TY  - JOUR
A1  - Sandev, Trifce
A1  - Iomin, Alexander
A1  - Kocarev, Ljupco
T1  - Hitting times in turbulent diffusion due to multiplicative noise
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - We study a distribution of times of the first arrivals to absorbing targets in turbulent diffusion, which is due to a multiplicative noise. Two examples of dynamical systems with a multiplicative noise are studied. The first one is a random process according to inhomogeneous diffusion, which is also known as a geometric Brownian motion in the Black-Scholes model. The second model is due to a random processes on a two-dimensional comb, where inhomogeneous advection is possible only along the backbone, while Brownian diffusion takes place inside the branches. It is shown that in both cases turbulent diffusion takes place as the one-dimensional random process with the log-normal distribution in the presence of absorbing targets, which are characterized by the Levy-Smirnov distribution for the first hitting times.
Y1  - 2020
U6  - https://doi.org/10.1103/PhysRevE.102.042109
SN  - 2470-0045
SN  - 2470-0053
VL  - 102
IS  - 4
PB  - American Institute of Physics
CY  - Woodbury, NY
ER  - 
TY  - JOUR
A1  - Sandev, Trifce
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  -