Related papers: Anomalous diffusion of volcanic earthquakes
We consider a branching model of triggered seismicity, the ETAS (epidemic-type aftershock sequence) model which assumes that each earthquake can trigger other earthquakes (``aftershocks''). An aftershock sequence results in this model from…
Frequency power spectra due to a super-position of uncorrelated Lorentzian pulses with a random distribution of amplitudes are considered. For pulses with constant duration, there is an exponential frequency spectrum which is independent of…
The dynamics of steps on crystal surfaces is considered. In general, the meandering of the steps obeys a subdiffusive behaviour. The characteristic asymptotic time laws depend on the microscopic mechanism for detachment and attachment of…
Random walk has wide applications in many fields, such as machine learning, biology, physics, and chemistry. Random walk can be discrete or continuous in time and space. Asymmetric random walk could be described by drift-diffusion equation.…
We find a general formula for the distribution of time-averaged observables for systems modeled according to the sub-diffusive continuous time random walk. For Gaussian random walks coupled to a thermal bath we recover ergodicity and…
A non--linear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additonal repulsive and attractive forces leading to a changed local mobiltiy. The…
Recently observation of random walks in complex environments like the cell and other glassy systems revealed that the spreading of particles, at its tails, follows a spatial exponential decay instead of the canonical Gaussian. We use the…
Experimental studies of the diffusion of biomolecules in the environment of biological cells are routinely confronted with multiple sources of stochasticity, whose identification renders the detailed data analysis of single molecule…
Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates fluctuations in a class of random dynamical systems, arising from randomly perturbing a…
We study the influence on diffusion in one dimension of a potential energy perturbation varying as a power in space and time. We concentrate on the case of a parabolic perturbation in space decaying as $t^{-\omega}$ which shows a rich…
We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
Avalanche-like plastic bursts in crystalline materials follow power law statistics, but the scaling exponents and cutoff parameters vary widely in the literature ($\alpha$ ranging from 1 to 2.2), hindering predictive modeling. Since…
Many systems in nature are conjectured to exist at a critical point, including the brain and earthquake faults. The primary reason for this conjecture is that the distribution of clusters (avalanches of firing neurons in the brain or…
We show that seismic waiting time distributions in California and Iceland have many features in common as, for example, a power-law decay with exponent $\alpha \approx 1.1$ for intermediate and with exponent $\gamma \approx 0.6$ for short…
We study the random walk of a particle in a compartmentalized environment, as realized in biological samples or solid state compounds. Each compartment is characterized by its length $L$ and the boundaries transmittance $T$. We identify two…
We propose a simple theory for the ``universal'' scaling law previously reported for the distributions of waiting times between earthquakes. It is based on a largely used benchmark model of seismicity, which just assumes no difference in…
The fluctuation scaling law has universally been observed in a wide variety of phenomena. For counting processes describing the number of events occurred during time intervals, it is expressed as a power function relationship between the…
It is considered to re-formulate quantum theory as it appears: A theory of continuous and causal time evolution, interrupted by discontinuous and stochastic jumps. To develop the (missing) theory of jumps a heuristic-phenomenological…
In this paper we consider heterogeneous diffusion processes with the power-law dependence of the diffusion coefficient on the position and investigate the influence of external forces on the resulting anomalous diffusion. The heterogeneous…