TY  - JOUR
A1  - Burnecki, Krzysztof
A1  - Wylomanska, Agnieszka
A1  - Beletskii, Aleksei
A1  - Gonchar, Vsevolod
A1  - Chechkin, Aleksei V.
T1  - Recognition of stable distribution with levy index alpha close to 2
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - We address the problem of recognizing alpha-stable Levy distribution with Levy index close to 2 from experimental data. We are interested in the case when the sample size of available data is not large, thus the power law asymptotics of the distribution is not clearly detectable, and the shape of the empirical probability density function is close to a Gaussian. We propose a testing procedure combining a simple visual test based on empirical fourth moment with the Anderson-Darling and Jarque-Bera statistical tests and we check the efficiency of the method on simulated data. Furthermore, we apply our method to the analysis of turbulent plasma density and potential fluctuations measured in the stellarator-type fusion device and demonstrate that the phenomenon of the L-H transition from low confinement, L mode, to a high confinement, H mode, which occurs in this device is accompanied by the transition from Levy to Gaussian fluctuation statistics.
Y1  - 2012
U6  - https://doi.org/10.1103/PhysRevE.85.056711
SN  - 1539-3755
VL  - 85
IS  - 5
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Chechkin, Aleksei V.
A1  - Lenz, F.
A1  - Klages, Rainer
T1  - Normal and anomalous fluctuation relations for gaussian stochastic dynamics
JF  - Journal of statistical mechanics: theory and experiment
N2  - We study transient work fluctuation relations (FRs) for Gaussian stochastic systems generating anomalous diffusion. For this purpose we use a Langevin approach by employing two different types of additive noise: (i) internal noise where the fluctuation dissipation relation of the second kind (FDR II) holds, and (ii) external noise without FDR II. For internal noise we demonstrate that the existence of FDR II implies the existence of the fluctuation dissipation relation of the first kind (FDR I), which in turn leads to conventional (normal) forms of transient work FRs. For systems driven by external noise we obtain violations of normal FRs, which we call anomalous FRs. We derive them in the long-time limit and demonstrate the existence of logarithmic factors in FRs for intermediate times. We also outline possible experimental verifications.
KW  - stochastic particle dynamics (theory)
KW  - fluctuations (theory)
KW  - stochastic processes (theory)
KW  - diffusion
Y1  - 2012
U6  - https://doi.org/10.1088/1742-5468/2012/11/L11001
SN  - 1742-5468
IS  - 4
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Chechkin, Aleksei V.
A1  - Zaid, Irwin M.
A1  - Lomholt, Michael A.
A1  - Sokolov, Igor M.
A1  - Metzler, Ralf
T1  - Bulk-mediated diffusion on a planar surface full solution
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - We consider the effective surface motion of a particle that intermittently unbinds from a planar surface and performs bulk excursions. Based on a random-walk approach, we derive the diffusion equations for surface and bulk diffusion including the surface-bulk coupling. From these exact dynamic equations, we analytically obtain the propagator of the effective surface motion. This approach allows us to deduce a superdiffusive, Cauchy-type behavior on the surface, together with exact cutoffs limiting the Cauchy form. Moreover, we study the long-time dynamics for the surface motion.
Y1  - 2012
U6  - https://doi.org/10.1103/PhysRevE.86.041101
SN  - 1539-3755
VL  - 86
IS  - 4
PB  - American Physical Society
CY  - College Park
ER  -