1,085 research outputs found
Understanding Anomalous Transport in Intermittent Maps: From Continuous Time Random Walks to Fractals
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 dynamical phase transition from normal to anomalous
diffusion marked by strong suppression of diffusion. Similarly, the probability
density of moving particles is governed by a time-fractional diffusion equation
on coarse scales while exhibiting a specific fine structure. Approximations
beyond stochastic theory are derived from a generalized Taylor-Green-Kubo
formula.Comment: 4 pages, 3 eps figure
Fractal dimension of transport coefficients in a deterministic dynamical system
In many low-dimensional dynamical systems transport coefficients are very
irregular, perhaps even fractal functions of control parameters. To analyse
this phenomenon we study a dynamical system defined by a piece-wise linear map
and investigate the dependence of transport coefficients on the slope of the
map. We present analytical arguments, supported by numerical calculations,
showing that both the Minkowski-Bouligand and Hausdorff fractal dimension of
the graphs of these functions is 1 with a logarithmic correction, and find that
the exponent controlling this correction is bounded from above by 1 or
2, depending on some detailed properties of the system. Using numerical
techniques we show local self-similarity of the graphs. The local
self-similarity scaling transformations turn out to depend (irregularly) on the
values of the system control parameters.Comment: 17 pages, 6 figures; ver.2: 18 pages, 7 figures (added section 5.2,
corrected typos, etc.
Deterministic diffusion in flower shape billiards
We propose a flower shape billiard in order to study the irregular parameter
dependence of chaotic normal diffusion. Our model is an open system consisting
of periodically distributed obstacles of flower shape, and it is strongly
chaotic for almost all parameter values. We compute the parameter dependent
diffusion coefficient of this model from computer simulations and analyze its
functional form by different schemes all generalizing the simple random walk
approximation of Machta and Zwanzig. The improved methods we use are based
either on heuristic higher-order corrections to the simple random walk model,
on lattice gas simulation methods, or they start from a suitable Green-Kubo
formula for diffusion. We show that dynamical correlations, or memory effects,
are of crucial importance to reproduce the precise parameter dependence of the
diffusion coefficent.Comment: 8 pages (revtex) with 9 figures (encapsulated postscript
Understanding deterministic diffusion by correlated random walks
Low-dimensional periodic arrays of scatterers with a moving point particle
are ideal models for studying deterministic diffusion. For such systems the
diffusion coefficient is typically an irregular function under variation of a
control parameter. Here we propose a systematic scheme of how to approximate
deterministic diffusion coefficients of this kind in terms of correlated random
walks. We apply this approach to two simple examples which are a
one-dimensional map on the line and the periodic Lorentz gas. Starting from
suitable Green-Kubo formulas we evaluate hierarchies of approximations for
their parameter-dependent diffusion coefficients. These approximations converge
exactly yielding a straightforward interpretation of the structure of these
irregular diffusion coeficients in terms of dynamical correlations.Comment: 13 pages (revtex) with 5 figures (postscript
Random walk approach to the d-dimensional disordered Lorentz gas
A correlated random walk approach to diffusion is applied to the disordered
nonoverlapping Lorentz gas. By invoking the Lu-Torquato theory for chord-length
distributions in random media [J. Chem. Phys. 98, 6472 (1993)], an analytic
expression for the diffusion constant in arbitrary number of dimensions d is
obtained. The result corresponds to an Enskog-like correction to the Boltzmann
prediction, being exact in the dilute limit, and better or nearly exact in
comparison to renormalized kinetic theory predictions for all allowed densities
in d=2,3. Extensive numerical simulations were also performed to elucidate the
role of the approximations involved.Comment: 5 pages, 5 figure
Is subdiffusional transport slower than normal?
We consider anomalous non-Markovian transport of Brownian particles in
viscoelastic fluid-like media with very large but finite macroscopic viscosity
under the influence of a constant force field F. The viscoelastic properties of
the medium are characterized by a power-law viscoelastic memory kernel which
ultra slow decays in time on the time scale \tau of strong viscoelastic
correlations. The subdiffusive transport regime emerges transiently for t<\tau.
However, the transport becomes asymptotically normal for t>>\tau. It is shown
that even though transiently the mean displacement and the variance both scale
sublinearly, i.e. anomalously slow, in time, ~ F t^\alpha,
~ t^\alpha, 0<\alpha<1, the mean displacement at each instant
of time is nevertheless always larger than one obtained for normal transport in
a purely viscous medium with the same macroscopic viscosity obtained in the
Markovian approximation. This can have profound implications for the
subdiffusive transport in biological cells as the notion of "ultra-slowness"
can be misleading in the context of anomalous diffusion-limited transport and
reaction processes occurring on nano- and mesoscales
Activation of G12/G13 Results in Shape Change and Rho/Rho-Kinase–mediated Myosin Light Chain Phosphorylation in Mouse Platelets
Platelets respond to various stimuli with rapid changes in shape followed by aggregation and secretion of their granule contents. Platelets lacking the α-subunit of the heterotrimeric G protein Gq do not aggregate and degranulate but still undergo shape change after activation through thromboxane-A2 (TXA2) or thrombin receptors. In contrast to thrombin, the TXA2 mimetic U46619 led to the selective activation of G12 and G13 in Gαq-deficient platelets indicating that these G proteins mediate TXA2 receptor-induced shape change. TXA2 receptor-mediated activation of G12/G13 resulted in tyrosine phosphorylation of pp72syk and stimulation of pp60c-src as well as in phosphorylation of myosin light chain (MLC) in Gαq-deficient platelets. Both MLC phosphorylation and shape change induced through G12/G13 in the absence of Gαq were inhibited by the C3 exoenzyme from Clostridium botulinum, by the Rho-kinase inhibitor Y-27632 and by cAMP-analogue Sp-5,6-DCl-cBIMPS. These data indicate that G12/G13 couple receptors to tyrosine kinases as well as to the Rho/Rho-kinase–mediated regulation of MLC phosphorylation. We provide evidence that G12/G13-mediated Rho/Rho-kinase–dependent regulation of MLC phosphorylation participates in receptor-induced platelet shape change
Stationary states for underdamped anharmonic oscillators driven by Cauchy noise
Using methods of stochastic dynamics, we have studied stationary states in
the underdamped anharmonic stochastic oscillators driven by Cauchy noise. Shape
of stationary states depend both on the potential type and the damping. If the
damping is strong enough, for potential wells which in the overdamped regime
produce multimodal stationary states, stationary states in the underdamped
regime can be multimodal with the same number of modes like in the overdamped
regime. For the parabolic potential, the stationary density is always unimodal
and it is given by the two dimensional -stable density. For the mixture
of quartic and parabolic single-well potentials the stationary density can be
bimodal. Nevertheless, the parabolic addition, which is strong enough, can
destroy bimodlity of the stationary state.Comment: 9 page
Asymptotic solutions of decoupled continuous-time random walks with superheavy-tailed waiting time and heavy-tailed jump length distributions
We study the long-time behavior of decoupled continuous-time random walks
characterized by superheavy-tailed distributions of waiting times and symmetric
heavy-tailed distributions of jump lengths. Our main quantity of interest is
the limiting probability density of the position of the walker multiplied by a
scaling function of time. We show that the probability density of the scaled
walker position converges in the long-time limit to a non-degenerate one only
if the scaling function behaves in a certain way. This function as well as the
limiting probability density are determined in explicit form. Also, we express
the limiting probability density which has heavy tails in terms of the Fox
-function and find its behavior for small and large distances.Comment: 16 pages, 1 figur
Anomalous diffusion in viscosity landscapes
Anomalous diffusion is predicted for Brownian particles in inhomogeneous
viscosity landscapes by means of scaling arguments, which are substantiated
through numerical simulations. Analytical solutions of the related
Fokker-Planck equation in limiting cases confirm our results. For an ensemble
of particles starting at a spatial minimum (maximum) of the viscous damping we
find subdiffusive (superdiffusive) motion. Superdiffusion occurs also for a
monotonically varying viscosity profile. We suggest different substances for
related experimental investigations.Comment: 15 page
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