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

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

Simultaneous BeppoSAX and Rossi X-ray Timing Explorer observations of 4U1812-12

4U1812-12 is a faint persistent and weakly variable neutron star X-ray binary. It was observed by BeppoSAX between April 20th and 21st, 2000 in a hard spectral state with a bolometric luminosity of ~2x10^36 ergs/s. Its broad band energy spectrum is characterized by the presence of a hard X-ray tail extending above ~100 keV. It can be represented as the sum of a dominant hard Comptonized component (electron temperature of ~36 keV and optical depth ~3) and a weak soft component. The latter component which can be fitted with a blackbody of about 0.6 keV and equivalent radius of ~2 km is likely to originate from the neutron star surface. We also report on the first measurement of the power density spectrum of the source rapid X-ray variability, as recorded during a simultaneous snapshot observation performed by the Rossi X-ray Timing Explorer. As expected for a neutron star system in such hard spectral state, its power density spectrum is characterized by the presence of a ~0.7 Hz low frequency quasi-periodic oscillation together with three broad noise components, one of which extends above ~200 Hz.Comment: 6 pages, 3 figures, accepted for publication in A&

Interplay Between Chaotic and Regular Motion in a Time-Dependent Barred Galaxy Model

We study the distinction and quantification of chaotic and regular motion in a time-dependent Hamiltonian barred galaxy model. Recently, a strong correlation was found between the strength of the bar and the presence of chaotic motion in this system, as models with relatively strong bars were shown to exhibit stronger chaotic behavior compared to those having a weaker bar component. Here, we attempt to further explore this connection by studying the interplay between chaotic and regular behavior of star orbits when the parameters of the model evolve in time. This happens for example when one introduces linear time dependence in the mass parameters of the model to mimic, in some general sense, the effect of self-consistent interactions of the actual N-body problem. We thus observe, in this simple time-dependent model also, that the increase of the bar's mass leads to an increase of the system's chaoticity. We propose a new way of using the Generalized Alignment Index (GALI) method as a reliable criterion to estimate the relative fraction of chaotic vs. regular orbits in such time-dependent potentials, which proves to be much more efficient than the computation of Lyapunov exponents. In particular, GALI is able to capture subtle changes in the nature of an orbit (or ensemble of orbits) even for relatively small time intervals, which makes it ideal for detecting dynamical transitions in time-dependent systems.Comment: 21 pages, 9 figures (minor typos fixed) to appear in J. Phys. A: Math. Theo

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

A look with BeppoSAX at the low-luminosity Galactic X-ray source 4U 2206+54

A pointed observation of the low-luminosity galactic source 4U 2206+54 was carried out in November 1998 with BeppoSAX. The light curve of 4U 2206+54 shows erratic variability on a timescale of about 1 hour; neither hardness variations nor time periodicities are detected throughout this 67 ks long observation. Thanks to the wide spectral coverage capabilities of BeppoSAX we could observe the source X-ray continuum over three energy decades, from 0.6 to 60 keV. The spectrum could be equally well fitted either with a blackbody plus Comptonization or with a high energy cutoff power law. No iron emission around 6.5 keV was detected, while a tentative detection of a cyclotron resonant feature in absorption is presented. Comparison of the present BeppoSAX data with the information available in the literature for this source suggests that 4U 2206+54 is a close binary system in which a (possibly magnetized) NS is accreting from the companion star wind.Comment: 9 pages, 5 figures, 2 tables; accepted for publication on Astronomy & Astrophysics, main journal. Final version of the paper including the A&A Language Editor's comment

Magnetic Fields of Accreting X-Ray Pulsars with the Rossi X-Ray Timing Explorer

Using a consistent set of models, we parameterized the X-ray spectra of all accreting pulsars in the Rossi X-ray Timing Explorer database which exhibit Cyclotron Resonance Scattering Features (CRSFs, or cyclotron lines). These sources in our sample are Her X-1, 4U 0115+63, Cen X-3, 4U 1626-67, XTE J1946-274, Vela X-1, 4U 1907+09, 4U 1538-52, GX 301-2, and 4U 0352+309 (X Per). We searched for correlations among the spectral parameters, concentrating on how the cyclotron line energy relates to the continuum and therefore how the neutron star B-field influences the X-Ray emission. As expected, we found a correlation between the CRSF energy and the spectral cutoff energy. However, with our consistent set of fits we found that the relationship is more complex than what has been reported previously. Also, we found that not only does the width of the cyclotron line correlate with the energy (as suggested by theory), but that the width scaled by the energy correlates with the depth of the feature. We discuss the implications of these results, including the possibility that accretion directly affects the relative alignment of the neutron star spin and dipole axes. Lastly, we comment on the current state of fitting phenomenological models to spectra in the RXTE/BeppoSAX era and the need for better theoretical models of the X-Ray continua of accreting pulsars.Comment: 36 Pages, 9 Figures, 9 Tables, ApJ in pres

A Cellular Automata Model for Citrus Variagated Chlorosis

A cellular automata model is proposed to analyze the progress of Citrus Variegated Chlorosis epidemics in S\~ao Paulo oranges plantation. In this model epidemiological and environmental features, such as motility of sharpshooter vectors which perform L\'evy flights, hydric and nutritional level of plant stress and seasonal climatic effects, are included. The observed epidemics data were quantitatively reproduced by the proposed model varying the parameters controlling vectors motility, plant stress and initial population of diseased plants.Comment: 10 pages, 10 figures, Scheduled tentatively for the issue of: 01Nov0

Systematic study of the pp -> pp omega reaction

A systematic study of the production of omega-mesons in proton-proton-collisions was carried out in a kinematically complete experiment at three excess energies(epsilon= 92, 128, 173MeV). Both protons were detected using the large-acceptance COSY-TOF spectrometer at an external beam line at the Cooler Synchrotron COSY at Forschungszentrum J\"ulich. The total cross section, angular distributions of both omega-mesons and protons were measured and presented in various reference frames such as the overall CMS, helicity and Jackson frame. In addition, the orientation of the omega-spin and invariant mass spectra were determined. We observe omega-production to take place dominantly in Ss and Sp final states at epsilon = 92, 128 MeV and, additionally, in Sd at epsilon= 173 MeV. No obvious indication of resonant omega-production via N^*-resonances was found, as proton angular distributions are almost isotropic and invariant mass spectra are compatible with phase space distributions. A dominant role of ^3P_1 and ^1S_0 initial partial waves for omega-production was concluded from the orientation of the decay plane of the omega-meson. Although the Jackson angle distributions in the omega-p-Jackson frame are anisotropic we argue that this is not an indication of a resonance but rather a kinematical effect reflecting the anisotropy of the omega angular distribution. The helicity angle distribution in the omega-p-helicity frame shows an anisotropy which probably reflects effects of the omega angular momenta in the final state; this observable may be, in addition to the orientation of the omega decay plane, the most sensitive one to judge the validity of theoretical descriptions of the production process.Comment: 17 pages, 16 figures, accepted for publication in EPJ

Production of Lambda and Sigma^0 hyperons in proton-proton collisions

This paper reports results on simultaneous measurements of the reaction channels pp -> pK+\Lambda and pp -> pK+\Sigma^0 at excess energies of 204, 239, and 284 MeV (\Lambda) and 127, 162, and 207 MeV (\Sigma^0). Total and differential cross sections are given for both reactions. It is concluded from the measured total cross sections that the high energy limit of the cross section ratio is almost reached at an excess energy of only about 200 MeV. From the differential distributions observed in the overall CMS as well as in the Jackson and helicity frames, a significant contribution of interfering nucleon resonances to the \Lambda production mechanism is concluded while resonant \Sigma^0-production seems to be of lesser importance and takes place only through specific partial waves of the entrance channel. The data also indicate that kaon exchange plays a minor role in the case of \Lambda- but an important role for \Sigma^0-production. Thus the peculiar energy dependence of the \Lambda-to-\Sigma^0 cross section ratio appears in a new light as its explanation requires more than mere differences between the p\Lambda and the p\Sigma^0 final state interaction. The data provide a benchmark for theoretical models already available or yet to come.Comment: 18 pages, 10 figures; accepted by The European Physical Journal A (EPJ A