28,264 research outputs found
Convective Instability and Boundary Driven Oscillations in a Reaction-Diffusion-Advection Model
In a reaction-diffusion-advection system, with a convectively unstable
regime, a perturbation creates a wave train that is advected downstream and
eventually leaves the system. We show that the convective instability coexists
with a local absolute instability when a fixed boundary condition upstream is
imposed. This boundary induced instability acts as a continuous wave source,
creating a local periodic excitation near the boundary, which initiates waves
traveling both up and downstream. To confirm this, we performed analytical
analysis and numerical simulations of a modified Martiel-Goldbeter
reaction-diffusion model with the addition of an advection term. We provide a
quantitative description of the wave packet appearing in the convectively
unstable regime, which we found to be in excellent agreement with the numerical
simulations. We characterize this new instability and show that in the limit of
high advection speed, it is suppressed. This type of instability can be
expected for reaction-diffusion systems that present both a convective
instability and an excitable regime. In particular, it can be relevant to
understand the signaling mechanism of the social amoeba Dictyostelium
discoideum that may experience fluid flows in its natural habitat.Comment: 10 pages, 13 figures, published in Chaos: An Interdisciplinary
Journal of Nonlinear Scienc
Effect of small-world topology on wave propagation on networks of excitable elements
We study excitation waves on a Newman-Watts small-world network model of
coupled excitable elements. Depending on the global coupling strength, we find
differing resilience to the added long-range links and different mechanisms of
propagation failure. For high coupling strengths, we show agreement between the
network and a reaction-diffusion model with additional mean-field term.
Employing this approximation, we are able to estimate the critical density of
long-range links for propagation failure.Comment: 19 pages, 8 figures and 5 pages supplementary materia
Introduction: Localized Structures in Dissipative Media: From Optics to Plant Ecology
Localised structures in dissipative appears in various fields of natural
science such as biology, chemistry, plant ecology, optics and laser physics.
The proposed theme issue is to gather specialists from various fields of
non-linear science toward a cross-fertilisation among active areas of research.
This is a cross-disciplinary area of research dominated by the nonlinear optics
due to potential applications for all-optical control of light, optical
storage, and information processing. This theme issue contains contributions
from 18 active groups involved in localized structures field and have all made
significant contributions in recent years.Comment: 14 pages, 0 figure, submitted to Phi. Trasaction Royal Societ
Nonlinear physics of electrical wave propagation in the heart: a review
The beating of the heart is a synchronized contraction of muscle cells
(myocytes) that are triggered by a periodic sequence of electrical waves (action
potentials) originating in the sino-atrial node and propagating over the atria and
the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF)
or ventricular tachycardia (VT) are caused by disruptions and instabilities of these
electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent
wave patterns (AF,VF). Numerous simulation and experimental studies during the
last 20 years have addressed these topics. In this review we focus on the nonlinear
dynamics of wave propagation in the heart with an emphasis on the theory of pulses,
spirals and scroll waves and their instabilities in excitable media and their application
to cardiac modeling. After an introduction into electrophysiological models for action
potential propagation, the modeling and analysis of spatiotemporal alternans, spiral
and scroll meandering, spiral breakup and scroll wave instabilities like negative line
tension and sproing are reviewed in depth and discussed with emphasis on their impact
in cardiac arrhythmias.Peer ReviewedPreprin
Transverse Patterns in Nonlinear Optical Resonators
The book is devoted to the formation and dynamics of localized structures
(vortices, solitons) and extended patterns (stripes, hexagons, tilted waves) in
nonlinear optical resonators such as lasers, optical parametric oscillators,
and photorefractive oscillators. The theoretical analysis is performed by
deriving order parameter equations, and also through numerical integration of
microscopic models of the systems under investigation. Experimental
observations, and possible technological implementations of transverse optical
patterns are also discussed. A comparison with patterns found in other
nonlinear systems, i.e. chemical, biological, and hydrodynamical systems, is
given. This article contains the table of contents and the introductory chapter
of the book.Comment: 37 pages, 14 figures. Table of contents and introductory chapter of
the boo
Theory of spiral wave dynamics in weakly excitable media: asymptotic reduction to a kinematic model and applications
In a weakly excitable medium, characterized by a large threshold stimulus,
the free end of an isolated broken plane wave (wave tip) can either rotate
(steadily or unsteadily) around a large excitable core, thereby producing a
spiral pattern, or retract causing the wave to vanish at boundaries. An
asymptotic analysis of spiral motion and retraction is carried out in this
weakly excitable large core regime starting from the free-boundary limit of the
reaction-diffusion models, valid when the excited region is delimited by a thin
interface. The wave description is shown to naturally split between the tip
region and a far region that are smoothly matched on an intermediate scale.
This separation allows us to rigorously derive an equation of motion for the
wave tip, with the large scale motion of the spiral wavefront slaved to the
tip. This kinematic description provides both a physical picture and exact
predictions for a wide range of wave behavior, including: (i) steady rotation
(frequency and core radius), (ii) exact treatment of the meandering instability
in the free-boundary limit with the prediction that the frequency of unstable
motion is half the primary steady frequency (iii) drift under external actions
(external field with application to axisymmetric scroll ring motion in
three-dimensions, and spatial or/and time-dependent variation of excitability),
and (iv) the dynamics of multi-armed spiral waves with the new prediction that
steadily rotating waves with two or more arms are linearly unstable. Numerical
simulations of FitzHug-Nagumo kinetics are used to test several aspects of our
results. In addition, we discuss the semi-quantitative extension of this theory
to finite cores and pinpoint mathematical subtleties related to the thin
interface limit of singly diffusive reaction-diffusion models
Spiral waves in a surface reaction: Model calculations
A systematic study of spiral waves in a realistic reactionâdiffusion model describing the isothermal CO oxidation on Pt(110) is carried out. Spirals exist under oscillatory, excitable, and bistable (doubly metastable) conditions. In the excitable region, two separate meandering transitions occur, both when the time scales become strongly different and when they become comparable. By the assumption of surface defects of the order of 10 ÎŒm, to which the spirals can be pinned, the continuous distribution of wavelengths observed experimentally can be explained. An external periodic perturbation generally causes a meandering motion of a free spiral, while a straight drift results, if the period of the perturbation divided by the rotation period is a natural number
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