770 research outputs found
On propagation failure in 1 and 2 dimensional excitable media
We present a non-perturbative technique to study pulse dynamics in excitable
media. The method is used to study propagation failure in one-dimensional and
two-dimensional excitable media. In one-dimensional media we describe the
behaviour of pulses and wave trains near the saddle node bifurcation, where
propagation fails. The generalization of our method to two dimensions captures
the point where a broken front (or finger) starts to retract. We obtain
approximate expressions for the pulse shape, pulse velocity and scaling
behavior. The results are compared with numerical simulations and show good
agreement.Comment: accepted for publication in Chao
A normal form for excitable media
We present a normal form for travelling waves in one-dimensional excitable
media in form of a differential delay equation. The normal form is built around
the well-known saddle-node bifurcation generically present in excitable media.
Finite wavelength effects are captured by a delay. The normal form describes
the behaviour of single pulses in a periodic domain and also the richer
behaviour of wave trains. The normal form exhibits a symmetry preserving Hopf
bifurcation which may coalesce with the saddle-node in a Bogdanov-Takens point,
and a symmetry breaking spatially inhomogeneous pitchfork bifurcation. We
verify the existence of these bifurcations in numerical simulations. The
parameters of the normal form are determined and its predictions are tested
against numerical simulations of partial differential equation models of
excitable media with good agreement.Comment: 22 pages, accepted for publication in Chao
What makes or breaks a campaign to stop an invading plant pathogen?
Diseases in humans, animals and plants remain an important challenge in our society. Effective control of invasive pathogens often requires coordinated concerted action of a large group of stakeholders. Both epidemiological and human behavioural factors influence the outcome of a disease control campaign. In mathematical models that are frequently used to guide such campaigns, human behaviour is often ill-represented, if at all. Existing models of human, animal and plant disease that do incorporate participation or compliance are often driven by pay-offs or direct observations of the disease state. It is however very well known that opinion is an important driving factor of human decision making. Here we consider the case study of Citrus Huanglongbing disease (HLB), which is an acute bacterial disease that threatens the sustainability of citrus production across the world. We show how by coupling an epidemiological model of this invasive disease with an opinion dynamics model we are able to answer the question: What makes or breaks the effectiveness of a disease control campaign? Frequent contact between stakeholders and advisors is shown to increase the probability of successful control. More surprisingly, we show that informing stakeholders about the effectiveness of control methods is of much greater importance than prematurely increasing their perceptions of the risk of infection. We discuss the overarching consequences of this finding and the effect on human as well as plant disease epidemics
Bifurcation analysis of a normal form for excitable media: Are stable dynamical alternans on a ring possible?
We present a bifurcation analysis of a normal form for travelling waves in
one-dimensional excitable media. The normal form which has been recently
proposed on phenomenological grounds is given in form of a differential delay
equation. The normal form exhibits a symmetry preserving Hopf bifurcation which
may coalesce with a saddle-node in a Bogdanov-Takens point, and a symmetry
breaking spatially inhomogeneous pitchfork bifurcation. We study here the Hopf
bifurcation for the propagation of a single pulse in a ring by means of a
center manifold reduction, and for a wave train by means of a multiscale
analysis leading to a real Ginzburg-Landau equation as the corresponding
amplitude equation. Both, the center manifold reduction and the multiscale
analysis show that the Hopf bifurcation is always subcritical independent of
the parameters. This may have links to cardiac alternans which have so far been
believed to be stable oscillations emanating from a supercritical bifurcation.
We discuss the implications for cardiac alternans and revisit the instability
in some excitable media where the oscillations had been believed to be stable.
In particular, we show that our condition for the onset of the Hopf bifurcation
coincides with the well known restitution condition for cardiac alternans.Comment: to be published in Chao
A superburst from 4U 1254-690
We report the detection with the BeppoSAX Wide Field Cameras of a superburst
from 4U 1254-690. The superburst is preceded by a normal type-I X-ray burst,
has a decay time that is the longest of all eight superbursts detected so far
and a peak luminosity that is the lowest. Like for the other seven superbursts,
the origin is a well-known type-I X-ray burster with a persistent luminosity
level close to one tenth of the Eddington limit. Based on WFC data of all
persistently bright X-ray bursters, the average rate of superbursts is
0.51+/-0.25 per year per persistently bright X-ray burster. Some systems may
have higher superburst rates. For all superbursters, we present evidence for a
pure helium layer which is burnt in an unstable as well as a stable manner.Comment: Accepted by A&A Letter
The broad-band X-ray spectrum of the dipping Low Mass X-ray Binary EXO0748--676
We present results of a 0.1-100 keV BeppoSAX observation of the dipping LMXRB
EXO 0748-676 performed in 2000 November. During the observation the source
exhibited X-ray eclipses, type I X-ray bursts and dipping activity over a wide
range of orbital phases. The 0.1-100keV "dip-free"(ie. dipping and eclipsing
intervals excluded) spectrum is complex,especially at low-energies where a soft
excess is present. Two very different spectral models give satisfactory fits.
The first is the progressive covering model, consisting of separately absorbed
black body and cut-off power-law components.The second model is an absorbed
cut-off power-law together with a moderately ionized absorber with a sub-solar
abundance of Fe and a 2.13 keV absorption feature (tentatively identified with
Si xiii). This ionized absorber may be the same feature as seen by Chandra
during dips from EXO 0748-676.Comment: 7 pages, 5 figures, paper accepted for publication in Astronomy and
Astrophysic
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