial moments, and concentration profiles for mobile-immobile models with power-law and mixed waiting time distributions JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - We present a framework for systems in which diffusion-advection transport of a tracer substance in a mobile zone is interrupted by trapping in an immobile zone. Our model unifies different model approaches based on distributed-order diffusion equations, exciton diffusion rate models, and random-walk models for multirate mobile-immobile mass transport. We study various forms for the trapping time dynamics and their effects on the tracer mass in the mobile zone. Moreover, we find the associated breakthrough curves, the tracer density at a fixed point in space as a function of time, and the mobile and immobile concentration profiles and the respective moments of the transport. Specifically, we derive explicit forms for the anomalous transport dynamics and an asymptotic power-law decay of the mobile mass for a Mittag-Leffler trapping time distribution. In our analysis we point out that even for exponential trapping time densities, transient anomalous transport is observed. Our results have direct applications in geophysical contexts, but also in biological, soft matter, and solid state systems. Y1 - 2022 U6 - https://doi.org/10.1103/PhysRevE.105.014105 SN - 2470-0045 SN - 2470-0053 SN - 2470-0061 VL - 105 IS - 1 PB - The American Institute of Physics CY - Woodbury, NY ER - TY - JOUR A1 - Varghese, Alan J. A1 - Chechkin, Aleksei A1 - Metzler, Ralf A1 - Sujith, Raman I. T1 - Capturing multifractality of pressure fluctuations in thermoacoustic systems using fractional-order derivatives JF - Chaos : an interdisciplinary journal of nonlinear science N2 - The stable operation of a turbulent combustor is not completely silent; instead, there is a background of small amplitude aperiodic acoustic fluctuations known as combustion noise. Pressure fluctuations during this state of combustion noise are multifractal due to the presence of multiple temporal scales that contribute to its dynamics. However, existing models are unable to capture the multifractality in the pressure fluctuations. We conjecture an underlying fractional dynamics for the thermoacoustic system and obtain a fractional-order model for pressure fluctuations. The data from this model has remarkable visual similarity to the experimental data and also has a wide multifractal spectrum during the state of combustion noise. Quantitative similarity with the experimental data in terms of the Hurst exponent and the multifractal spectrum is observed during the state of combustion noise. This model is also able to produce pressure fluctuations that are qualitatively similar to the experimental data acquired during intermittency and thermoacoustic instability. Furthermore, we argue that the fractional dynamics vanish as we approach the state of thermoacoustic instability. Y1 - 2021 U6 - https://doi.org/10.1063/5.0032585 SN - 1054-1500 SN - 1089-7682 VL - 31 IS - 3 PB - American Institute of Physics, AIP CY - Melville ER -