3,194 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
Dynamic Front Transitions and Spiral-Vortex Nucleation
This is a study of front dynamics in reaction diffusion systems near
Nonequilibrium Ising-Bloch bifurcations. We find that the relation between
front velocity and perturbative factors, such as external fields and curvature,
is typically multivalued. This unusual form allows small perturbations to
induce dynamic transitions between counter-propagating fronts and nucleate
spiral vortices. We use these findings to propose explanations for a few
numerical and experimental observations including spiral breakup driven by
advective fields, and spot splitting
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
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
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
Boundary effects on localized structures in spatially extended systems
We present a general method of analyzing the influence of finite size and
boundary effects on the dynamics of localized solutions of non-linear spatially
extended systems. The dynamics of localized structures in infinite systems
involve solvability conditions that require projection onto a Goldstone mode.
Our method works by extending the solvability conditions to finite sized
systems, by incorporating the finite sized modifications of the Goldstone mode
and associated nonzero eigenvalue. We apply this method to the special case of
non-equilibrium domain walls under the influence of Dirichlet boundary
conditions in a parametrically forced complex Ginzburg Landau equation, where
we examine exotic nonuniform domain wall motion due to the influence of
boundary conditions.Comment: 9 pages, 5 figures, submitted to Physical Review
A Method for Reducing the Severity of Epidemics by Allocating Vaccines According to Centrality
One long-standing question in epidemiological research is how best to
allocate limited amounts of vaccine or similar preventative measures in order
to minimize the severity of an epidemic. Much of the literature on the problem
of vaccine allocation has focused on influenza epidemics and used mathematical
models of epidemic spread to determine the effectiveness of proposed methods.
Our work applies computational models of epidemics to the problem of
geographically allocating a limited number of vaccines within several Texas
counties. We developed a graph-based, stochastic model for epidemics that is
based on the SEIR model, and tested vaccine allocation methods based on
multiple centrality measures. This approach provides an alternative method for
addressing the vaccine allocation problem, which can be combined with more
conventional approaches to yield more effective epidemic suppression
strategies. We found that allocation methods based on in-degree and inverse
betweenness centralities tended to be the most effective at containing
epidemics.Comment: 10 pages, accepted to ACM BCB 201
Four-phase patterns in forced oscillatory systems
We investigate pattern formation in self-oscillating systems forced by an
external periodic perturbation. Experimental observations and numerical studies
of reaction-diffusion systems and an analysis of an amplitude equation are
presented. The oscillations in each of these systems entrain to rational
multiples of the perturbation frequency for certain values of the forcing
frequency and amplitude. We focus on the subharmonic resonant case where the
system locks at one fourth the driving frequency, and four-phase rotating
spiral patterns are observed at low forcing amplitudes. The spiral patterns are
studied using an amplitude equation for periodically forced oscillating
systems. The analysis predicts a bifurcation (with increasing forcing) from
rotating four-phase spirals to standing two-phase patterns. This bifurcation is
also found in periodically forced reaction-diffusion equations, the
FitzHugh-Nagumo and Brusselator models, even far from the onset of oscillations
where the amplitude equation analysis is not strictly valid. In a
Belousov-Zhabotinsky chemical system periodically forced with light we also
observe four-phase rotating spiral wave patterns. However, we have not observed
the transition to standing two-phase patterns, possibly because with increasing
light intensity the reaction kinetics become excitable rather than oscillatory.Comment: 11 page
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