TY  - GEN
A1  - Bodrova, Anna S.
A1  - Chechkin, Aleksei V.
A1  - Cherstvy, Andrey G.
A1  - Safdari, Hadiseh
A1  - Sokolov, Igor M.
A1  - Metzler, Ralf
T1  - Underdamped scaled Brownian motion
BT  - (non-)existence of the overdamped limit in anomalous diffusion
N2  - It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 267 
Y1  - 2016
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-97158
ER  - 
TY  - GEN
A1  - Molina-Garcia, Daniel
A1  - Sandev, Trifce
A1  - Safdari, Hadiseh
A1  - Pagnini, Gianni
A1  - Chechkin, Aleksei V.
A1  - Metzler, Ralf
T1  - Crossover from anomalous to normal diffusion
BT  - truncated power-law noise correlations and applications to dynamics in lipid bilayers
T2  - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe
N2  - Abstract

The emerging diffusive dynamics in many complex systems show a characteristic crossover behaviour from anomalous to normal diffusion which is otherwise fitted by two independent power-laws. A prominent example for a subdiffusive–diffusive crossover are viscoelastic systems such as lipid bilayer membranes, while superdiffusive–diffusive crossovers occur in systems of actively moving biological cells. We here consider the general dynamics of a stochastic particle driven by so-called tempered fractional Gaussian noise, that is noise with Gaussian amplitude and power-law correlations, which are cut off at some mesoscopic time scale. Concretely we consider such noise with built-in exponential or power-law tempering, driving an overdamped Langevin equation (fractional Brownian motion) and fractional Langevin equation motion. We derive explicit expressions for the mean squared displacement and correlation functions, including different shapes of the crossover behaviour depending on the concrete tempering, and discuss the physical meaning of the tempering. In the case of power-law tempering we also find a crossover behaviour from faster to slower superdiffusion and slower to faster subdiffusion. As a direct application of our model we demonstrate that the obtained dynamics quantitatively describes the subdiffusion–diffusion and subdiffusion–subdiffusion crossover in lipid bilayer systems. We also show that a model of tempered fractional Brownian motion recently proposed by Sabzikar and Meerschaert leads to physically very different behaviour with a seemingly paradoxical ballistic long time scaling.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 507 
KW  - anomalous diffusion
KW  - truncated power-law correlated noise
KW  - lipid bilayer membrane dynamics
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-422590
SN  - 1866-8372
IS  - 507
ER  -