TY - JOUR A1 - Cherstvy, Andrey G. A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Ageing and confinement in non-ergodic heterogeneous diffusion processes JF - Journal of physics : A, Mathematical and theoretical N2 - We study the effects of ageing-the time delay between initiation of the physical process at t = 0 and start of observation at some time t(a) > 0-and spatial confinement on the properties of heterogeneous diffusion processes (HDPs) with deterministic power-law space-dependent diffusivities, D(x) = D-0 vertical bar x vertical bar(alpha). From analysis of the ensemble and time averaged mean squared displacements and the ergodicity breaking parameter quantifying the inherent degree of irreproducibility of individual realizations of the HDP we obtain striking similarities to ageing subdiffusive continuous time random walks with scale-free waiting time distributions. We also explore how both processes can be distinguished. For confined HDPs we study the long-time saturation of the ensemble and time averaged particle displacements as well as the magnitude of the inherent scatter of time averaged displacements and contrast the outcomes to the results known for other anomalous diffusion processes under confinement. KW - stochastic processes KW - anomalous diffusion KW - ageing KW - weak ergodicity breaking Y1 - 2014 U6 - https://doi.org/10.1088/1751-8113/47/48/485002 SN - 1751-8113 SN - 1751-8121 VL - 47 IS - 48 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Chechkin, Aleksei V. A1 - Kantz, Holger A1 - Metzler, Ralf T1 - Ageing effects in ultraslow continuous time random walks JF - The European physical journal : B, Condensed matter and complex systems N2 - In ageing systems physical observables explicitly depend on the time span elapsing between the original initiation of the system and the actual start of the recording of the particle motion. We here study the signatures of ageing in the framework of ultraslow continuous time random walk processes with super-heavy tailed waiting time densities. We derive the density for the forward or recurrent waiting time of the motion as function of the ageing time, generalise the Montroll-Weiss equation for this process, and analyse the ageing behaviour of the ensemble and time averaged mean squared displacements. Y1 - 2017 U6 - https://doi.org/10.1140/epjb/e2017-80270-9 SN - 1434-6028 SN - 1434-6036 VL - 90 PB - Springer CY - New York ER - TY - JOUR A1 - Safdari, Hadiseh A1 - Chechkin, Aleksei V. A1 - Jafari, Gholamreza R. A1 - Metzler, Ralf T1 - Aging scaled Brownian motion JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - Scaled Brownian motion (SBM) is widely used to model anomalous diffusion of passive tracers in complex and biological systems. It is a highly nonstationary process governed by the Langevin equation for Brownian motion, however, with a power-law time dependence of the noise strength. Here we study the aging properties of SBM for both unconfined and confined motion. Specifically, we derive the ensemble and time averaged mean squared displacements and analyze their behavior in the regimes of weak, intermediate, and strong aging. A very rich behavior is revealed for confined aging SBM depending on different aging times and whether the process is sub- or superdiffusive. We demonstrate that the information on the aging factorizes with respect to the lag time and exhibits a functional form that is identical to the aging behavior of scale-free continuous time random walk processes. While SBM exhibits a disparity between ensemble and time averaged observables and is thus weakly nonergodic, strong aging is shown to effect a convergence of the ensemble and time averaged mean squared displacement. Finally, we derive the density of first passage times in the semi-infinite domain that features a crossover defined by the aging time. Y1 - 2015 U6 - https://doi.org/10.1103/PhysRevE.91.042107 SN - 1539-3755 SN - 1550-2376 VL - 91 IS - 4 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Safdari, Hadiseh A1 - Cherstvy, Andrey G. A1 - Chechkin, Aleksei V. A1 - Bodrova, Anna A1 - Metzler, Ralf T1 - Aging underdamped scaled Brownian motion BT - Ensemble- and time-averaged particle displacements, nonergodicity, and the failure of the overdamping approximation JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - We investigate both analytically and by computer simulations the ensemble- and time-averaged, nonergodic, and aging properties of massive particles diffusing in a medium with a time dependent diffusivity. We call this stochastic diffusion process the (aging) underdamped scaled Brownian motion (UDSBM). We demonstrate how the mean squared displacement (MSD) and the time-averaged MSD of UDSBM are affected by the inertial term in the Langevin equation, both at short, intermediate, and even long diffusion times. In particular, we quantify the ballistic regime for the MSD and the time-averaged MSD as well as the spread of individual time-averaged MSD trajectories. One of the main effects we observe is that, both for the MSD and the time-averaged MSD, for superdiffusive UDSBM the ballistic regime is much shorter than for ordinary Brownian motion. In contrast, for subdiffusive UDSBM, the ballistic region extends to much longer diffusion times. Therefore, particular care needs to be taken under what conditions the overdamped limit indeed provides a correct description, even in the long time limit. We also analyze to what extent ergodicity in the Boltzmann-Khinchin sense in this nonstationary system is broken, both for subdiffusive and superdiffusive UDSBM. Finally, the limiting case of ultraslow UDSBM is considered, with a mixed logarithmic and power-law dependence of the ensemble-and time-averaged MSDs of the particles. In the limit of strong aging, remarkably, the ordinary UDSBM and the ultraslow UDSBM behave similarly in the short time ballistic limit. The approaches developed here open ways for considering other stochastic processes under physically important conditions when a finite particle mass and aging in the system cannot be neglected. Y1 - 2017 U6 - https://doi.org/10.1103/PhysRevE.95.012120 SN - 2470-0045 SN - 2470-0053 VL - 95 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Dieterich, Peter A1 - Lindemann, Otto A1 - Moskopp, Mats Leif A1 - Tauzin, Sebastien A1 - Huttenlocher, Anna A1 - Klages, Rainer A1 - Chechkin, Aleksei V. A1 - Schwab, Albrecht T1 - Anomalous diffusion and asymmetric tempering memory in neutrophil chemotaxis JF - PLoS Computational Biology : a new community journal N2 - Neutrophil granulocytes are essential for the first host defense. After leaving the blood circulation they migrate efficiently towards sites of inflammation. They are guided by chemoattractants released from cells within the inflammatory foci. On a cellular level, directional migration is a consequence of cellular front-rear asymmetry which is induced by the concentration gradient of the chemoattractants. The generation and maintenance of this asymmetry, however, is not yet fully understood. Here we analyzed the paths of chemotacting neutrophils with different stochastic models to gain further insight into the underlying mechanisms. Wildtype chemotacting neutrophils show an anomalous superdiffusive behavior. CXCR2 blockade and TRPC6-knockout cause the tempering of temporal correlations and a reduction of chemotaxis. Importantly, such tempering is found both in vitro and in vivo. These findings indicate that the maintenance of anomalous dynamics is crucial for chemotactic behavior and the search efficiency of neutrophils. The motility of neutrophils and their ability to sense and to react to chemoattractants in their environment are of central importance for the innate immunity. Neutrophils are guided towards sites of inflammation following the activation of G-protein coupled chemoattractant receptors such as CXCR2 whose signaling strongly depends on the activity of Ca2+ permeable TRPC6 channels. It is the aim of this study to analyze data sets obtained in vitro (murine neutrophils) and in vivo (zebrafish neutrophils) with a stochastic mathematical model to gain deeper insight into the underlying mechanisms. The model is based on the analysis of trajectories of individual neutrophils. Bayesian data analysis, including the covariances of positions for fractional Brownian motion as well as for exponentially and power-law tempered model variants, allows the estimation of parameters and model selection. Our model-based analysis reveals that wildtype neutrophils show pure superdiffusive fractional Brownian motion. This so-called anomalous dynamics is characterized by temporal long-range correlations for the movement into the direction of the chemotactic CXCL1 gradient. Pure superdiffusion is absent vertically to this gradient. This points to an asymmetric 'memory' of the migratory machinery, which is found both in vitro and in vivo. CXCR2 blockade and TRPC6-knockout cause tempering of temporal correlations in the chemotactic gradient. This can be interpreted as a progressive loss of memory, which leads to a marked reduction of chemotaxis and search efficiency of neutrophils. In summary, our findings indicate that spatially differential regulation of anomalous dynamics appears to play a central role in guiding efficient chemotactic behavior. KW - neutrophils KW - chemotaxis KW - autocorrelation KW - zebrafish KW - cell migration KW - covariance KW - brownian motion KW - stochastic processes Y1 - 2022 U6 - https://doi.org/10.1371/journal.pcbi.1010089 SN - 1553-734X SN - 1553-7358 VL - 18 IS - 5 PB - PLoS CY - San Fransisco ER - TY - JOUR A1 - Cherstvy, Andrey G. A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes JF - New journal of physics : the open-access journal for physics N2 - We demonstrate the non-ergodicity of a simple Markovian stochastic process with space-dependent diffusion coefficient D(x). For power-law forms D(x) similar or equal to vertical bar x vertical bar(alpha), this process yields anomalous diffusion of the form < x(2)(t)> similar or equal to t(2/(2-alpha)). Interestingly, in both the sub- and superdiffusive regimes we observe weak ergodicity breaking: the scaling of the time-averaged mean-squared displacement <(delta(2)(Delta))over bar> remains linear in the lag time Delta and thus differs from the corresponding ensemble average < x(2)(t)>. We analyse the non-ergodic behaviour of this process in terms of the time-averaged mean- squared displacement (delta(2)) over bar and its random features, i.e. the statistical distribution of (delta(2)) over bar and the ergodicity breaking parameters. The heterogeneous diffusion model represents an alternative approach to non- ergodic, anomalous diffusion that might be particularly relevant for diffusion in heterogeneous media. Y1 - 2013 U6 - https://doi.org/10.1088/1367-2630/15/8/083039 SN - 1367-2630 VL - 15 IS - 15 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Doerries, Timo J. A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Apparent anomalous diffusion and non-Gaussian distributions in a simple mobile-immobile transport model with Poissonian switching JF - Interface : journal of the Royal Society N2 - We analyse mobile-immobile transport of particles that switch between the mobile and immobile phases with finite rates. Despite this seemingly simple assumption of Poissonian switching, we unveil a rich transport dynamics including significant transient anomalous diffusion and non-Gaussian displacement distributions. Our discussion is based on experimental parameters for tau proteins in neuronal cells, but the results obtained here are expected to be of relevance for a broad class of processes in complex systems. Specifically, we obtain that, when the mean binding time is significantly longer than the mean mobile time, transient anomalous diffusion is observed at short and intermediate time scales, with a strong dependence on the fraction of initially mobile and immobile particles. We unveil a Laplace distribution of particle displacements at relevant intermediate time scales. For any initial fraction of mobile particles, the respective mean squared displacement (MSD) displays a plateau. Moreover, we demonstrate a short-time cubic time dependence of the MSD for immobile tracers when initially all particles are immobile. KW - diffusion KW - mobile-immobile model KW - tau proteins Y1 - 2022 U6 - https://doi.org/10.1098/rsif.2022.0233 SN - 1742-5689 SN - 1742-5662 VL - 19 IS - 192 PB - Royal Society CY - London ER - TY - JOUR A1 - Delle Side, Domenico A1 - Nassisi, Vincenzo A1 - Pennetta, Cecilia A1 - Alifano, Pietro A1 - Di Salvo, Marco A1 - Tala, Adelfia A1 - Chechkin, Aleksei V. A1 - Seno, Flavio A1 - Trovato, Antonio T1 - Bacterial bioluminescence onset and quenching: a dynamical model for a quorum sensing-mediated property JF - Royal Society Open Science N2 - We present an effective dynamical model for the onset of bacterial bioluminescence, one of the most studied quorum sensing-mediated traits. Our model is built upon simple equations that describe the growth of the bacterial colony, the production and accumulation of autoinducer signal molecules, their sensing within bacterial cells, and the ensuing quorum activation mechanism that triggers bioluminescent emission. The model is directly tested to quantitatively reproduce the experimental distributions of photon emission times, previously measured for bacterial colonies of Vibrio jasicida, a luminescent bacterium belonging to the Harveyi clade, growing in a highly drying environment. A distinctive and novel feature of the proposed model is bioluminescence ‘quenching’ after a given time elapsed from activation. Using an advanced fitting procedure based on the simulated annealing algorithm, we are able to infer from the experimental observations the biochemical parameters used in the model. Such parameters are in good agreement with the literature data. As a further result, we find that, at least in our experimental conditions, light emission in bioluminescent bacteria appears to originate from a subtle balance between colony growth and quorum activation due to autoinducers diffusion, with the two phenomena occurring on the same time scale. This finding is consistent with a negative feedback mechanism previously reported for Vibrio harveyi. KW - quorum sensing KW - bioluminescence KW - biophysical model KW - Vibrio Harveyi clade KW - oxygen quenching KW - Gompertz growth function Y1 - 2017 U6 - https://doi.org/10.1098/rsos.171586 SN - 2054-5703 VL - 4 PB - Royal Society CY - London ER - TY - JOUR A1 - Sandev, Trifce A1 - Sokolov, Igor M. A1 - Metzler, Ralf A1 - Chechkin, Aleksei V. T1 - Beyond monofractional kinetics JF - Chaos, solitons & fractals : applications in science and engineering ; an interdisciplinary journal of nonlinear science N2 - We discuss generalized integro-differential diffusion equations whose integral kernels are not of a simple power law form, and thus these equations themselves do not belong to the family of fractional diffusion equations exhibiting a monoscaling behavior. They instead generate a broad class of anomalous nonscaling patterns, which correspond either to crossovers between different power laws, or to a non-power-law behavior as exemplified by the logarithmic growth of the width of the distribution. We consider normal and modified forms of these generalized diffusion equations and provide a brief discussion of three generic types of integral kernels for each form, namely, distributed order, truncated power law and truncated distributed order kernels. For each of the cases considered we prove the non-negativity of the solution of the corresponding generalized diffusion equation and calculate the mean squared displacement. (C) 2017 Elsevier Ltd. All rights reserved. KW - Distributed order diffusion-wave equations KW - Complete Bernstein function KW - Completely monotone function Y1 - 2017 U6 - https://doi.org/10.1016/j.chaos.2017.05.001 SN - 0960-0779 SN - 1873-2887 VL - 102 SP - 210 EP - 217 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Chechkin, Aleksei V. A1 - Seno, Flavio A1 - Metzler, Ralf A1 - Sokolov, Igor M. T1 - Brownian yet Non-Gaussian Diffusion: From Superstatistics to Subordination of Diffusing Diffusivities JF - Physical review : X, Expanding access N2 - A growing number of biological, soft, and active matter systems are observed to exhibit normal diffusive dynamics with a linear growth of the mean-squared displacement, yet with a non-Gaussian distribution of increments. Based on the Chubinsky-Slater idea of a diffusing diffusivity, we here establish and analyze a minimal model framework of diffusion processes with fluctuating diffusivity. In particular, we demonstrate the equivalence of the diffusing diffusivity process with a superstatistical approach with a distribution of diffusivities, at times shorter than the diffusivity correlation time. At longer times, a crossover to a Gaussian distribution with an effective diffusivity emerges. Specifically, we establish a subordination picture of Brownian but non-Gaussian diffusion processes, which can be used for a wide class of diffusivity fluctuation statistics. Our results are shown to be in excellent agreement with simulations and numerical evaluations. Y1 - 2017 U6 - https://doi.org/10.1103/PhysRevX.7.021002 SN - 2160-3308 VL - 7 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Chechkin, Aleksei V. A1 - Zaid, Irwin M. A1 - Lomholt, Michael A. A1 - Sokolov, Igor M. A1 - Metzler, Ralf T1 - Bulk-mediated diffusion on a planar surface full solution JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - We consider the effective surface motion of a particle that intermittently unbinds from a planar surface and performs bulk excursions. Based on a random-walk approach, we derive the diffusion equations for surface and bulk diffusion including the surface-bulk coupling. From these exact dynamic equations, we analytically obtain the propagator of the effective surface motion. This approach allows us to deduce a superdiffusive, Cauchy-type behavior on the surface, together with exact cutoffs limiting the Cauchy form. Moreover, we study the long-time dynamics for the surface motion. Y1 - 2012 U6 - https://doi.org/10.1103/PhysRevE.86.041101 SN - 1539-3755 VL - 86 IS - 4 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Chechkin, Aleksei V. A1 - Zaid, I. M. A1 - Lomholt, M. A. A1 - Sokolov, Igor M. A1 - Metzler, Ralf T1 - Bulk-mediated surface diffusion on a cylinder in the fast exchange limit JF - Mathematical modelling of natural phenomena N2 - In various biological systems and small scale technological applications particles transiently bind to a cylindrical surface. Upon unbinding the particles diffuse in the vicinal bulk before rebinding to the surface. Such bulk-mediated excursions give rise to an effective surface translation, for which we here derive and discuss the dynamic equations, including additional surface diffusion. We discuss the time evolution of the number of surface-bound particles, the effective surface mean squared displacement, and the surface propagator. In particular, we observe sub- and superdiffusive regimes. A plateau of the surface mean-squared displacement reflects a stalling of the surface diffusion at longer times. Finally, the corresponding first passage problem for the cylindrical geometry is analysed. KW - Bulk-mediated diffusion KW - anomalous diffusion KW - Levy flights KW - stochastic processes Y1 - 2013 U6 - https://doi.org/10.1051/mmnp/20138208 SN - 0973-5348 VL - 8 IS - 2 SP - 114 EP - 126 PB - EDP Sciences CY - Les Ulis ER - TY - JOUR A1 - Sandev, T. A1 - Iomin, Alexander A1 - Kantz, Holger A1 - Metzler, Ralf A1 - Chechkin, Aleksei V. T1 - Comb Model with Slow and Ultraslow Diffusion JF - Mathematical modelling of natural phenomena N2 - We consider a generalized diffusion equation in two dimensions for modeling diffusion on a comb-like structures. We analyze the probability distribution functions and we derive the mean squared displacement in x and y directions. Different forms of the memory kernels (Dirac delta, power-law, and distributed order) are considered. It is shown that anomalous diffusion may occur along both x and y directions. Ultraslow diffusion and some more general diffusive processes are observed as well. We give the corresponding continuous time random walk model for the considered two dimensional diffusion-like equation on a comb, and we derive the probability distribution functions which subordinate the process governed by this equation to the Wiener process. KW - comb-like model KW - anomalous diffusion KW - mean squared displacement KW - probability density function Y1 - 2016 U6 - https://doi.org/10.1051/mmnp/201611302 SN - 0973-5348 SN - 1760-6101 VL - 11 SP - 18 EP - 33 PB - EDP Sciences CY - Les Ulis ER - TY - JOUR A1 - Palyulin, Vladimir V. A1 - Mantsevich, Vladimir N. A1 - Klages, Rainer A1 - Metzler, Ralf A1 - Chechkin, Aleksei V. T1 - Comparison of pure and combined search strategies for single and multiple targets JF - The European physical journal : B, Condensed matter and complex systems N2 - We address the generic problem of random search for a point-like target on a line. Using the measures of search reliability and efficiency to quantify the random search quality, we compare Brownian search with Levy search based on long-tailed jump length distributions. We then compare these results with a search process combined of two different long-tailed jump length distributions. Moreover, we study the case of multiple targets located by a Levy searcher. Y1 - 2017 U6 - https://doi.org/10.1140/epjb/e2017-80372-4 SN - 1434-6028 SN - 1434-6036 VL - 90 SP - 20 EP - 37 PB - Springer CY - New York ER - TY - JOUR A1 - Kurilovich, Aleksandr A. A1 - Mantsevich, Vladimir A1 - Stevenson, Keith J. A1 - Chechkin, Aleksei V. A1 - Palyulin, V. V. T1 - Complex diffusion-based kinetics of photoluminescence in semiconductor nanoplatelets JF - Physical chemistry, chemical physics : a journal of European Chemical Societies N2 - We present a diffusion-based simulation and theoretical models for explanation of the photoluminescence (PL) emission intensity in semiconductor nanoplatelets. It is shown that the shape of the PL intensity curves can be reproduced by the interplay of recombination, diffusion and trapping of excitons. The emission intensity at short times is purely exponential and is defined by recombination. At long times, it is governed by the release of excitons from surface traps and is characterized by a power-law tail. We show that the crossover from one limit to another is controlled by diffusion properties. This intermediate region exhibits a rich behaviour depending on the value of diffusivity. The proposed approach reproduces all the features of experimental curves measured for different nanoplatelet systems. Y1 - 2020 U6 - https://doi.org/10.1039/d0cp03744c SN - 1463-9076 SN - 1463-9084 VL - 22 IS - 42 SP - 24686 EP - 24696 PB - Royal Society of Chemistry CY - Cambridge ER - TY - JOUR A1 - Dybiec, Bartlomiej A1 - Capala, Karol A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Conservative random walks in confining potentials JF - Journal of physics : A, Mathematical and theoretical N2 - Levy walks are continuous time random walks with spatio-temporal coupling of jump lengths and waiting times, often used to model superdiffusive spreading processes such as animals searching for food, tracer motion in weakly chaotic systems, or even the dynamics in quantum systems such as cold atoms. In the simplest version Levy walks move with a finite speed. Here, we present an extension of the Levy walk scenario for the case when external force fields influence the motion. The resulting motion is a combination of the response to the deterministic force acting on the particle, changing its velocity according to the principle of total energy conservation, and random velocity reversals governed by the distribution of waiting times. For the fact that the motion stays conservative, that is, on a constant energy surface, our scenario is fundamentally different from thermal motion in the same external potentials. In particular, we present results for the velocity and position distributions for single well potentials of different steepness. The observed dynamics with its continuous velocity changes enriches the theory of Levy walk processes and will be of use in a variety of systems, for which the particles are externally confined. KW - Levy walk KW - conservative random walks KW - Levy flight Y1 - 2018 U6 - https://doi.org/10.1088/1751-8121/aaefc2 SN - 1751-8113 SN - 1751-8121 VL - 52 IS - 1 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Schulz, Johannes H. P. A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Correlated continuous time random walks - combining scale-invariance with long-range memory for spatial and temporal dynamics JF - Journal of physics : A, Mathematical and theoretical N2 - Standard continuous time random walk (CTRW) models are renewal processes in the sense that at each jump a new, independent pair of jump length and waiting time are chosen. Globally, anomalous diffusion emerges through scale-free forms of the jump length and/or waiting time distributions by virtue of the generalized central limit theorem. Here we present a modified version of recently proposed correlated CTRW processes, where we incorporate a power-law correlated noise on the level of both jump length and waiting time dynamics. We obtain a very general stochastic model, that encompasses key features of several paradigmatic models of anomalous diffusion: discontinuous, scale-free displacements as in Levy flights, scale-free waiting times as in subdiffusive CTRWs, and the long-range temporal correlations of fractional Brownian motion (FBM). We derive the exact solutions for the single-time probability density functions and extract the scaling behaviours. Interestingly, we find that different combinations of the model parameters lead to indistinguishable shapes of the emerging probability density functions and identical scaling laws. Our model will be useful for describing recent experimental single particle tracking data that feature a combination of CTRW and FBM properties. Y1 - 2013 U6 - https://doi.org/10.1088/1751-8113/46/47/475001 SN - 1751-8113 SN - 1751-8121 VL - 46 IS - 47 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Molina-Garcia, Daniel A1 - Sandev, Trifce A1 - Safdari, Hadiseh A1 - Pagnini, Gianni A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Crossover from anomalous to normal diffusion BT - truncated power-law noise correlations and applications to dynamics in lipid bilayers JF - New Journal of Physics N2 - Abstract The emerging diffusive dynamics in many complex systems show a characteristic crossover behaviour from anomalous to normal diffusion which is otherwise fitted by two independent power-laws. A prominent example for a subdiffusive–diffusive crossover are viscoelastic systems such as lipid bilayer membranes, while superdiffusive–diffusive crossovers occur in systems of actively moving biological cells. We here consider the general dynamics of a stochastic particle driven by so-called tempered fractional Gaussian noise, that is noise with Gaussian amplitude and power-law correlations, which are cut off at some mesoscopic time scale. Concretely we consider such noise with built-in exponential or power-law tempering, driving an overdamped Langevin equation (fractional Brownian motion) and fractional Langevin equation motion. We derive explicit expressions for the mean squared displacement and correlation functions, including different shapes of the crossover behaviour depending on the concrete tempering, and discuss the physical meaning of the tempering. In the case of power-law tempering we also find a crossover behaviour from faster to slower superdiffusion and slower to faster subdiffusion. As a direct application of our model we demonstrate that the obtained dynamics quantitatively describes the subdiffusion–diffusion and subdiffusion–subdiffusion crossover in lipid bilayer systems. We also show that a model of tempered fractional Brownian motion recently proposed by Sabzikar and Meerschaert leads to physically very different behaviour with a seemingly paradoxical ballistic long time scaling. KW - anomalous diffusion KW - truncated power-law correlated noise KW - lipid bilayer membrane dynamics Y1 - 2018 U6 - https://doi.org/10.1088/1367-2630/aae4b2 SN - 1367-2630 VL - 20 PB - IOP Publishing Ltd CY - London und Bad Honnef ER - TY - JOUR A1 - Sandev, Trifce A1 - Chechkin, Aleksei V. A1 - Kantz, Holger A1 - Metzler, Ralf T1 - Diffusion and fokker-planck-smoluchowski equations with generalized memory kernel JF - Fractional calculus and applied analysis : an international journal for theory and applications N2 - We consider anomalous stochastic processes based on the renewal continuous time random walk model with different forms for the probability density of waiting times between individual jumps. In the corresponding continuum limit we derive the generalized diffusion and Fokker-Planck-Smoluchowski equations with the corresponding memory kernels. We calculate the qth order moments in the unbiased and biased cases, and demonstrate that the generalized Einstein relation for the considered dynamics remains valid. The relaxation of modes in the case of an external harmonic potential and the convergence of the mean squared displacement to the thermal plateau are analyzed. KW - continuous time random walk (CTRW) KW - Fokker-Planck-Smoluchowski equation KW - Mittag-Leffler functions KW - anomalous diffusion KW - multi-scaling Y1 - 2015 U6 - https://doi.org/10.1515/fca-2015-0059 SN - 1311-0454 SN - 1314-2224 VL - 18 IS - 4 SP - 1006 EP - 1038 PB - De Gruyter CY - Berlin ER - TY - JOUR A1 - Pavlyukevich, Ilya A1 - Li, Yongge A1 - Xu, Yong A1 - Chechkin, Aleksei V. T1 - Directed transport induced by spatially modulated Levy flights JF - Journal of physics : A, Mathematical and theoretical N2 - In this paper we study the dynamics of a particle in a ratchet potential subject to multiplicative alpha-stable Levy noise, alpha is an element of(0, 2), in the limit of a noise amplitude epsilon -> 0. We compare the dynamics for Ito and Marcus multiplicative noises and obtain the explicit asymptotics of the escape time in the wells and transition probabilities between the wells. A detailed analysis of the noise-induced current is performed for the Seebeck ratchet with a weak multiplicative noise for alpha is an element of(0, 2]. KW - Levy flights KW - multiplicative noise KW - Seebeck ratchet KW - directed transport Y1 - 2015 U6 - https://doi.org/10.1088/1751-8113/48/49/495004 SN - 1751-8113 SN - 1751-8121 VL - 48 IS - 49 PB - IOP Publ. Ltd. CY - Bristol ER -