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

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 Comparison of Some Fuzzy Relation-based Linguistic Preference Models for Multiple-Factor Project Assessment

Some approaches to the use of linguistic-preference models based on fuzzy relations in the context of multiple factor project assessment are considered. Projects are characterized in terms of linguistic expressions of 'performance' with respect to factors or impacts and the 'importance' of those factors and impacts. Some variations of methods by Wilhelm and Parsaei (1991) and Eldukair and Ayyub (1992) are considered with some possible analogous methods. A simple illustrative, hypothetical example is developed to compare methods in the context of a proposed bridge river crossing in the city of Brisbane, Queensland, Australia, assessed against six factors: (1) cost, (2) lifespan, (3) usage, (4) aesthetics, (5) construction time, and (6) environmental impact

Resonance ionization spectroscopy of thorium isotopes - towards a laser spectroscopic identification of the low-lying 7.6 eV isomer of Th-229

In-source resonance ionization spectroscopy was used to identify an efficient and selective three step excitation/ionization scheme of thorium, suitable for titanium:sapphire (Ti:sa) lasers. The measurements were carried out in preparation of laser spectroscopic investigations for an identification of the low-lying Th-229m isomer predicted at 7.6 +- 0.5 eV above the nuclear ground state. Using a sample of Th-232, a multitude of optical transitions leading to over 20 previously unknown intermediate states of even parity as well as numerous high-lying odd parity auto-ionizing states were identified. Level energies were determined with an accuracy of 0.06 cm-1 for intermediate and 0.15 cm-1 for auto-ionizing states. Using different excitation pathways an assignment of total angular momenta for several energy levels was possible. One particularly efficient ionization scheme of thorium, exhibiting saturation in all three optical transitions, was studied in detail. For all three levels in this scheme, the isotope shifts of the isotopes Th-228, Th-229, and Th-230 relative to Th-232 were measured. An overall efficiency including ionization, transport and detection of 0.6 was determined, which was predominantly limited by the transmission of the mass spectrometer ion optics

A Chandra survey of fluorescence Fe lines in X-ray Binaries at high resolution

In this paper we present a comprehensive survey of 41 X-ray binaries (10 HMXBs and 31 LMXBs) with Chandra, with specific emphasis on the Fe K region and the narrow Fe Kalpha line, at the highest resolution possible. We find that: a) The Fe Kalpha line is always centered at 1.9387 +- 0.0016 Angstroms, compatible with Fe I up to Fe X; we detect no shifts to higher ionization states nor any difference between HMXBs and LMXBs. b) The line is very narrow, with FWHM < 5 mAngstroms, which means that the reprocessing material is not rotating at high speeds. c) Fe Kalpha fluorescence is present in all the HMXB in the survey while such emissions are very rare (~ 10% ) among LMXBs. d) The lack of Fe line emission is always accompanied by the lack of any detectable K edge. e) We obtain the empirical curve of growth of the equivalent width of the Fe Kalpha line versus the density column of the reprocessing material, i.e. EW_{Kalpha} vs N_{H}, and show that it is consistent with a reprocessing region spherically distributed around the compact object. f) We show that fluorescence in X-ray binaries follows the X-ray Baldwin effect. We interpret this finding as evidence of decreasing neutral Fe abundance with increasing X-ray illumination and use it to explain some spectral states of Cyg X-1 and as a possible cause of the lack of narrow Fe line emission in LMXBs. g) Finally, we study anomalous morphologies. We present the first evidence of a Compton shoulder in the HMXB X1908+075. Also the Fe Kalpha lines of 4U1700-37 and LMC X-4 present asymmetric wings suggesting the presence of highly structured stellar winds in these systems.Comment: 12 pages, 11 figures, accepted for publication in Ap

Analysis of the Spatial Spread of Sharka (Plum Pox Virus) in Apricot and Peach Orchards in Eastern Spain

Spatial patterns of sharka disease, caused by plum pox virus (PPV) and vectored by several species of aphid, were determined by double antibody sandwich-enzyme-linked immunosorbent assay using polyclonal antibodies in newly infected, mature apricot and peach orchards in eastern Spain. Among yearly assessments of plots examined for within- and across-row aggregation of adjacent sharka-diseased trees, only a few transects were found to have aggregation by ordinary runs analyses. Analyses, using beta-binomial index of dispersion (I-beta) to determine if spatial aggregation was present in each plot for data partitioned into quadrats of different spatial dimension, demonstrated occasional aggregation and results were generally inconclusive. Significant (I-beta) values, when present, were generally found associated with plots with higher disease incidence. No disease gradients were discernible for any of the plots and years. More rigorous spatial analyses were used to test for spatial relationships over longer distances. Two-dimensional distance class analyses indicated a spatial dependency of PPV-infected stone-fruit trees over distance, a general scarcity of significant distance classes near the origin, and the presence of significant distance classes occasionally comprising small loose clusters at distances near the center or distal end of the proximity matrices especially during the initial stages of the epidemics. Geostatistical analysis confirmed the lack of significant associations among immediately adjacent trees and the trend for higher order spatial associations in semivariograms for distances corresponding to the center and distal ends of the proximity matrices. This trend in semivariance over distance was best described by linear or exponential increase models compared with transitional models commonly used in geostatistics. Correlation analysis indicated a significant conservation of orientation of localized systemic infections in scaffold branches over years. The spatial patterns of sharka suggest the lack of movement of PPV-viruliferous aphid vectors to immediately adjacent trees and their preferential movement to trees several tree spaces away

Cuspons, peakons and regular gap solitons between three dispersion curves

A general wave model with the cubic nonlinearity is introduced to describe a situation when the linear dispersion relation has three branches, which would intersect in the absence of linear couplings between the three waves. Actually, the system contains two waves with a strong linear coupling between them, to which a third wave is then coupled. This model has two gaps in its linear spectrum. Realizations of this model can be made in terms of temporal or spatial evolution of optical fields in, respectively, a planar waveguide or a bulk-layered medium resembling a photonic-crystal fiber. Another physical system described by the same model is a set of three internal wave modes in a density-stratified fluid. A nonlinear analysis is performed for solitons which have zero velocity in the reference frame in which the group velocity of the third wave vanishes. Disregarding the self-phase modulation (SPM) term in the equation for the third wave, we find two coexisting families of solitons: regular ones, which may be regarded as a smooth deformation of the usual gap solitons in a two-wave system, and cuspons with a singularity in the first derivative at their center. Even in the limit when the linear coupling of the third wave to the first two vanishes, the soliton family remains drastically different from that in the linearly uncoupled system; in this limit, regular solitons whose amplitude exceeds a certain critical value are replaced by peakons. While the regular solitons, cuspons, and peakons are found in an exact analytical form, their stability is tested numerically, which shows that they all may be stable. If the SPM terms are retained, we find that there again coexist two different families of generic stable soliton solutions, namely, regular ones and peakons.Comment: a latex file with the text and 10 pdf files with figures. Physical Review E, in pres

A stochastic optimization method to estimate the spatial distribution of a pathogen from a sample

Information on the spatial distribution of plant disease can be utilized to implement efficient and spatially targeted disease management interventions. We present a pathogen-generic method to estimate the spatial distribution of a plant pathogen using a stochastic optimization process which is epidemiologically motivated. Based on an initial sample, the method simulates the individual spread processes of a pathogen between patches of host to generate optimized spatial distribution maps. The method was tested on data sets of Huanglongbing of citrus and was compared with a kriging method from the field of geostatistics using the well-established kappa statistic to quantify map accuracy. Our method produced accurate maps of disease distribution with kappa values as high as 0.46 and was able to outperform the kriging method across a range of sample sizes based on the kappa statistic. As expected, map accuracy improved with sample size but there was a high amount of variation between different random sample placements (i.e., the spatial distribution of samples). This highlights the importance of sample placement on the ability to estimate the spatial distribution of a plant pathogen and we thus conclude that further research into sampling design and its effect on the ability to estimate disease distribution is necessary. </jats:p