357 research outputs found
A twist localizes three-dimensional patterns
A mechanism for the localization of spatially periodic, self-organized
patterns in anisotropic media which requires systems extended in all three
spatial dimensions is presented: When the anisotropy axis is twisted the
pattern becomes localized in planes parallel to the anisotropy axis. An
analytic description of the effect is developed and used to interpret recent
experiments in the high-frequency regime of electroconvection by Bohatsch and
Stannarius [Phys. Rev. E {\bf 60}, 5591 (1999)]. The localization width is
found to be of the order of magnitude of the geometrical average of pattern
wavelength and the inverse twist.Comment: 7 pages, 2 figures, submitted to PRE; minor changes in resubmissio
On the limits of spectral methods for frequency estimation
An algorithm is presented which generates pairs of oscillatory random time
series which have identical periodograms but differ in the number of
oscillations. This result indicate the intrinsic limitations of spectral
methods when it comes to the task of measuring frequencies. Other examples, one
from medicine and one from bifurcation theory, are given, which also exhibit
these limitations of spectral methods. For two methods of spectral estimation
it is verified that the particular way end points are treated, which is
specific to each method, is, for long enough time series, not relevant for the
main result.Comment: 18 pages, 6 figures (Referee did not like the previous title. Many
other changes
A frequency measure robust to linear filtering
A definition of frequency (cycles per unit-time) based on an approximate
reconstruction of the phase-space trajectory of an oscillator from a signal is
introduced. It is shown to be invariant under linear filtering, and therefore
inaccessible by spectral methods. The effect of filtering on frequency in cases
where this definition does not perfectly apply is quantified.Comment: 10 pages, 2 figure
Pattern Formation from Defect Chaos --- A Theory of Chevrons
For over 25 years it is known that the roll structure of electroconvection
(EC) in the dielectric regime in planarly aligned nematic liquid crystals has,
after a transition to defect chaos, the tendency to form chevron structures. We
show, with the help of a coarse-grained model, that this effect can generally
be expected for systems with spontaneously broken isotropy, that is lifted by a
small external perturbation. The linearized model as well as a nonlinear
extension are compared to simulations of a system of coupled amplitude
equations which generate chevrons out of defect chaos. The mechanism of chevron
formation is similar to the development of Turing patterns in reaction
diffusion systems.Comment: 17 pages, Latex, 11 PS-figures, submitted to Physica
Weakly Nonlinear Theory of Pattern-Forming Systems with Spontaneously Broken Isotropy
Quasi two-dimensional pattern forming systems with spontaneously broken
isotropy represent a novel symmetry class, that is experimentally accessible in
electroconvection of homeotropically aligned liquid crystals. We present a
weakly nonlinear analysis leading to amplitude equations which couple the
short-wavelength patterning mode with the Goldstone mode resulting from the
broken isotropy. The new coefficients in these equations are calculated from
the hydrodynamics. Simulations exhibit a new type of spatio-temporal chaos at
onset. The results are compared with experiments.Comment: 4 pages, RevTeX, 4 PS-figures, to appear in PR
Food Webs: Experts Consuming Families of Experts
The question what determines the structure of natural food webs has been
listed among the nine most important unanswered questions in ecology. It arises
naturally from many problems related to ecosystem stability and resilience. The
traditional view is that population-dynamical stability is crucial for
understanding the observed structures. But phylogeny (evolutionary history) has
also been suggested as the dominant mechanism. Here we show that observed
topological features of predatory food webs can be reproduced to unprecedented
accuracy by a mechanism taking into account only phylogeny, size constraints,
and the heredity of the trophically relevant traits of prey and predators. The
analysis reveals a tendency to avoid resource competition rather than apparent
competition. In food webs with many parasites this pattern is reversed.Comment: 16 pages, 3 figures, 1 table + Appendix of 36 pages, 18 figures.
movie available from http://ag.rossberg.net/matching.mp
Modulated structures in electroconvection in nematic liquid crystals
Motivated by experiments in electroconvection in nematic liquid crystals with
homeotropic alignment we study the coupled amplitude equations describing the
formation of a stationary roll pattern in the presence of a weakly-damped mode
that breaks isotropy. The equations can be generalized to describe the planarly
aligned case if the orienting effect of the boundaries is small, which can be
achieved by a destabilizing magnetic field. The slow mode represents the
in-plane director at the center of the cell. The simplest uniform states are
normal rolls which may undergo a pitchfork bifurcation to abnormal rolls with a
misaligned in-plane director.We present a new class of defect-free solutions
with spatial modulations perpendicular to the rolls. In a parameter range where
the zig-zag instability is not relevant these solutions are stable attractors,
as observed in experiments. We also present two-dimensionally modulated states
with and without defects which result from the destabilization of the
one-dimensionally modulated structures. Finally, for no (or very small)
damping, and away from the rotationally symmetric case, we find static chevrons
made up of a periodic arrangement of defect chains (or bands of defects)
separating homogeneous regions of oblique rolls with very small amplitude.
These states may provide a model for a class of poorly understood stationary
structures observed in various highly-conducting materials ("prechevrons" or
"broad domains").Comment: 13 pages, 13 figure
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