355 research outputs found
Characterisation of spatial network-like patterns from junctions' geometry
We propose a new method for quantitative characterization of spatial
network-like patterns with loops, such as surface fracture patterns, leaf vein
networks and patterns of urban streets. Such patterns are not well
characterized by purely topological estimators: also patterns that both look
different and result from different morphogenetic processes can have similar
topology. A local geometric cue -the angles formed by the different branches at
junctions- can complement topological information and allow to quantify the
large scale spatial coherence of the pattern. For patterns that grow over time,
such as fracture lines on the surface of ceramics, the rank assigned by our
method to each individual segment of the pattern approximates the order of
appearance of that segment. We apply the method to various network-like
patterns and we find a continuous but sharp dichotomy between two classes of
spatial networks: hierarchical and homogeneous. The first class results from a
sequential growth process and presents large scale organization, the latter
presents local, but not global organization.Comment: version 2, 14 page
Delay of Disorder by Diluted Polymers
We study the effect of diluted flexible polymers on a disordered capillary
wave state. The waves are generated at an interface of a dyed water sugar
solution and a low viscous silicon oil. This allows for a quantitative
measurement of the spatio-temporal Fourier spectrum. The primary pattern after
the first bifurcation from the flat interface are squares. With increasing
driving strength we observe a melting of the square pattern. It is replaced by
a weak turbulent cascade. The addition of a small amount of polymers to the
water layer does not affect the critical acceleration but shifts the disorder
transition to higher driving strenghs and the short wave length - high
frequency fluctuations are suppressed
Potential energy curves and spin-orbit coupling of light alkali-heavy rare gas molecules
The potential energy curves of the X, A, and B states of alkali-rare gas diatomic molecules, MKr and MXe, are investigated for M = Li, Na, K. The molecular spin-orbit coefficients a(R) = ă2Î 1/2|Ä€SO|2Î 1/2ă and b(R) = ă2Î -1/2|Ä€SO| 2ÎŁ1/2ă are calculated as a function the interatomic distance R. We show that a(R) increases and b(R) decreases as R decreases. This effect becomes less and less important as the mass of the alkali increases. A comparison of the rovibrational properties deduced from our calculations with experimental measurements recorded for NaKr and NaXe shows the quality of the calculation
Heap Formation in Granular Media
Using molecular dynamics (MD) simulations, we find the formation of heaps in
a system of granular particles contained in a box with oscillating bottom and
fixed sidewalls. The simulation includes the effect of static friction, which
is found to be crucial in maintaining a stable heap. We also find another
mechanism for heap formation in systems under constant vertical shear. In both
systems, heaps are formed due to a net downward shear by the sidewalls. We
discuss the origin of net downward shear for the vibration induced heap.Comment: 11 pages, 4 figures available upon request, Plain TeX, HLRZ-101/9
Rigidity of escaping dynamics for transcendental entire functions
We prove an analog of Boettcher's theorem for transcendental entire functions
in the Eremenko-Lyubich class B. More precisely, let f and g be entire
functions with bounded sets of singular values and suppose that f and g belong
to the same parameter space (i.e., are *quasiconformally equivalent* in the
sense of Eremenko and Lyubich). Then f and g are conjugate when restricted to
the set of points which remain in some sufficiently small neighborhood of
infinity under iteration. Furthermore, this conjugacy extends to a
quasiconformal self-map of the plane.
We also prove that this conjugacy is essentially unique. In particular, we
show that an Eremenko-Lyubich class function f has no invariant line fields on
its escaping set.
Finally, we show that any two hyperbolic Eremenko-Lyubich class functions f
and g which belong to the same parameter space are conjugate on their sets of
escaping points.Comment: 28 pages; 2 figures. Final version (October 2008). Various
modificiations were made, including the introduction of Proposition 3.6,
which was not formally stated previously, and the inclusion of a new figure.
No major changes otherwis
Scarred Patterns in Surface Waves
Surface wave patterns are investigated experimentally in a system geometry
that has become a paradigm of quantum chaos: the stadium billiard. Linear waves
in bounded geometries for which classical ray trajectories are chaotic are
known to give rise to scarred patterns. Here, we utilize parametrically forced
surface waves (Faraday waves), which become progressively nonlinear beyond the
wave instability threshold, to investigate the subtle interplay between
boundaries and nonlinearity. Only a subset (three main types) of the computed
linear modes of the stadium are observed in a systematic scan. These correspond
to modes in which the wave amplitudes are strongly enhanced along paths
corresponding to certain periodic ray orbits. Many other modes are found to be
suppressed, in general agreement with a prediction by Agam and Altshuler based
on boundary dissipation and the Lyapunov exponent of the associated orbit.
Spatially asymmetric or disordered (but time-independent) patterns are also
found even near onset. As the driving acceleration is increased, the
time-independent scarred patterns persist, but in some cases transitions
between modes are noted. The onset of spatiotemporal chaos at higher forcing
amplitude often involves a nonperiodic oscillation between spatially ordered
and disordered states. We characterize this phenomenon using the concept of
pattern entropy. The rate of change of the patterns is found to be reduced as
the state passes temporarily near the ordered configurations of lower entropy.
We also report complex but highly symmetric (time-independent) patterns far
above onset in the regime that is normally chaotic.Comment: 9 pages, 10 figures (low resolution gif files). Updated and added
references and text. For high resolution images:
http://physics.clarku.edu/~akudrolli/stadium.htm
Non-Gaussian Distributions in Extended Dynamical Systems
We propose a novel mechanism for the origin of non-Gaussian tails in the
probability distribution functions (PDFs) of local variables in nonlinear,
diffusive, dynamical systems including passive scalars advected by chaotic
velocity fields. Intermittent fluctuations on appropriate time scales in the
amplitude of the (chaotic) noise can lead to exponential tails. We provide
numerical evidence for such behavior in deterministic, discrete-time passive
scalar models. Different possibilities for PDFs are also outlined.Comment: 12 pages and 6 figs obtainable from the authors, LaTex file,
OSU-preprint-
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