2,889 research outputs found
Aging Scaled Brownian Motion
Scaled Brownian motion (SBM) is widely used to model anomalous diffusion of
passive tracers in complex and biological systems. It is a highly
non-stationary process governed by the Langevin equation for Brownian motion,
however, with a power-law time dependence of the noise strength. Here we study
the aging properties of SBM for both unconfined and confined motion.
Specifically, we derive the ensemble and time averaged mean squared
displacements and analyze their behavior in the regimes of weak, intermediate,
and strong aging. A very rich behavior is revealed for confined aging SBM
depending on different aging times and whether the process is sub- or
superdiffusive. We demonstrate that the information on the aging factorizes
with respect to the lag time and exhibits a functional form, that is identical
to the aging behavior of scale free continuous time random walk processes.
While SBM exhibits a disparity between ensemble and time averaged observables
and is thus weakly non-ergodic, strong aging is shown to effect a convergence
of the ensemble and time averaged mean squared displacement. Finally, we derive
the density of first passage times in the semi-infinite domain that features a
crossover defined by the aging time.Comment: 10 pages, 8 figures, REVTe
Occurrence of normal and anomalous diffusion in polygonal billiard channels
From extensive numerical simulations, we find that periodic polygonal
billiard channels with angles which are irrational multiples of pi generically
exhibit normal diffusion (linear growth of the mean squared displacement) when
they have a finite horizon, i.e. when no particle can travel arbitrarily far
without colliding. For the infinite horizon case we present numerical tests
showing that the mean squared displacement instead grows asymptotically as t
log t. When the unit cell contains accessible parallel scatterers, however, we
always find anomalous super-diffusion, i.e. power-law growth with an exponent
larger than 1. This behavior cannot be accounted for quantitatively by a simple
continuous-time random walk model. Instead, we argue that anomalous diffusion
correlates with the existence of families of propagating periodic orbits.
Finally we show that when a configuration with parallel scatterers is
approached there is a crossover from normal to anomalous diffusion, with the
diffusion coefficient exhibiting a power-law divergence.Comment: 9 pages, 15 figures. Revised after referee reports: redrawn figures,
additional comments. Some higher quality figures available at
http://www.fis.unam.mx/~dsander
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
Blinking statistics of a molecular beacon triggered by end-denaturation of DNA
We use a master equation approach based on the Poland-Scheraga free energy
for DNA denaturation to investigate the (un)zipping dynamics of a denaturation
wedge in a stretch of DNA, that is clamped at one end. In particular, we
quantify the blinking dynamics of a fluorophore-quencher pair mounted within
the denaturation wedge. We also study the behavioural changes in the presence
of proteins, that selectively bind to single-stranded DNA. We show that such a
setup could be well-suited as an easy-to-implement nanodevice for sensing
environmental conditions in small volumes.Comment: 14 pages, 5 figures, LaTeX, IOP style. Accepted to J Phys Cond Mat
special issue on diffusio
Fractional Klein-Kramers equation for superdiffusive transport: normal versus anomalous time evolution in a differential L{\'e}vy walk model
We introduce a fractional Klein-Kramers equation which describes
sub-ballistic superdiffusion in phase space in the presence of a
space-dependent external force field. This equation defines the differential
L{\'e}vy walk model whose solution is shown to be non-negative. In the velocity
coordinate, the probability density relaxes in Mittag-Leffler fashion towards
the Maxwell distribution whereas in the space coordinate, no stationary
solution exists and the temporal evolution of moments exhibits a competition
between Brownian and anomalous contributions.Comment: 4 pages, REVTe
Universal Multifractality in Quantum Hall Systems with Long-Range Disorder Potential
We investigate numerically the localization-delocalization transition in
quantum Hall systems with long-range disorder potential with respect to
multifractal properties. Wavefunctions at the transition energy are obtained
within the framework of the generalized Chalker--Coddington network model. We
determine the critical exponent characterizing the scaling behavior
of the local order parameter for systems with potential correlation length
up to magnetic lengths . Our results show that does not
depend on the ratio . With increasing , effects due to classical
percolation only cause an increase of the microscopic length scale, whereas the
critical behavior on larger scales remains unchanged. This proves that systems
with long-range disorder belong to the same universality class as those with
short-range disorder.Comment: 4 pages, 2 figures, postsript, uuencoded, gz-compresse
Bubble coalescence in breathing DNA: Two vicious walkers in opposite potentials
We investigate the coalescence of two DNA-bubbles initially located at weak
segments and separated by a more stable barrier region in a designed construct
of double-stranded DNA. The characteristic time for bubble coalescence and the
corresponding distribution are derived, as well as the distribution of
coalescence positions along the barrier. Below the melting temperature, we find
a Kramers-type barrier crossing behaviour, while at high temperatures, the
bubble corners perform drift-diffusion towards coalescence. The results are
obtained by mapping the bubble dynamics on the problem of two vicious walkers
in opposite potentials.Comment: 7 pages, 4 figure
Bubble dynamics in DNA
The formation of local denaturation zones (bubbles) in double-stranded DNA is
an important example for conformational changes of biological macromolecules.
We study the dynamics of bubble formation in terms of a Fokker-Planck equation
for the probability density to find a bubble of size n base pairs at time t, on
the basis of the free energy in the Poland-Scheraga model. Characteristic
bubble closing and opening times can be determined from the corresponding first
passage time problem, and are sensitive to the specific parameters entering the
model. A multistate unzipping model with constant rates recently applied to DNA
breathing dynamics [G. Altan-Bonnet et al, Phys. Rev. Lett. 90, 138101 (2003)]
emerges as a limiting case.Comment: 9 pages, 2 figure
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