Dokument-ID Dokumenttyp Verfasser/Autoren Herausgeber Haupttitel Abstract Auflage Verlagsort Verlag Erscheinungsjahr Seitenzahl Schriftenreihe Titel Schriftenreihe Bandzahl ISBN Quelle der Hochschulschrift Konferenzname Quelle:Titel Quelle:Jahrgang Quelle:Heftnummer Quelle:Erste Seite Quelle:Letzte Seite URN DOI Abteilungen OPUS4-38814 Wissenschaftlicher Artikel Bodrova, Anna S.; Chechkin, Aleksei V.; Cherstvy, Andrey G.; Metzler, Ralf Ultraslow scaled Brownian motion We define and study in detail utraslow scaled Brownian motion (USBM) characterized by a time dependent diffusion coefficient of the form D(t) similar or equal to 1/t. For unconfined motion the mean squared displacement (MSD) of USBM exhibits an ultraslow, logarithmic growth as function of time, in contrast to the conventional scaled Brownian motion. In a harmonic potential the MSD of USBM does not saturate but asymptotically decays inverse-proportionally to time, reflecting the highly non-stationary character of the process. We show that the process is weakly non-ergodic in the sense that the time averaged MSD does not converge to the regular MSD even at long times, and for unconfined motion combines a linear lag time dependence with a logarithmic term. The weakly non-ergodic behaviour is quantified in terms of the ergodicity breaking parameter. The USBM process is also shown to be ageing: observables of the system depend on the time gap between initiation of the test particle and start of the measurement of its motion. Our analytical results are shown to agree excellently with extensive computer simulations. Bristol IOP Publ. Ltd. 2015 16 New journal of physics : the open-access journal for physics 17 10.1088/1367-2630/17/6/063038 Institut für Physik und Astronomie OPUS4-38753 Wissenschaftlicher Artikel Dieterich, Peter; Klages, Rainer; Chechkin, Aleksei V. Fluctuation relations for anomalous dynamics generated by time-fractional Fokker-Planck equations Anomalous dynamics characterized by non-Gaussian probability distributions (PDFs) and/or temporal long-range correlations can cause subtle modifications of conventional fluctuation relations (FRs). As prototypes we study three variants of a generic time-fractional Fokker-Planck equation with constant force. Type A generates superdiffusion, type B subdiffusion and type C both super-and subdiffusion depending on parameter variation. Furthermore type C obeys a fluctuation-dissipation relation whereas A and B do not. We calculate analytically the position PDFs for all three cases and explore numerically their strongly non-Gaussian shapes. While for type C we obtain the conventional transient work FR, type A and type B both yield deviations by featuring a coefficient that depends on time and by a nonlinear dependence on the work. We discuss possible applications of these types of dynamics and FRs to experiments. Bristol IOP Publ. Ltd. 2015 14 New journal of physics : the open-access journal for physics 17 10.1088/1367-2630/17/7/075004 Institut für Physik und Astronomie OPUS4-38747 Wissenschaftlicher Artikel Krüsemann, Henning; Godec, Aljaz; Metzler, Ralf Ageing first passage time density in continuous time random walks and quenched energy landscapes We study the first passage dynamics of an ageing stochastic process in the continuous time random walk (CTRW) framework. In such CTRW processes the test particle performs a random walk, in which successive steps are separated by random waiting times distributed in terms of the waiting time probability density function Psi (t) similar or equal to t(-1-alpha) (0 <= alpha <= 2). An ageing stochastic process is defined by the explicit dependence of its dynamic quantities on the ageing time t(a), the time elapsed between its preparation and the start of the observation. Subdiffusive ageing CTRWs with 0 < alpha < 1 describe systems such as charge carriers in amorphous semiconducters, tracer dispersion in geological and biological systems, or the dynamics of blinking quantum dots. We derive the exact forms of the first passage time density for an ageing subdiffusive CTRW in the semi-infinite, confined, and biased case, finding different scaling regimes for weakly, intermediately, and strongly aged systems: these regimes, with different scaling laws, are also found when the scaling exponent is in the range 1 < alpha < 2, for sufficiently long ta. We compare our results with the ageing motion of a test particle in a quenched energy landscape. We test our theoretical results in the quenched landscape against simulations: only when the bias is strong enough, the correlations from returning to previously visited sites become insignificant and the results approach the ageing CTRW results. With small bias or without bias, the ageing effects disappear and a change in the exponent compared to the case of a completely annealed landscape can be found, reflecting the build-up of correlations in the quenched landscape. Bristol IOP Publ. Ltd. 2015 20 Journal of physics : A, Mathematical and theoretical 48 28 10.1088/1751-8113/48/28/285001 Institut für Physik und Astronomie OPUS4-7860 Wissenschaftlicher Artikel Metzler, Ralf; Cherstvy, Andrey G.; Chechkin, Aleksei V.; Bodrova, Anna S. Ultraslow scaled Brownian motion We define and study in detail utraslow scaled Brownian motion (USBM) characterized by a time dependent diffusion coefficient of the form . For unconfined motion the mean squared displacement (MSD) of USBM exhibits an ultraslow, logarithmic growth as function of time, in contrast to the conventional scaled Brownian motion. In a harmonic potential the MSD of USBM does not saturate but asymptotically decays inverse-proportionally to time, reflecting the highly non-stationary character of the process. We show that the process is weakly non-ergodic in the sense that the time averaged MSD does not converge to the regular MSD even at long times, and for unconfined motion combines a linear lag time dependence with a logarithmic term. The weakly non-ergodic behaviour is quantified in terms of the ergodicity breaking parameter. The USBM process is also shown to be ageing: observables of the system depend on the time gap between initiation of the test particle and start of the measurement of its motion. Our analytical results are shown to agree excellently with extensive computer simulations. Bad Honnef, London Dt. Physikalische Ges., IOP 2015 New journal of physics : the open-access journal for physics 17 063038 10.1088/1367-2630/17/6/063038 Institut für Physik und Astronomie OPUS4-38596 Wissenschaftlicher Artikel Safdari, Hadiseh; Cherstvy, Andrey G.; Chechkin, Aleksei V.; Thiel, Felix; Sokolov, Igor M.; Metzler, Ralf Quantifying the non-ergodicity of scaled Brownian motion We examine the non-ergodic properties of scaled Brownian motion (SBM), a non-stationary stochastic process with a time dependent diffusivity of the form D(t) similar or equal to t(alpha-1). We compute the ergodicity breaking parameter EB in the entire range of scaling exponents a, both analytically and via extensive computer simulations of the stochastic Langevin equation. We demonstrate that in the limit of long trajectory lengths T and short lag times Delta the EB parameter as function of the scaling exponent a has no divergence at alpha - 1/2 and present the asymptotes for EB in different limits. We generalize the analytical and simulations results for the time averaged and ergodic properties of SBM in the presence of ageing, that is, when the observation of the system starts only a finite time span after its initiation. The approach developed here for the calculation of the higher time averaged moments of the particle displacement can be applied to derive the ergodic properties of other stochastic processes such as fractional Brownian motion. Bristol IOP Publ. Ltd. 2015 18 Journal of physics : A, Mathematical and theoretical 48 37 10.1088/1751-8113/48/37/375002 Institut für Physik und Astronomie OPUS4-38715 Wissenschaftlicher Artikel Sandev, Trifce; Chechkin, Aleksei V.; Kantz, Holger; Metzler, Ralf Diffusion and fokker-planck-smoluchowski equations with generalized memory kernel 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. Berlin De Gruyter 2015 33 Fractional calculus and applied analysis : an international journal for theory and applications 18 4 1006 1038 10.1515/fca-2015-0059 Institut für Physik und Astronomie OPUS4-38449 Wissenschaftlicher Artikel Shin, Jaeoh; Cherstvy, Andrey G.; Metzler, Ralf Self-subdiffusion in solutions of star-shaped crowders: non-monotonic effects of inter-particle interactions We examine by extensive computer simulations the self-diffusion of anisotropic star-like particles in crowded two-dimensional solutions. We investigate the implications of the area coverage fraction phi of the crowders and the crowder-crowder adhesion properties on the regime of transient anomalous diffusion. We systematically compute the mean squared displacement (MSD) of the particles, their time averaged MSD, and the effective diffusion coefficient. The diffusion is ergodic in the limit of long traces, such that the mean time averaged MSD converges towards the ensemble averaged MSD, and features a small residual amplitude spread of the time averaged MSD from individual trajectories. At intermediate time scales, we quantify the anomalous diffusion in the system. Also, we show that the translational-but not rotational-diffusivity of the particles Dis a nonmonotonic function of the attraction strength between them. Both diffusion coefficients decrease as the power law D(phi) similar to (1 - phi/phi*)(2 ... 2.4) with the area fraction phi occupied by the crowders and the critical value phi*. Our results might be applicable to rationalising the experimental observations of non-Brownian diffusion for a number of standard macromolecular crowders used in vitro to mimic the cytoplasmic conditions of living cells. Bristol IOP Publ. Ltd. 2015 12 New journal of physics : the open-access journal for physics 17 10.1088/1367-2630/17/11/113028 Institut für Physik und Astronomie