TY  - JOUR
A1  - Petreska, Irina
A1  - Pejov, Ljupco
A1  - Sandev, Trifce
A1  - Kocarev, Ljupčo
A1  - Metzler, Ralf
T1  - Tuning of the dielectric relaxation and complex susceptibility in a system of polar molecules: a generalised model based on rotational diffusion with resetting
JF  - Fractal and fractional
N2  - The application of the fractional calculus in the mathematical modelling of relaxation processes in complex heterogeneous media has attracted a considerable amount of interest lately. 
The reason for this is the successful implementation of fractional stochastic and kinetic equations in the studies of non-Debye relaxation. 
In this work, we consider the rotational diffusion equation with a generalised memory kernel in the context of dielectric relaxation processes in a medium composed of polar molecules. We give an overview of existing models on non-exponential relaxation and introduce an exponential resetting dynamic in the corresponding process. 
The autocorrelation function and complex susceptibility are analysed in detail. 
We show that stochastic resetting leads to a saturation of the autocorrelation function to a constant value, in contrast to the case without resetting, for which it decays to zero. The behaviour of the autocorrelation function, as well as the complex susceptibility in the presence of resetting, confirms that the dielectric relaxation dynamics can be tuned by an appropriate choice of the resetting rate. 
The presented results are general and flexible, and they will be of interest for the theoretical description of non-trivial relaxation dynamics in heterogeneous systems composed of polar molecules.
KW  - rotational diffusion
KW  - memory kernel
KW  - Fokker-Planck equation
KW  - non-exponential relaxation
KW  - autocorrelation function
KW  - complex
KW  - susceptibility
Y1  - 2022
U6  - https://doi.org/10.3390/fractalfract6020088
SN  - 2504-3110
VL  - 6
IS  - 2
PB  - MDPI AG, Fractal Fract Editorial Office
CY  - Basel
ER  - 
TY  - JOUR
A1  - Sandev, Trifce
A1  - Domazetoski, Viktor
A1  - Kocarev, Ljupco
A1  - Metzler, Ralf
A1  - Chechkin, Aleksei
T1  - Heterogeneous diffusion with stochastic resetting
JF  - Journal of physics : A, Mathematical and theoretical
N2  - We study a heterogeneous diffusion process (HDP) with position-dependent diffusion coefficient and Poissonian stochastic resetting. 

We find exact results for the mean squared displacement and the probability density function. The nonequilibrium steady state reached in the long time limit is studied. 
We also analyse the transition to the non-equilibrium steady state by finding the large deviation function. 

We found that similarly to the case of the normal diffusion process where the diffusion length grows like t (1/2) while the length scale xi(t) of the inner core region of the nonequilibrium steady state grows linearly with time t, in the HDP with diffusion length increasing like t ( p/2) the length scale xi(t) grows like t ( p ). 

The obtained results are verified by numerical solutions of the corresponding Langevin equation.
KW  - heterogeneous diffusion
KW  - Fokker-Planck equation
KW  - Langevin equation
KW  - stochastic resetting
KW  - nonequilibrium stationary state
KW  - large deviation function
Y1  - 2022
U6  - https://doi.org/10.1088/1751-8121/ac491c
SN  - 1751-8113
SN  - 1751-8121
VL  - 55
IS  - 7
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -