13,292 research outputs found
Measurement of Anomalous Diffusion Using Recurrent Neural Networks
Anomalous diffusion occurs in many physical and biological phenomena, when
the growth of the mean squared displacement (MSD) with time has an exponent
different from one. We show that recurrent neural networks (RNN) can
efficiently characterize anomalous diffusion by determining the exponent from a
single short trajectory, outperforming the standard estimation based on the MSD
when the available data points are limited, as is often the case in
experiments. Furthermore, the RNN can handle more complex tasks where there are
no standard approaches, such as determining the anomalous diffusion exponent
from a trajectory sampled at irregular times, and estimating the switching time
and anomalous diffusion exponents of an intermittent system that switches
between different kinds of anomalous diffusion. We validate our method on
experimental data obtained from sub-diffusive colloids trapped in speckle light
fields and super-diffusive microswimmers.Comment: 6 pages, 4 figures. Supplemental material available as separate file
in the Ancillary Files sectio
Subordinated Langevin Equations for Anomalous Diffusion in External Potentials - Biasing and Decoupled Forces
The role of external forces in systems exhibiting anomalous diffusion is
discussed on the basis of the describing Langevin equations. Since there exist
different possibilities to include the effect of an external field the concept
of {\it biasing} and {\it decoupled} external fields is introduced.
Complementary to the recently established Langevin equations for anomalous
diffusion in a time-dependent external force-field [{\it Magdziarz et al.,
Phys. Rev. Lett. {\bf 101}, 210601 (2008)}] the Langevin formulation of
anomalous diffusion in a decoupled time-dependent force-field is derived
On the strong anomalous diffusion
The superdiffusion behavior, i.e. , with , in general is not completely characherized by a unique exponent. We study
some systems exhibiting strong anomalous diffusion, i.e. where and is not a linear function of .
This feature is different from the weak superdiffusion regime, i.e.
, as in random shear flows. The strong anomalous diffusion
can be generated by nontrivial chaotic dynamics, e.g. Lagrangian motion in
time-dependent incompressible velocity fields, symplectic maps and
intermittent maps. Typically the function is piecewise linear. This
corresponds to two mechanisms: a weak anomalous diffusion for the typical
events and a ballistic transport for the rare excursions. In order to have
strong anomalous diffusion one needs a violation of the hypothesis of the
central limit theorem, this happens only in a very narrow region of the control
parameters space.Comment: 27 pages, 14 figure
Anomalous Diffusion at Edge and Core of a Magnetized Cold Plasma
Progress in the theory of anomalous diffusion in weakly turbulent cold
magnetized plasmas is explained. Several proposed models advanced in the
literature are discussed. Emphasis is put on a new proposed mechanism for
anomalous diffusion transport mechanism based on the coupled action of
conductive walls (excluding electrodes) bounding the plasma drain current (edge
diffusion) together with the magnetic field flux "cutting" the area traced by
the charged particles in their orbital motion. The same reasoning is shown to
apply to the plasma core anomalous diffusion. The proposed mechanism is
expected to be valid in regimes when plasma diffusion scales as Bohm diffusion
and at high , when collisions are of secondary importance.Comment: 9 pages, 4 figure
Anomalous diffusion in the dynamics of complex processes
Anomalous diffusion, process in which the mean-squared displacement of system
states is a non-linear function of time, is usually identified in real
stochastic processes by comparing experimental and theoretical displacements at
relatively small time intervals. This paper proposes an interpolation
expression for the identification of anomalous diffusion in complex signals for
the cases when the dynamics of the system under study reaches a steady state
(large time intervals). This interpolation expression uses the chaotic
difference moment (transient structural function) of the second order as an
average characteristic of displacements. A general procedure for identifying
anomalous diffusion and calculating its parameters in real stochastic signals,
which includes the removal of the regular (low-frequency) components from the
source signal and the fitting of the chaotic part of the experimental
difference moment of the second order to the interpolation expression, is
presented. The procedure was applied to the analysis of the dynamics of
magnetoencephalograms, blinking fluorescence of quantum dots, and X-ray
emission from accreting objects. For all three applications, the interpolation
was able to adequately describe the chaotic part of the experimental difference
moment, which implies that anomalous diffusion manifests itself in these
natural signals. The results of this study make it possible to broaden the
range of complex natural processes in which anomalous diffusion can be
identified. The relation between the interpolation expression and a diffusion
model, which is derived in the paper, allows one to simulate the chaotic
processes in the open complex systems with anomalous diffusion.Comment: 47 pages, 15 figures; Submitted to Physical Review
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