30 research outputs found
Dynamics of aeolian sand ripples
We analyze theoretically the dynamics of aeolian sand ripples. In order to
put the study in the context we first review existing models. We argue on the
local character of sand ripple formation. Using a hydrodynamical model we
derive a nonlinear equation for the sand profile. We show how the
hydrodynamical model may be modified to recover the missing terms that are
dictated by symmetries. The symmetry and conservation arguments are powerful in
that the form of the equation is model-independent. We then present an
extensive numerical and analytical analysis of the generic sand ripple
equation. We find that at the initial stage the wavelength of the ripple is
that corresponding to the linearly most dangerous mode. At later stages the
profile undergoes a coarsening process leading to a significant increase of the
wavelength. We find that including the next higher order nonlinear term in the
equation, leads naturally to a saturation of the local slope. We analyze both
analytically and numerically the coarsening stage, in terms of a dynamical
exponent for the mean wavelength increase. We discuss some future lines of
investigations.Comment: 22 pages and 10 postscript figure
Scaling Relations and Exponents in the Growth of Rough Interfaces Through Random Media
The growth of a rough interface through a random media is modelled by a
continuous stochastic equation with a quenched noise. By use of the Novikov
theorem we can transform the dependence of the noise on the interface height
into an effective temporal correlation for different regimes of the evolution
of the interface. The exponents characterizing the roughness of the interface
can thus be computed by simple scaling arguments showing a good agreement with
recent experiments and numerical simulations.Comment: 4 pages, RevTex, twocolumns, two figures (upon request). To appear in
Europhysics Letter
The Non-local Kardar-Parisi-Zhang Equation With Spatially Correlated Noise
The effects of spatially correlated noise on a phenomenological equation
equivalent to a non-local version of the Kardar-Parisi-Zhang equation are
studied via the dynamic renormalization group (DRG) techniques. The correlated
noise coupled with the long ranged nature of interactions prove the existence
of different phases in different regimes, giving rise to a range of roughness
exponents defined by their corresponding critical dimensions. Finally
self-consistent mode analysis is employed to compare the non-KPZ exponents
obtained as a result of the long range -long range interactions with the DRG
results.Comment: Plain Latex, 10 pages, 2 figures in one ps fil
Novel type of phase transition in a system of self-driven particles
A simple model with a novel type of dynamics is introduced in order to
investigate the emergence of self-ordered motion in systems of particles with
biologically motivated interaction. In our model particles are driven with a
constant absolute velocity and at each time step assume the average direction
of motion of the particles in their neighborhood with some random perturbation
() added. We present numerical evidence that this model results in a
kinetic phase transition from no transport (zero average velocity, ) to finite net transport through spontaneous symmetry breaking of the
rotational symmetry. The transition is continuous since is
found to scale as with
Single-vehicle data of highway traffic - a statistical analysis
In the present paper single-vehicle data of highway traffic are analyzed in
great detail. By using the single-vehicle data directly empirical time-headway
distributions and speed-distance relations can be established. Both quantities
yield relevant information about the microscopic states. Several fundamental
diagrams are also presented, which are based on time-averaged quantities and
compared with earlier empirical investigations. In the remaining part
time-series analyses of the averaged as well as the single-vehicle data are
carried out. The results will be used in order to propose objective criteria
for an identification of the different traffic states, e.g. synchronized
traffic.Comment: 12 pages, 19 figures, RevTe
Asymptotic function for multi-growth surfaces using power-law noise
Numerical simulations are used to investigate the multiaffine exponent
and multi-growth exponent of ballistic deposition growth
for noise obeying a power-law distribution. The simulated values of
are compared with the asymptotic function that is
approximated from the power-law behavior of the distribution of height
differences over time. They are in good agreement for large . The simulated
is found in the range . This implies that large rare events tend to break the KPZ
universality scaling-law at higher order .Comment: 5 pages, 4 figures, to be published in Phys. Rev.
An Exactly Solvable Two-Way Traffic Model With Ordered Sequential Update
Within the formalism of matrix product ansatz, we study a two-species
asymmetric exclusion process with backward and forward site-ordered sequential
update. This model, which was originally introduced with the random sequential
update, describes a two-way traffic flow with a dynamic impurity and shows a
phase transition between the free flow and traffic jam. We investigate the
characteristics of this jamming and examine similarities and differences
between our results and those with random sequential update.Comment: 25 pages, Revtex, 7 ps file
Nonlinear Measures for Characterizing Rough Surface Morphologies
We develop a new approach to characterizing the morphology of rough surfaces
based on the analysis of the scaling properties of contour loops, i.e. loops of
constant height. Given a height profile of the surface we perform independent
measurements of the fractal dimension of contour loops, and the exponent that
characterizes their size distribution. Scaling formulas are derived and used to
relate these two geometrical exponents to the roughness exponent of a
self-affine surface, thus providing independent measurements of this important
quantity. Furthermore, we define the scale dependent curvature and demonstrate
that by measuring its third moment departures of the height fluctuations from
Gaussian behavior can be ascertained. These nonlinear measures are used to
characterize the morphology of computer generated Gaussian rough surfaces,
surfaces obtained in numerical simulations of a simple growth model, and
surfaces observed by scanning-tunneling-microscopes. For experimentally
realized surfaces the self-affine scaling is cut off by a correlation length,
and we generalize our theory of contour loops to take this into account.Comment: 39 pages and 18 figures included; comments to
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