2,443 research outputs found
Stratified spatiotemporal chaos in anisotropic reaction-diffusion systems
Numerical simulations of two dimensional pattern formation in an anisotropic
bistable reaction-diffusion medium reveal a new dynamical state, stratified
spatiotemporal chaos, characterized by strong correlations along one of the
principal axes. Equations that describe the dependence of front motion on the
angle illustrate the mechanism leading to stratified chaos
Differential amplification of rDNA repeats in barley translocation and duplication lines: role of a specific segment
Variation in restriction pattern, relative amounts of the two ribosomal DNA (rDNA) repeats, and the overall content of rDNA were compared among twelve segmental duplications and eleven parental translocations involving NOR6 and NOR7 of cultivated barley. Southern blot hybridization revealed two rDNA repeats of 9.9 kb and 9.0 kb. While all duplications snowed dimers for these rDNA repeats, the duplication lines D29 and D47 displayed trimers in addition to a higher proportion of rDNA repeats as dimers. The rDNA of Dl, D29 and D47 showed resistance to Bam HI and Taq I digestion, indicating possible melhylation of cytosine and adenine. Densitometric scans of autoradiographs revealed variations in the relative amounts of the 9.0 kb and 9.9 kb rDNA repeats among different karyotypes. Dot blot hybridizations indicated variation in the overall rDNA content. Comparison of the 9.0/9.9 kb ratios and the percentage of genomic DNA hybridizing to an rDNA clone of barley illustrates differential amplification for the two rDNA repeats. When the segmental composition of these deviating lines were compared, it was evident that the relative position of the segment 12-16 of chromosome 6 determines differential amplification while duplication of the same segment controls the overall rDNA content
Breathing Spots in a Reaction-Diffusion System
A quasi-2-dimensional stationary spot in a disk-shaped chemical reactor is
observed to bifurcate to an oscillating spot when a control parameter is
increased beyond a critical value. Further increase of the control parameter
leads to the collapse and disappearance of the spot. Analysis of a bistable
activator-inhibitor model indicates that the observed behavior is a consequence
of interaction of the front with the boundary near a parity breaking front
bifurcation.Comment: 4 pages RevTeX, see also http://chaos.ph.utexas.edu/ and
http://t7.lanl.gov/People/Aric
Multi-Phase Patterns in Periodically Forced Oscillatory Systems
Periodic forcing of an oscillatory system produces frequency locking bands
within which the system frequency is rationally related to the forcing
frequency. We study extended oscillatory systems that respond to uniform
periodic forcing at one quarter of the forcing frequency (the 4:1 resonance).
These systems possess four coexisting stable states, corresponding to uniform
oscillations with successive phase shifts of . Using an amplitude
equation approach near a Hopf bifurcation to uniform oscillations, we study
front solutions connecting different phase states. These solutions divide into
two groups: -fronts separating states with a phase shift of and
-fronts separating states with a phase shift of . We find a new
type of front instability where a stationary -front ``decomposes'' into a
pair of traveling -fronts as the forcing strength is decreased. The
instability is degenerate for an amplitude equation with cubic nonlinearities.
At the instability point a continuous family of pair solutions exists,
consisting of -fronts separated by distances ranging from zero to
infinity. Quintic nonlinearities lift the degeneracy at the instability point
but do not change the basic nature of the instability. We conjecture the
existence of similar instabilities in higher 2n:1 resonances (n=3,4,..) where
stationary -fronts decompose into n traveling -fronts. The
instabilities designate transitions from stationary two-phase patterns to
traveling 2n-phase patterns. As an example, we demonstrate with a numerical
solution the collapse of a four-phase spiral wave into a stationary two-phase
pattern as the forcing strength within the 4:1 resonance is increased
Propagation Failure in Excitable Media
We study a mechanism of pulse propagation failure in excitable media where
stable traveling pulse solutions appear via a subcritical pitchfork
bifurcation. The bifurcation plays a key role in that mechanism. Small
perturbations, externally applied or from internal instabilities, may cause
pulse propagation failure (wave breakup) provided the system is close enough to
the bifurcation point. We derive relations showing how the pitchfork
bifurcation is unfolded by weak curvature or advective field perturbations and
use them to demonstrate wave breakup. We suggest that the recent observations
of wave breakup in the Belousov-Zhabotinsky reaction induced either by an
electric field or a transverse instability are manifestations of this
mechanism.Comment: 8 pages. Aric Hagberg: http://cnls.lanl.gov/~aric; Ehud
Meron:http://www.bgu.ac.il/BIDR/research/staff/meron.htm
Controlling domain patterns far from equilibrium
A high degree of control over the structure and dynamics of domain patterns
in nonequilibrium systems can be achieved by applying nonuniform external
fields near parity breaking front bifurcations. An external field with a linear
spatial profile stabilizes a propagating front at a fixed position or induces
oscillations with frequency that scales like the square root of the field
gradient. Nonmonotonic profiles produce a variety of patterns with controllable
wavelengths, domain sizes, and frequencies and phases of oscillations.Comment: Published version, 4 pages, RevTeX. More at
http://t7.lanl.gov/People/Aric
Order Parameter Equations for Front Transitions: Planar and Circular Fronts
Near a parity breaking front bifurcation, small perturbations may reverse the
propagation direction of fronts. Often this results in nonsteady asymptotic
motion such as breathing and domain breakup. Exploiting the time scale
differences of an activator-inhibitor model and the proximity to the front
bifurcation, we derive equations of motion for planar and circular fronts. The
equations involve a translational degree of freedom and an order parameter
describing transitions between left and right propagating fronts.
Perturbations, such as a space dependent advective field or uniform curvature
(axisymmetric spots), couple these two degrees of freedom. In both cases this
leads to a transition from stationary to oscillating fronts as the parity
breaking bifurcation is approached. For axisymmetric spots, two additional
dynamic behaviors are found: rebound and collapse.Comment: 9 pages. Aric Hagberg: http://t7.lanl.gov/People/Aric/; Ehud Meron:
http://www.bgu.ac.il/BIDR/research/staff/meron.htm
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