2,223 research outputs found
Crossing Patterns in Nonplanar Road Networks
We define the crossing graph of a given embedded graph (such as a road
network) to be a graph with a vertex for each edge of the embedding, with two
crossing graph vertices adjacent when the corresponding two edges of the
embedding cross each other. In this paper, we study the sparsity properties of
crossing graphs of real-world road networks. We show that, in large road
networks (the Urban Road Network Dataset), the crossing graphs have connected
components that are primarily trees, and that the remaining non-tree components
are typically sparse (technically, that they have bounded degeneracy). We prove
theoretically that when an embedded graph has a sparse crossing graph, it has
other desirable properties that lead to fast algorithms for shortest paths and
other algorithms important in geographic information systems. Notably, these
graphs have polynomial expansion, meaning that they and all their subgraphs
have small separators.Comment: 9 pages, 4 figures. To appear at the 25th ACM SIGSPATIAL
International Conference on Advances in Geographic Information Systems(ACM
SIGSPATIAL 2017
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
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
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
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
Resonance tongues and patterns in periodically forced reaction-diffusion systems
Various resonant and near-resonant patterns form in a light-sensitive
Belousov-Zhabotinsky (BZ) reaction in response to a spatially-homogeneous
time-periodic perturbation with light. The regions (tongues) in the forcing
frequency and forcing amplitude parameter plane where resonant patterns form
are identified through analysis of the temporal response of the patterns.
Resonant and near-resonant responses are distinguished. The unforced BZ
reaction shows both spatially-uniform oscillations and rotating spiral waves,
while the forced system shows patterns such as standing-wave labyrinths and
rotating spiral waves. The patterns depend on the amplitude and frequency of
the perturbation, and also on whether the system responds to the forcing near
the uniform oscillation frequency or the spiral wave frequency. Numerical
simulations of a forced FitzHugh-Nagumo reaction-diffusion model show both
resonant and near-resonant patterns similar to the BZ chemical system
Phase Dynamics of Nearly Stationary Patterns in Activator-Inhibitor Systems
The slow dynamics of nearly stationary patterns in a FitzHugh-Nagumo model
are studied using a phase dynamics approach. A Cross-Newell phase equation
describing slow and weak modulations of periodic stationary solutions is
derived. The derivation applies to the bistable, excitable, and the Turing
unstable regimes. In the bistable case stability thresholds are obtained for
the Eckhaus and the zigzag instabilities and for the transition to traveling
waves. Neutral stability curves demonstrate the destabilization of stationary
planar patterns at low wavenumbers to zigzag and traveling modes. Numerical
solutions of the model system support the theoretical findings
Self-replication and splitting of domain patterns in reaction-diffusion systems with fast inhibitor
An asymptotic equation of motion for the pattern interface in the
domain-forming reaction-diffusion systems is derived. The free boundary problem
is reduced to the universal equation of non-local contour dynamics in two
dimensions in the parameter region where a pattern is not far from the points
of the transverse instabilities of its walls. The contour dynamics is studied
numerically for the reaction-diffusion system of the FitzHugh-Nagumo type. It
is shown that in the asymptotic limit the transverse instability of the
localized domains leads to their splitting and formation of the multidomain
pattern rather than fingering and formation of the labyrinthine pattern.Comment: 9 pages (ReVTeX), 5 figures (postscript). To be published in Phys.
Rev.
Fetal electrocardiogram: ST waveform analysis in intrapartum surveillance
ST waveform analysis of fetal electrocardiogram (ECG) for intrapartum surveillance (STAN) is a newly introduced method for fetal surveillance. The purpose of this commentary is to assist in the proper use of fetal ECG in combination with cardiotocography (CTG) during labour. Guidelines and recommendations concerning CTG and ST waveform interpretation and classification are stated that were agreed on by the European experts on ST waveform analysis for intrapartum surveillance during a meeting in Utretcht, the Netherlands in January 2007
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