TY - JOUR A1 - Wang, Wei A1 - Cherstvy, Andrey G. A1 - Kantz, Holger A1 - Metzler, Ralf A1 - Sokolov, Igor M. T1 - Time averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - How different are the results of constant-rate resetting of anomalous-diffusion processes in terms of their ensemble-averaged versus time-averaged mean-squared displacements (MSDs versus TAMSDs) and how does stochastic resetting impact nonergodicity? We examine, both analytically and by simulations, the implications of resetting on the MSD- and TAMSD-based spreading dynamics of particles executing fractional Brownian motion (FBM) with a long-time memory, heterogeneous diffusion processes (HDPs) with a power-law space-dependent diffusivity D(x) = D0|x|gamma and their "combined" process of HDP-FBM. We find, inter alia, that the resetting dynamics of originally ergodic FBM for superdiffusive Hurst exponents develops disparities in scaling and magnitudes of the MSDs and mean TAMSDs indicating weak ergodicity breaking. For subdiffusive HDPs we also quantify the nonequivalence of the MSD and TAMSD and observe a new trimodal form of the probability density function. For reset FBM, HDPs and HDP-FBM we compute analytically and verify by simulations the short-time MSD and TAMSD asymptotes and long-time plateaus reminiscent of those for processes under confinement. We show that certain characteristics of these reset processes are functionally similar despite a different stochastic nature of their nonreset variants. Importantly, we discover nonmonotonicity of the ergodicitybreaking parameter EB as a function of the resetting rate r. For all reset processes studied we unveil a pronounced resetting-induced nonergodicity with a maximum of EB at intermediate r and EB similar to(1/r )-decay at large r. Alongside the emerging MSD-versus-TAMSD disparity, this r-dependence of EB can be an experimentally testable prediction. We conclude by discussing some implications to experimental systems featuring resetting dynamics. Y1 - 2021 U6 - https://doi.org/10.1103/PhysRevE.104.024105 SN - 2470-0045 SN - 2470-0053 VL - 104 IS - 2 PB - American Institute of Physics CY - Woodbury, NY ER - TY - JOUR A1 - Vinod, Deepak A1 - Cherstvy, Andrey G. A1 - Wang, Wei A1 - Metzler, Ralf A1 - Sokolov, Igor M. T1 - Nonergodicity of reset geometric Brownian motion JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - We derive. the ensemble-and time-averaged mean-squared displacements (MSD, TAMSD) for Poisson-reset geometric Brownian motion (GBM), in agreement with simulations. We find MSD and TAMSD saturation for frequent resetting, quantify the spread of TAMSDs via the ergodicity-breaking parameter and compute distributions of prices. General MSD-TAMSD nonequivalence proves reset GBM nonergodic. Y1 - 2022 U6 - https://doi.org/10.1103/PhysRevE.105.L012106 SN - 2470-0045 SN - 2470-0053 VL - 105 IS - 1 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Wang, Wei A1 - Metzler, Ralf A1 - Cherstvy, Andrey G. T1 - Anomalous diffusion, aging, and nonergodicity of scaled Brownian motion with fractional Gaussian noise: overview of related experimental observations and models JF - Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies N2 - How does a systematic time-dependence of the diffusion coefficient D(t) affect the ergodic and statistical characteristics of fractional Brownian motion (FBM)? Here, we answer this question via studying the characteristics of a set of standard statistical quantifiers relevant to single-particle-tracking (SPT) experiments. We examine, for instance, how the behavior of the ensemble- and time-averaged mean-squared displacements-denoted as the standard MSD < x(2)(Delta)> and TAMSD <<(delta(2)(Delta))over bar>> quantifiers-of FBM featuring < x(2) (Delta >> = <<(delta(2)(Delta >)over bar>> proportional to Delta(2H) (where H is the Hurst exponent and Delta is the [lag] time) changes in the presence of a power-law deterministically varying diffusivity D-proportional to(t) proportional to t(alpha-1) -germane to the process of scaled Brownian motion (SBM)-determining the strength of fractional Gaussian noise. The resulting compound "scaled-fractional" Brownian motion or FBM-SBM is found to be nonergodic, with < x(2)(Delta >> proportional to Delta(alpha+)(2H)(-1) and <(delta 2(Delta >) over bar > proportional to Delta(2H). We also detect a stalling behavior of the MSDs for very subdiffusive SBM and FBM, when alpha + 2H - 1 < 0. The distribution of particle displacements for FBM-SBM remains Gaussian, as that for the parent processes of FBM and SBM, in the entire region of scaling exponents (0 < alpha < 2 and 0 < H < 1). The FBM-SBM process is aging in a manner similar to SBM. The velocity autocorrelation function (ACF) of particle increments of FBM-SBM exhibits a dip when the parent FBM process is subdiffusive. Both for sub- and superdiffusive FBM contributions to the FBM-SBM process, the SBM exponent affects the long-time decay exponent of the ACF. Applications of the FBM-SBM-amalgamated process to the analysis of SPT data are discussed. A comparative tabulated overview of recent experimental (mainly SPT) and computational datasets amenable for interpretation in terms of FBM-, SBM-, and FBM-SBM-like models of diffusion culminates the presentation. The statistical aspects of the dynamics of a wide range of biological systems is compared in the table, from nanosized beads in living cells, to chromosomal loci, to water diffusion in the brain, and, finally, to patterns of animal movements. Y1 - 2022 U6 - https://doi.org/10.1039/d2cp01741e SN - 1463-9076 SN - 1463-9084 VL - 24 IS - 31 SP - 18482 EP - 18504 PB - RSC Publ. CY - Cambridge ER - TY - JOUR A1 - Wang, Wei A1 - Cherstvy, Andrey G. A1 - Liu, Xianbin A1 - Metzler, Ralf T1 - Anomalous diffusion and nonergodicity for heterogeneous diffusion processes with fractional Gaussian noise JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - Heterogeneous diffusion processes (HDPs) feature a space-dependent diffusivity of the form D(x) = D-0|x|(alpha). Such processes yield anomalous diffusion and weak ergodicity breaking, the asymptotic disparity between ensemble and time averaged observables, such as the mean-squared displacement. Fractional Brownian motion (FBM) with its long-range correlated yet Gaussian increments gives rise to anomalous and ergodic diffusion. Here, we study a combined model of HDPs and FBM to describe the particle dynamics in complex systems with position-dependent diffusivity driven by fractional Gaussian noise. This type of motion is, inter alia, relevant for tracer-particle diffusion in biological cells or heterogeneous complex fluids. We show that the long-time scaling behavior predicted theoretically and by simulations for the ensemble-and time-averaged mean-squared displacements couple the scaling exponents alpha of HDPs and the Hurst exponent H of FBM in a characteristic way. Our analysis of the simulated data in terms of the rescaled variable y similar to |x|(1/(2/(2-alpha)))/t(H) coupling particle position x and time t yields a simple, Gaussian probability density function (PDF), PHDP-FBM(y) = e(-y2)/root pi. Its universal shape agrees well with theoretical predictions for both uni- and bimodal PDF distributions. Y1 - 2020 U6 - https://doi.org/10.1103/PhysRevE.102.012146 SN - 2470-0045 SN - 2470-0053 SN - 1063-651X SN - 1539-3755 SN - 2470-0061 VL - 102 IS - 1 SP - 012146-1 EP - 012146-16 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Wang, Wei A1 - Cherstvy, Andrey G. A1 - Chechkin, Aleksei V. A1 - Thapa, Samudrajit A1 - Seno, Flavio A1 - Liu, Xianbin A1 - Metzler, Ralf T1 - Fractional Brownian motion with random diffusivity BT - emerging residual nonergodicity below the correlation time JF - Journal of physics : A, Mathematical and theoretical N2 - Numerous examples for a priori unexpected non-Gaussian behaviour for normal and anomalous diffusion have recently been reported in single-particle tracking experiments. Here, we address the case of non-Gaussian anomalous diffusion in terms of a random-diffusivity mechanism in the presence of power-law correlated fractional Gaussian noise. We study the ergodic properties of this model via examining the ensemble- and time-averaged mean-squared displacements as well as the ergodicity breaking parameter EB quantifying the trajectory-to-trajectory fluctuations of the latter. For long measurement times, interesting crossover behaviour is found as function of the correlation time tau characterising the diffusivity dynamics. We unveil that at short lag times the EB parameter reaches a universal plateau. The corresponding residual value of EB is shown to depend only on tau and the trajectory length. The EB parameter at long lag times, however, follows the same power-law scaling as for fractional Brownian motion. We also determine a corresponding plateau at short lag times for the discrete representation of fractional Brownian motion, absent in the continuous-time formulation. These analytical predictions are in excellent agreement with results of computer simulations of the underlying stochastic processes. Our findings can help distinguishing and categorising certain nonergodic and non-Gaussian features of particle displacements, as observed in recent single-particle tracking experiments. KW - stochastic processes KW - anomalous diffusion KW - fractional Brownian motion KW - diffusing diffusivity KW - weak ergodicity breaking Y1 - 2020 U6 - https://doi.org/10.1088/1751-8121/aba467 SN - 1751-8113 SN - 1751-8121 VL - 53 IS - 47 PB - IOP Publ. Ltd. CY - Bristol ER - TY - GEN A1 - Wang, Wei A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf A1 - Sokolov, Igor M. T1 - Restoring ergodicity of stochastically reset anomalous-diffusion processes T2 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - How do different reset protocols affect ergodicity of a diffusion process in single-particle-tracking experiments? We here address the problem of resetting of an arbitrary stochastic anomalous-diffusion process (ADP) from the general mathematical points of view and assess ergodicity of such reset ADPs for an arbitrary resetting protocol. The process of stochastic resetting describes the events of the instantaneous restart of a particle’s motion via randomly distributed returns to a preset initial position (or a set of those). The waiting times of such resetting events obey the Poissonian, Gamma, or more generic distributions with specified conditions regarding the existence of moments. Within these general approaches, we derive general analytical results and support them by computer simulations for the behavior of the reset mean-squared displacement (MSD), the new reset increment-MSD (iMSD), and the mean reset time-averaged MSD (TAMSD). For parental nonreset ADPs with the MSD(t)∝ tμ we find a generic behavior and a switch of the short-time growth of the reset iMSD and mean reset TAMSDs from ∝ _μ for subdiffusive to ∝ _1 for superdiffusive reset ADPs. The critical condition for a reset ADP that recovers its ergodicity is found to be more general than that for the nonequilibrium stationary state, where obviously the iMSD and the mean TAMSD are equal. The consideration of the new statistical quantifier, the iMSD—as compared to the standard MSD—restores the ergodicity of an arbitrary reset ADP in all situations when the μth moment of the waiting-time distribution of resetting events is finite. Potential applications of these new resetting results are, inter alia, in the area of biophysical and soft-matter systems. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1261 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-560377 SN - 1866-8372 SP - 013161-1 EP - 013161-13 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Wang, Wei A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf A1 - Sokolov, Igor M. T1 - Restoring ergodicity of stochastically reset anomalous-diffusion processes JF - Physical Review Research N2 - How do different reset protocols affect ergodicity of a diffusion process in single-particle-tracking experiments? We here address the problem of resetting of an arbitrary stochastic anomalous-diffusion process (ADP) from the general mathematical points of view and assess ergodicity of such reset ADPs for an arbitrary resetting protocol. The process of stochastic resetting describes the events of the instantaneous restart of a particle’s motion via randomly distributed returns to a preset initial position (or a set of those). The waiting times of such resetting events obey the Poissonian, Gamma, or more generic distributions with specified conditions regarding the existence of moments. Within these general approaches, we derive general analytical results and support them by computer simulations for the behavior of the reset mean-squared displacement (MSD), the new reset increment-MSD (iMSD), and the mean reset time-averaged MSD (TAMSD). For parental nonreset ADPs with the MSD(t)∝ tμ we find a generic behavior and a switch of the short-time growth of the reset iMSD and mean reset TAMSDs from ∝ _μ for subdiffusive to ∝ _1 for superdiffusive reset ADPs. The critical condition for a reset ADP that recovers its ergodicity is found to be more general than that for the nonequilibrium stationary state, where obviously the iMSD and the mean TAMSD are equal. The consideration of the new statistical quantifier, the iMSD—as compared to the standard MSD—restores the ergodicity of an arbitrary reset ADP in all situations when the μth moment of the waiting-time distribution of resetting events is finite. Potential applications of these new resetting results are, inter alia, in the area of biophysical and soft-matter systems. Y1 - 2022 U6 - https://doi.org/10.1103/PhysRevResearch.4.013161 SN - 2643-1564 VL - 4 SP - 013161-1 EP - 013161-13 PB - American Physical Society CY - College Park, Maryland, United States ET - 1 ER - TY - JOUR A1 - Wang, Wei A1 - Seno, Flavio A1 - Sokolov, Igor M. A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Unexpected crossovers in correlated random-diffusivity processes JF - New Journal of Physics N2 - The passive and active motion of micron-sized tracer particles in crowded liquids and inside living biological cells is ubiquitously characterised by 'viscoelastic' anomalous diffusion, in which the increments of the motion feature long-ranged negative and positive correlations. While viscoelastic anomalous diffusion is typically modelled by a Gaussian process with correlated increments, so-called fractional Gaussian noise, an increasing number of systems are reported, in which viscoelastic anomalous diffusion is paired with non-Gaussian displacement distributions. Following recent advances in Brownian yet non-Gaussian diffusion we here introduce and discuss several possible versions of random-diffusivity models with long-ranged correlations. While all these models show a crossover from non-Gaussian to Gaussian distributions beyond some correlation time, their mean squared displacements exhibit strikingly different behaviours: depending on the model crossovers from anomalous to normal diffusion are observed, as well as a priori unexpected dependencies of the effective diffusion coefficient on the correlation exponent. Our observations of the non-universality of random-diffusivity viscoelastic anomalous diffusion are important for the analysis of experiments and a better understanding of the physical origins of 'viscoelastic yet non-Gaussian' diffusion. KW - diffusion KW - anomalous diffusion KW - non-Gaussianity KW - fractional Brownian motion Y1 - 2020 U6 - https://doi.org/10.1088/1367-2630/aba390 SN - 1367-2630 VL - 22 PB - Dt. Physikalische Ges. CY - Bad Honnef ER - TY - GEN A1 - Wang, Wei A1 - Seno, Flavio A1 - Sokolov, Igor M. A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Unexpected crossovers in correlated random-diffusivity processes N2 - The passive and active motion of micron-sized tracer particles in crowded liquids and inside living biological cells is ubiquitously characterised by 'viscoelastic' anomalous diffusion, in which the increments of the motion feature long-ranged negative and positive correlations. While viscoelastic anomalous diffusion is typically modelled by a Gaussian process with correlated increments, so-called fractional Gaussian noise, an increasing number of systems are reported, in which viscoelastic anomalous diffusion is paired with non-Gaussian displacement distributions. Following recent advances in Brownian yet non-Gaussian diffusion we here introduce and discuss several possible versions of random-diffusivity models with long-ranged correlations. While all these models show a crossover from non-Gaussian to Gaussian distributions beyond some correlation time, their mean squared displacements exhibit strikingly different behaviours: depending on the model crossovers from anomalous to normal diffusion are observed, as well as a priori unexpected dependencies of the effective diffusion coefficient on the correlation exponent. Our observations of the non-universality of random-diffusivity viscoelastic anomalous diffusion are important for the analysis of experiments and a better understanding of the physical origins of 'viscoelastic yet non-Gaussian' diffusion. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1006 KW - diffusion KW - anomalous diffusion KW - non-Gaussianity KW - fractional Brownian motion Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-480049 SN - 1866-8372 IS - 1006 ER -