Refine
Year of publication
Language
- English (79) (remove)
Is part of the Bibliography
- yes (79)
Keywords
- anomalous diffusion (24)
- diffusion (11)
- stochastic processes (10)
- Levy flights (6)
- ageing (5)
- living cells (4)
- financial time series (3)
- first-hitting time (3)
- first-passage time (3)
- fractional Brownian motion (3)
- geometric Brownian motion (3)
- time averaging (3)
- Chebyshev inequality (2)
- Levy walk (2)
- Lévy flights (2)
- Lévy walks (2)
- Mittag-Leffler functions (2)
- Ornstein–Uhlenbeck process (2)
- Sinai diffusion (2)
- adenoassociated virus (2)
- behavior (2)
- coefficients (2)
- continuous time random walk (CTRW) (2)
- cytoplasm (2)
- dynamics (2)
- endosomal escape (2)
- ensemble and time averaged mean squared displacement (2)
- escherichia-coli (2)
- first passage (2)
- fluctuations (theory) (2)
- infection pathway (2)
- intracellular-transport (2)
- large-deviation statistic (2)
- lipid bilayer membrane dynamics (2)
- membrane (2)
- models (2)
- non-Gaussianity (2)
- nonergodicity (2)
- random-walks (2)
- single-particle tracking (2)
- stationary stochastic process (2)
- stochastic processes (theory) (2)
- subdiffusion (2)
- time-averaged mean squared displacement (2)
- trafficking (2)
- transport (2)
- truncated power-law correlated noise (2)
- weak ergodicity breaking (2)
- Anomalous diffusion exponent (1)
- Boltzmann distribution (1)
- Brownian motion (1)
- Bulk-mediated diffusion (1)
- Bulk-mediated diffusion; (1)
- Complete Bernstein function (1)
- Completely monotone function (1)
- Distributed order diffusion-wave equations (1)
- Fokker-Planck equations (1)
- Fokker-Planck-Smoluchowski equation (1)
- Fractional Brownian motion (1)
- Gaussian processes (1)
- Gompertz growth function (1)
- Langevin equation (1)
- Large deviation statistics (1)
- Levy flight (1)
- Levy foraging hypothesis (1)
- Levy walks (1)
- Mittag-Leffler function (1)
- Seebeck ratchet (1)
- Sub-gamma random variable (1)
- Vibrio Harveyi clade (1)
- autocorrelation (1)
- biological transport (1)
- bioluminescence (1)
- biophysical model (1)
- brownian motion (1)
- cell migration (1)
- chemotaxis (1)
- clustering (1)
- comb-like model (1)
- conservative random walks (1)
- convergence (1)
- covariance (1)
- diffusing diffusivity (1)
- diffusion-wave equation (1)
- directed transport (1)
- driven diffusive systems (theory) (1)
- edge turbulence (1)
- first arrival (1)
- first-passage (1)
- fluctuation relations (1)
- fluctuations (1)
- fractional diffusion (1)
- fractional dynamics (1)
- generalized diffusion equation (1)
- heterogeneous ensemble of Brownian particles (1)
- levy fight (1)
- local equilibrium (1)
- mean squared displacement (1)
- mobile-immobile model (1)
- multi-scaling (1)
- multiplicative noise (1)
- neutrophils (1)
- non-Gaussian distribution (1)
- oxygen quenching (1)
- power-law (1)
- probability density function (1)
- quenched energy landscape (1)
- quorum sensing (1)
- random search process (1)
- scaled Brownian motion (1)
- scaling laws (1)
- search dynamics (1)
- search optimization (1)
- stable laws (1)
- statistical-analysis (1)
- stochastic particle dynamics (theory) (1)
- stochastic thermodynamics (1)
- stochastic-process (1)
- superstatistics (1)
- tau proteins (1)
- zebrafish (1)
Institute
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.
It is generally believed that random search processes based on scale-free, Levy stable jump length distributions (Levy flights) optimize the search for sparse targets. Here we show that this popular search advantage is less universal than commonly assumed. We study the efficiency of a minimalist search model based on Levy flights in the absence and presence of an external drift (underwater current, atmospheric wind, a preference of the walker owing to prior experience, or a general bias in an abstract search space) based on two different optimization criteria with respect to minimal search time and search reliability (cumulative arrival probability). Although Levy flights turn out to be efficient search processes when the target is far from the starting point, or when relative to the starting point the target is upstream, we show that for close targets and for downstream target positioning regular Brownian motion turns out to be the advantageous search strategy. Contrary to claims that Levy flights with a critical exponent alpha = 1 are optimal for the search of sparse targets in different settings, based on our optimization parameters the optimal a may range in the entire interval (1, 2) and especially include Brownian motion as the overall most efficient search strategy.
Fluctuation relations for anomalous dynamics generated by time-fractional Fokker-Planck equations
(2015)
Anomalous dynamics characterized by non-Gaussian probability distributions (PDFs) and/or temporal long-range correlations can cause subtle modifications of conventional fluctuation relations (FRs). As prototypes we study three variants of a generic time-fractional Fokker-Planck equation with constant force. Type A generates superdiffusion, type B subdiffusion and type C both super-and subdiffusion depending on parameter variation. Furthermore type C obeys a fluctuation-dissipation relation whereas A and B do not. We calculate analytically the position PDFs for all three cases and explore numerically their strongly non-Gaussian shapes. While for type C we obtain the conventional transient work FR, type A and type B both yield deviations by featuring a coefficient that depends on time and by a nonlinear dependence on the work. We discuss possible applications of these types of dynamics and FRs to experiments.
We study the properties of the probability density function (PDF) of a bistable system driven by heavy tailed white symmetric L,vy noise. The shape of the stationary PDF is found analytically for the particular case of the L,vy index alpha = 1 (Cauchy noise). For an arbitrary L,vy index we employ numerical methods based on the solution of the stochastic Langevin equation and space fractional kinetic equation. In contrast to the bistable system driven by Gaussian noise, in the L,vy case, the positions of maxima of the stationary PDF do not coincide with the positions of minima of the bistable potential. We provide a detailed study of the distance between the maxima and the minima as a function of the depth of the potential and the L,vy noise parameters.
We study ultraslow diffusion processes with logarithmic mean squared displacement (MSD) < x(2)(t)> similar or equal to log(gamma)t. Comparison of annealed (renewal) continuous time random walks (CTRWs) with logarithmic waiting time distribution psi(tau) similar or equal to 1/(tau log(1+gamma)tau) and Sinai diffusion in quenched random landscapes reveals striking similarities, despite the great differences in their physical nature. In particular, they exhibit a weakly non-ergodic disparity of the time-averaged and ensemble-averaged MSDs. Remarkably, for the CTRW we observe that the fluctuations of time averages become universal, with an exponential suppression of mobile trajectories. We discuss the fundamental connection between the Golosov localization effect and non-ergodicity in the sense of the disparity between ensemble-averaged MSD and time-averaged MSD.
We study the effects of ageing-the time delay between initiation of the physical process at t = 0 and start of observation at some time t(a) > 0-and spatial confinement on the properties of heterogeneous diffusion processes (HDPs) with deterministic power-law space-dependent diffusivities, D(x) = D-0 vertical bar x vertical bar(alpha). From analysis of the ensemble and time averaged mean squared displacements and the ergodicity breaking parameter quantifying the inherent degree of irreproducibility of individual realizations of the HDP we obtain striking similarities to ageing subdiffusive continuous time random walks with scale-free waiting time distributions. We also explore how both processes can be distinguished. For confined HDPs we study the long-time saturation of the ensemble and time averaged particle displacements as well as the magnitude of the inherent scatter of time averaged displacements and contrast the outcomes to the results known for other anomalous diffusion processes under confinement.
We study the thermal Markovian diffusion of tracer particles in a 2D medium with spatially varying diffusivity D(r), mimicking recently measured, heterogeneous maps of the apparent diffusion coefficient in biological cells. For this heterogeneous diffusion process (HDP) we analyse the mean squared displacement (MSD) of the tracer particles, the time averaged MSD, the spatial probability density function, and the first passage time dynamics from the cell boundary to the nucleus. Moreover we examine the non-ergodic properties of this process which are important for the correct physical interpretation of time averages of observables obtained from single particle tracking experiments. From extensive computer simulations of the 2D stochastic Langevin equation we present an in-depth study of this HDP. In particular, we find that the MSDs along the radial and azimuthal directions in a circular domain obey anomalous and Brownian scaling, respectively. We demonstrate that the time averaged MSD stays linear as a function of the lag time and the system thus reveals a weak ergodicity breaking. Our results will enable one to rationalise the diffusive motion of larger tracer particles such as viruses or submicron beads in biological cells.
A considerable number of systems have recently been reported in which
Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability density function of the particle displacement is distinctly non-Gaussian, and often of exponential(Laplace) shape. This apparently ubiquitous behaviour observed in very different physical systems has been interpreted as resulting from diffusion in inhomogeneous environments and mathematically represented through a variable, stochastic diffusion coefficient. Indeed different models describing a fluctuating diffusivity have been studied. Here we present a new view of the stochastic basis describing time dependent random diffusivities within a broad spectrum of distributions. Concretely, our study is based on the very generic class of the generalised Gamma distribution. Two models for the particle spreading in such random diffusivity settings are studied. The first belongs to the class of generalised grey Brownian motion while the second follows from the idea of diffusing diffusivities. The two processes exhibit significant characteristics which reproduce experimental results from different biological and physical systems. We promote these two physical models for the description of stochastic particle motion in complex environments.
Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability density function of the particle displacement is distinctly non-Gaussian, and often of exponential(Laplace) shape. This apparently ubiquitous behaviour observed in very different physical systems has been interpreted as resulting from diffusion in inhomogeneous environments and mathematically represented through a variable, stochastic diffusion coefficient. Indeed different models describing a fluctuating diffusivity have been studied. Here we present a new view of the stochastic basis describing time dependent random diffusivities within a broad spectrum of distributions. Concretely, our study is based on the very generic class of the generalised Gamma distribution. Two models for the particle spreading in such random diffusivity settings are studied. The first belongs to the class of generalised grey Brownian motion while the second follows from the idea of diffusing diffusivities. The two processes exhibit significant characteristics which reproduce experimental results from different biological and physical systems. We promote these two physical models for the description of stochastic particle motion in complex environments.
In this paper we propose an algorithm to distinguish between light- and heavy-tailed probability laws underlying random datasets. The idea of the algorithm, which is visual and easy to implement, is to check whether the underlying law belongs to the domain of attraction of the Gaussian or non-Gaussian stable distribution by examining its rate of convergence. The method allows to discriminate between stable and various non-stable distributions. The test allows to differentiate between distributions, which appear the same according to standard Kolmogorov-Smirnov test. In particular, it helps to distinguish between stable and Student's t probability laws as well as between the stable and tempered stable, the cases which are considered in the literature as very cumbersome. Finally, we illustrate the procedure on plasma data to identify cases with so-called L-H transition.