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  - 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  -