546 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
The large core limit of spiral waves in excitable media: A numerical approach
We modify the freezing method introduced by Beyn & Thuemmler, 2004, for
analyzing rigidly rotating spiral waves in excitable media. The proposed method
is designed to stably determine the rotation frequency and the core radius of
rotating spirals, as well as the approximate shape of spiral waves in unbounded
domains. In particular, we introduce spiral wave boundary conditions based on
geometric approximations of spiral wave solutions by Archimedean spirals and by
involutes of circles. We further propose a simple implementation of boundary
conditions for the case when the inhibitor is non-diffusive, a case which had
previously caused spurious oscillations.
We then utilize the method to numerically analyze the large core limit. The
proposed method allows us to investigate the case close to criticality where
spiral waves acquire infinite core radius and zero rotation frequency, before
they begin to develop into retracting fingers. We confirm the linear scaling
regime of a drift bifurcation for the rotation frequency and the core radius of
spiral wave solutions close to criticality. This regime is unattainable with
conventional numerical methods.Comment: 32 pages, 17 figures, as accepted by SIAM Journal on Applied
Dynamical Systems on 20/03/1
Formation of Polymorphic Cluster Phases for Purely Repulsive Soft Spheres
We present results from density functional theory and computer simulations
that unambiguously predict the occurrence of first-order freezing transitions
for a large class of ultrasoft model systems into cluster crystals. The
clusters consist of fully overlapping particles and arise without the existence
of attractive forces. The number of particles participating in a cluster scales
linearly with density, therefore the crystals feature density-independent
lattice constants. Clustering is accompanied by polymorphic bcc-fcc
transitions, with fcc being the stable phase at high densities.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Let
On the Validity of the 0-1 Test for Chaos
In this paper, we present a theoretical justification of the 0-1 test for
chaos. In particular, we show that with probability one, the test yields 0 for
periodic and quasiperiodic dynamics, and 1 for sufficiently chaotic dynamics
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
Why do ultrasoft repulsive particles cluster and crystallize? Analytical results from density functional theory
We demonstrate the accuracy of the hypernetted chain closure and of the
mean-field approximation for the calculation of the fluid-state properties of
systems interacting by means of bounded and positive-definite pair potentials
with oscillating Fourier transforms. Subsequently, we prove the validity of a
bilinear, random-phase density functional for arbitrary inhomogeneous phases of
the same systems. On the basis of this functional, we calculate analytically
the freezing parameters of the latter. We demonstrate explicitly that the
stable crystals feature a lattice constant that is independent of density and
whose value is dictated by the position of the negative minimum of the Fourier
transform of the pair potential. This property is equivalent with the existence
of clusters, whose population scales proportionally to the density. We
establish that regardless of the form of the interaction potential and of the
location on the freezing line, all cluster crystals have a universal Lindemann
ratio L = 0.189 at freezing. We further make an explicit link between the
aforementioned density functional and the harmonic theory of crystals. This
allows us to establish an equivalence between the emergence of clusters and the
existence of negative Fourier components of the interaction potential. Finally,
we make a connection between the class of models at hand and the system of
infinite-dimensional hard spheres, when the limits of interaction steepness and
space dimension are both taken to infinity in a particularly described fashion.Comment: 19 pages, 5 figures, submitted to J. Chem. Phys; new version: minor
changes in structure of pape
Exclusive photoproduction of hard dijets and magnetic susceptibility of QCD vacuum
We argue that coherent production of hard dijets by linearly polarized real
photons can provide direct evidence for chirality violation in hard processes,
the first measurement of the magnetic susceptibility of the quark condensate
and the photon distribution amplitude. It can also serve as a sensitive probe
of the generalized gluon parton distribution. Numerical calculations are
presented for HERA kinematics.Comment: 4 pages, 4 figure
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
The Low Quiescent X-Ray Luminosity of the Transient X-Ray Burster EXO 1747-214
We report on X-ray and optical observations of the X-ray burster EXO
1747-214. This source is an X-ray transient, and its only known outburst was
observed in 1984-1985 by the EXOSAT satellite. We re-analyzed the EXOSAT data
to derive the source position, column density, and a distance upper limit using
its peak X-ray burst flux. We observed the EXO 1747-214 field in 2003 July with
the Chandra X-ray Observatory to search for the quiescent counterpart. We found
one possible candidate just outside the EXOSAT error circle, but we cannot rule
out the possibility that the source is unrelated to EXO 1747-214. Our
conclusion is that the upper limit on the unabsorbed 0.3-8 keV luminosity is L
< 7E31 erg/s, making EXO 1747-214 one of the faintest neutron star transients
in quiescence. We compare this luminosity upper limit to the quiescent
luminosities of 19 neutron star and 14 black hole systems and discuss the
results in the context of the differences between neutron stars and black
holes. Based on the theory of deep crustal heating by Brown and coworkers, the
luminosity implies an outburst recurrence time of >1300 yr unless some form of
enhanced cooling occurs within the neutron star. The position of the possible
X-ray counterpart is consistent with three blended optical/IR sources with
R-magnitudes between 19.4 and 19.8 and J-magnitudes between 17.2 and 17.6. One
of these sources could be the quiescent optical/IR counterpart of EXO 1747-214.Comment: 7 pages, accepted by the Astrophysical Journa
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