104 research outputs found
Generalized Elastic Model: thermal vs non-thermal initial conditions. Universal scaling, roughening, ageing and ergodicity
We study correlation properties of the generalized elastic model which
accounts for the dynamics of polymers, membranes, surfaces and fluctuating
interfaces, among others. We develop a theoretical framework which leads to the
emergence of universal scaling laws for systems starting from thermal
(equilibrium) or non-thermal (non-equilibrium) initial conditions. Our analysis
incorporates and broadens previous results such as observables' double scaling
regimes, (super)roughening and anomalous diffusion, and furnishes a new scaling
behavior for correlation functions at small times (long distances). We discuss
ageing and ergodic properties of the generalized elastic model in
non-equilibrium conditions, providing a comparison with the situation occurring
in continuous time random walk. Our analysis also allows to assess which
observable is able to distinguish whether the system is in or far from
equilibrium conditions in an experimental set-up
Correlated continuous-time random walks: combining scale-invariance with long-range memory for spatial and temporal dynamics
Standard continuous time random walk (CTRW) models are renewal processes in
the sense that at each jump a new, independent pair of jump length and waiting
time are chosen. Globally, anomalous diffusion emerges through action of the
generalized central limit theorem leading to scale-free forms of the jump
length or waiting time distributions. Here we present a modified version of
recently proposed correlated CTRW processes, where we incorporate a power-law
correlated noise on the level of both jump length and waiting time dynamics. We
obtain a very general stochastic model, that encompasses key features of
several paradigmatic models of anomalous diffusion: discontinuous, scale-free
displacements as in Levy flights, scale-free waiting times as in subdiffusive
CTRWs, and the long-range temporal correlations of fractional Brownian motion
(FBM). We derive the exact solutions for the single-time probability density
functions and extract the scaling behaviours. Interestingly, we find that
different combinations of the model parameters lead to indistinguishable shapes
of the emerging probability density functions and identical scaling laws. Our
model will be useful to describe recent experimental single particle tracking
data, that feature a combination of CTRW and FBM properties.Comment: 25 pages, IOP style, 5 figure
- …