TY - JOUR A1 - Mutothya, Nicholas Mwilu A1 - Xu, Yong A1 - Li, Yongge A1 - Metzler, Ralf T1 - Characterising stochastic motion in heterogeneous media driven by coloured non-Gaussian noise JF - Journal of physics : A, Mathematical and theoretical N2 - We study the stochastic motion of a test particle in a heterogeneous medium in terms of a position dependent diffusion coefficient mimicking measured deterministic diffusivity gradients in biological cells or the inherent heterogeneity of geophysical systems. Compared to previous studies we here investigate the effect of the interplay of anomalous diffusion effected by position dependent diffusion coefficients and coloured non-Gaussian noise. The latter is chosen to be distributed according to Tsallis' q-distribution, representing a popular example for a non-extensive statistic. We obtain the ensemble and time averaged mean squared displacements for this generalised process and establish its non-ergodic properties as well as analyse the non-Gaussian nature of the associated displacement distribution. We consider both non-stratified and stratified environments. KW - diffusion KW - anomalous diffusion KW - non-extensive statistics KW - coloured KW - noise KW - heterogeneous diffusion process Y1 - 2021 U6 - https://doi.org/10.1088/1751-8121/abfba6 SN - 1751-8113 SN - 1751-8121 VL - 54 IS - 29 PB - IOP Publ. Ltd. CY - Bristol 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 - TY - JOUR A1 - Mutothya, Nicholas Mwilu A1 - Xu, Yong A1 - Li, Yongge A1 - Metzler, Ralf A1 - Mutua, Nicholas Muthama T1 - First passage dynamics of stochastic motion in heterogeneous media driven by correlated white Gaussian and coloured non-Gaussian noises JF - Journal of physics. Complexity N2 - We study the first passage dynamics for a diffusing particle experiencing a spatially varying diffusion coefficient while driven by correlated additive Gaussian white noise and multiplicative coloured non-Gaussian noise. We consider three functional forms for position dependence of the diffusion coefficient: power-law, exponential, and logarithmic. The coloured non-Gaussian noise is distributed according to Tsallis' q-distribution. Tracks of the non-Markovian systems are numerically simulated by using the fourth-order Runge-Kutta algorithm and the first passage times (FPTs) are recorded. The FPT density is determined along with the mean FPT (MFPT). Effects of the noise intensity and self-correlation of the multiplicative noise, the intensity of the additive noise, the cross-correlation strength, and the non-extensivity parameter on the MFPT are discussed. KW - first passage KW - diffusion KW - non-Gaussian KW - correlated noise Y1 - 2021 U6 - https://doi.org/10.1088/2632-072X/ac35b5 SN - 2632-072X VL - 2 PB - IOP Publishing CY - Bristol ER - TY - JOUR A1 - Xu, Yong A1 - Liu, Xuemei A1 - Li, Yongge A1 - Metzler, Ralf T1 - Heterogeneous diffusion processes and nonergodicity with Gaussian colored noise in layered diffusivity landscapes JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - Heterogeneous diffusion processes (HDPs) with space-dependent diffusion coefficients D(x) are found in a number of real-world systems, such as for diffusion of macromolecules or submicron tracers in biological cells. Here, we examine HDPs in quenched-disorder systems with Gaussian colored noise (GCN) characterized by a diffusion coefficient with a power-law dependence on the particle position and with a spatially random scaling exponent. Typically, D(x) is considered to be centerd at the origin and the entire x axis is characterized by a single scaling exponent a. In this work we consider a spatially random scenario: in periodic intervals ("layers") in space D(x) is centerd to the midpoint of each interval. In each interval the scaling exponent alpha is randomly chosen from a Gaussian distribution. The effects of the variation of the scaling exponents, the periodicity of the domains ("layer thickness") of the diffusion coefficient in this stratified system, and the correlation time of the GCN are analyzed numerically in detail. We discuss the regimes of superdiffusion, subdiffusion, and normal diffusion realisable in this system. We observe and quantify the domains where nonergodic and non-Gaussian behaviors emerge in this system. Our results provide new insights into the understanding of weak ergodicity breaking for HDPs driven by colored noise, with potential applications in quenched layered systems, typical model systems for diffusion in biological cells and tissues, as well as for diffusion in geophysical systems. Y1 - 2020 U6 - https://doi.org/10.1103/PhysRevE.102.062106 SN - 2470-0045 SN - 2470-0053 VL - 102 IS - 6 PB - American Physical Society CY - College Park ER - TY - GEN A1 - Li, Yongge A1 - Mei, Ruoxing A1 - Xu, Yong A1 - Kurths, Jürgen A1 - Duan, Jinqiao A1 - Metzler, Ralf T1 - Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - This work focuses on the dynamics of particles in a confined geometry with position-dependent diffusivity, where the confinement is modelled by a periodic channel consisting of unit cells connected by narrow passage ways. We consider three functional forms for the diffusivity, corresponding to the scenarios of a constant (D ₀), as well as a low (D ₘ) and a high (D d) mobility diffusion in cell centre of the longitudinally symmetric cells. Due to the interaction among the diffusivity, channel shape and external force, the system exhibits complex and interesting phenomena. By calculating the probability density function, mean velocity and mean first exit time with the Itô calculus form, we find that in the absence of external forces the diffusivity D d will redistribute particles near the channel wall, while the diffusivity D ₘ will trap them near the cell centre. The superposition of external forces will break their static distributions. Besides, our results demonstrate that for the diffusivity D d, a high dependence on the x coordinate (parallel with the central channel line) will improve the mean velocity of the particles. In contrast, for the diffusivity D ₘ, a weak dependence on the x coordinate will dramatically accelerate the moving speed. In addition, it shows that a large external force can weaken the influences of different diffusivities; inversely, for a small external force, the types of diffusivity affect significantly the particle dynamics. In practice, one can apply these results to achieve a prominent enhancement of the particle transport in two- or three-dimensional channels by modulating the local tracer diffusivity via an engineered gel of varying porosity or by adding a cold tube to cool down the diffusivity along the central line, which may be a relevant effect in engineering applications. Effects of different stochastic calculi in the evaluation of the underlying multiplicative stochastic equation for different physical scenarios are discussed. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 974 KW - diffusion KW - channel KW - space-dependent diffusivity Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-474542 SN - 1866-8372 IS - 974 ER - TY - JOUR A1 - Li, Yongge A1 - Mei, Ruoxing A1 - Xu, Yong A1 - Kurths, Jürgen A1 - Duan, Jinqiao A1 - Metzler, Ralf T1 - Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity JF - New Journal of Physics N2 - This work focuses on the dynamics of particles in a confined geometry with position-dependent diffusivity, where the confinement is modelled by a periodic channel consisting of unit cells connected by narrow passage ways. We consider three functional forms for the diffusivity, corresponding to the scenarios of a constant (D ₀), as well as a low (D ₘ) and a high (D d) mobility diffusion in cell centre of the longitudinally symmetric cells. Due to the interaction among the diffusivity, channel shape and external force, the system exhibits complex and interesting phenomena. By calculating the probability density function, mean velocity and mean first exit time with the Itô calculus form, we find that in the absence of external forces the diffusivity D d will redistribute particles near the channel wall, while the diffusivity D ₘ will trap them near the cell centre. The superposition of external forces will break their static distributions. Besides, our results demonstrate that for the diffusivity D d, a high dependence on the x coordinate (parallel with the central channel line) will improve the mean velocity of the particles. In contrast, for the diffusivity D ₘ, a weak dependence on the x coordinate will dramatically accelerate the moving speed. In addition, it shows that a large external force can weaken the influences of different diffusivities; inversely, for a small external force, the types of diffusivity affect significantly the particle dynamics. In practice, one can apply these results to achieve a prominent enhancement of the particle transport in two- or three-dimensional channels by modulating the local tracer diffusivity via an engineered gel of varying porosity or by adding a cold tube to cool down the diffusivity along the central line, which may be a relevant effect in engineering applications. Effects of different stochastic calculi in the evaluation of the underlying multiplicative stochastic equation for different physical scenarios are discussed. KW - diffusion KW - channel KW - space-dependent diffusivity Y1 - 2020 U6 - https://doi.org/10.1088/1367-2630/ab81b9 SN - 1367-2630 VL - 22 PB - Dt. Physikalische Ges. CY - Bad Honnef ER - TY - JOUR A1 - Li, Hua A1 - Xu, Yong A1 - Li, Yongge A1 - Metzler, Ralf T1 - Transition path dynamics across rough inverted parabolic potential barrier JF - The European physical journal : Plus N2 - Transition path dynamics have been widely studied in chemical, physical, and technological systems. Mostly, the transition path dynamics is obtained for smooth barrier potentials, for instance, generic inverse-parabolic shapes. We here present analytical results for the mean transition path time, the distribution of transition path times, the mean transition path velocity, and the mean transition path shape in a rough inverted parabolic potential function under the driving of Gaussian white noise. These are validated against extensive simulations using the forward flux sampling scheme in parallel computations. We observe how precisely the potential roughness, the barrier height, and the noise intensity contribute to the particle transition in the rough inverted barrier potential. Y1 - 2020 U6 - https://doi.org/10.1140/epjp/s13360-020-00752-7 SN - 2190-5444 VL - 135 IS - 9 PB - Springer CY - Berlin ; Heidelberg ER -