530 Physik
Refine
Has Fulltext
- no (113) (remove)
Year of publication
Language
- English (113) (remove)
Is part of the Bibliography
- yes (113)
Keywords
- diffusion (21)
- anomalous diffusion (19)
- fractional Brownian motion (4)
- nonergodicity (4)
- Fokker-Planck equation (3)
- first passage time (3)
- first-passage (3)
- first-passage time (3)
- geometric Brownian motion (3)
- stochastic processes (3)
- subdiffusion (3)
- superstatistics (3)
- Boltzmann distribution (2)
- Brownian motion (2)
- Langevin equation (2)
- Levy flights (2)
- Levy walks (2)
- diffusing diffusivity (2)
- dynamics (2)
- first passage (2)
- first-hitting time (2)
- models (2)
- nanoparticles (2)
- power spectral analysis (2)
- random diffusivity (2)
- stochastic resetting (2)
- transport (2)
- 15 (1)
- 4 (1)
- Adam-Delbruck scenario (1)
- Biological Physics (1)
- Black– Scholes model (1)
- Brownian diffusion (1)
- Brownian yet non-Gaussian diffusion (1)
- Cattaneo equation (1)
- Chebyshev inequality (1)
- Debye screening (1)
- Econophysics (1)
- Fokker– Planck equation (1)
- Fox H-functions (1)
- Interdisciplinary Physics (1)
- Levy flight (1)
- Levy walk (1)
- Lévy flights (1)
- Lévy walks (1)
- Markov additive processes (1)
- Mittag-Leffler functions (1)
- Ornstein–Uhlenbeck process (1)
- Pareto law (1)
- Scaling exponents (1)
- Sinai diffusion (1)
- Statistical Physics (1)
- Wealth and income distribution (1)
- ageing (1)
- and surface diffusion (1)
- anomalous (or non-Fickian) diffusion (1)
- anomalous heat conduction (1)
- approximate methods (1)
- aspect ratio (1)
- asymmetric Levy flights (1)
- asymptotic analysis (1)
- autocorrelation function (1)
- autoregressive models (1)
- barrier escape (1)
- behavior (1)
- biological physics (1)
- bulk (1)
- cambridge cb4 0wf (1)
- cambs (1)
- cellular signalling (1)
- channel (1)
- clustering (1)
- codifference (1)
- coefficient (1)
- coefficients (1)
- coloured (1)
- complex (1)
- conservative random walks (1)
- continuous time random (1)
- continuous time random walk (1)
- continuous time random walk (CTRW) (1)
- correlated noise (1)
- coupled initial boundary value problem (1)
- critical adsorption (1)
- critical phenomena (1)
- crossover anomalous diffusion dynamics (1)
- crossover dynamics (1)
- cylindrical geometry (1)
- density (1)
- dimensional reduction (1)
- dynamical systems (1)
- dynamics simulation (1)
- ecological (1)
- econophysics (1)
- electrostatic interactions (1)
- electrostatics (1)
- england (1)
- ensemble and time averaged mean squared displacement (1)
- equation approach (1)
- exact results (1)
- exclusion process (1)
- exclusion processes (1)
- expanding medium (1)
- extremal values (1)
- fastest first-passage time of N walkers (1)
- financial time series (1)
- first-arrival density (1)
- first-passage time distribution (1)
- first-passage times (1)
- first-reaction time (1)
- fractional dynamic equations (1)
- fractional dynamics (1)
- gene regulatory networks (1)
- generalised langevin equation (1)
- generalized diffusion equation (1)
- heterogeneous diffusion (1)
- heterogeneous diffusion process (1)
- kinetic-theory (1)
- large deviation function (1)
- large-deviation statistic (1)
- lattice gas (1)
- lipid bilayer membrane dynamics (1)
- living cells (1)
- local equilibrium (1)
- maximum and range (1)
- mean versus most probable reaction times (1)
- membrane (1)
- membrane channel (1)
- memory kernel (1)
- milton rd (1)
- mixed boundary conditions (1)
- mobile-immobile model (1)
- molecular overcrowding (1)
- monte-carlo (1)
- motion (1)
- movement data (1)
- multidimensional fractional diffusion equation (1)
- narrow escape problem (1)
- noise (1)
- non-Gaussian (1)
- non-Gaussian diffusion (1)
- non-Gaussian distribution (1)
- non-Gaussian probability (1)
- non-Gaussianity (1)
- non-exponential relaxation (1)
- non-extensive statistics (1)
- nonequilibrium stationary state (1)
- nonstationary diffusivity (1)
- option pricing (1)
- osmotic-pressure (1)
- persistence (1)
- phase-transition boundary (1)
- polyelectrolyte adsorption (1)
- polyelectrolytes (1)
- posttranslational protein translocation (1)
- power spectral density (1)
- power spectrum (1)
- probability density function (1)
- protein search (1)
- random search processes (1)
- random-walk (1)
- random-walks (1)
- reaction cascade (1)
- reflecting boundary conditions (1)
- resetting (1)
- rotational diffusion (1)
- royal soc chemistry (1)
- scaled Brownian motion (1)
- science park (1)
- search dynamics (1)
- search efficiency (1)
- shell-like geometries (1)
- single trajectories (1)
- single trajectory analysis (1)
- single-particle tracking (1)
- single-stranded-dna (1)
- single-trajectory analysis (1)
- solid-state nanopores (1)
- space-dependent diffusivity (1)
- stationary stochastic process (1)
- statistics (1)
- stochastic dynamics (1)
- stochastic time series (1)
- structured polynucleotides (1)
- superdiffusion and (1)
- susceptibility (1)
- tau proteins (1)
- telegrapher's equation (1)
- thomas graham house (1)
- time averaging (1)
- time series analysis (1)
- time-averaged mean squared displacement (1)
- time-series analysis (1)
- truncated power-law correlated noise (1)
- walks (1)
- water diffusion in the brain (1)
- weak ergodicity breaking (1)
Institute
We study the diffusive motion of a particle in a subharmonic potential of the form U(x) = |x|( c ) (0 < c < 2) driven by long-range correlated, stationary fractional Gaussian noise xi ( alpha )(t) with 0 < alpha <= 2. In the absence of the potential the particle exhibits free fractional Brownian motion with anomalous diffusion exponent alpha. While for an harmonic external potential the dynamics converges to a Gaussian stationary state, from extensive numerical analysis we here demonstrate that stationary states for shallower than harmonic potentials exist only as long as the relation c > 2(1 - 1/alpha) holds. We analyse the motion in terms of the mean squared displacement and (when it exists) the stationary probability density function. Moreover we discuss analogies of non-stationarity of Levy flights in shallow external potentials.
Fixational eye movements show scaling behaviour of the positional mean-squared displacement with a characteristic transition from persistence to antipersistence for increasing time-lag. These statistical patterns were found to be mainly shaped by microsaccades (fast, small-amplitude movements). However, our re-analysis of fixational eye-movement data provides evidence that the slow component (physiological drift) of the eyes exhibits scaling behaviour of the mean-squared displacement that varies across human participants. These results suggest that drift is a correlated movement that interacts with microsaccades. Moreover, on the long time scale, the mean-squared displacement of the drift shows oscillations, which is also present in the displacement auto-correlation function. This finding lends support to the presence of time-delayed feedback in the control of drift movements. Based on an earlier non-linear delayed feedback model of fixational eye movements, we propose and discuss different versions of a new model that combines a self-avoiding walk with time delay. As a result, we identify a model that reproduces oscillatory correlation functions, the transition from persistence to antipersistence, and microsaccades.
We consider a sequential cascade of molecular first-reaction events towards a terminal reaction centre in which each reaction step is controlled by diffusive motion of the particles. The model studied here represents a typical reaction setting encountered in diverse molecular biology systems, in which, e.g. a signal transduction proceeds via a series of consecutive 'messengers': the first messenger has to find its respective immobile target site triggering a launch of the second messenger, the second messenger seeks its own target site and provokes a launch of the third messenger and so on, resembling a relay race in human competitions. For such a molecular relay race taking place in infinite one-, two- and three-dimensional systems, we find exact expressions for the probability density function of the time instant of the terminal reaction event, conditioned on preceding successful reaction events on an ordered array of target sites. The obtained expressions pertain to the most general conditions: number of intermediate stages and the corresponding diffusion coefficients, the sizes of the target sites, the distances between them, as well as their reactivities are arbitrary.