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

Dynamic Front Transitions and Spiral-Vortex Nucleation

This is a study of front dynamics in reaction diffusion systems near Nonequilibrium Ising-Bloch bifurcations. We find that the relation between front velocity and perturbative factors, such as external fields and curvature, is typically multivalued. This unusual form allows small perturbations to induce dynamic transitions between counter-propagating fronts and nucleate spiral vortices. We use these findings to propose explanations for a few numerical and experimental observations including spiral breakup driven by advective fields, and spot splitting

Accuracy of core mass estimates in simulated observations of dust emission

We study the reliability of mass estimates obtained for molecular cloud cores using sub-millimetre and infrared dust emission. We use magnetohydrodynamic simulations and radiative transfer to produce synthetic observations with spatial resolution and noise levels typical of Herschel surveys. We estimate dust colour temperatures using different pairs of intensities, calculate column densities and compare the estimated masses with the true values. We compare these results to the case when all five Herschel wavelengths are available. We investigate the effects of spatial variations of dust properties and the influence of embedded heating sources. Wrong assumptions of dust opacity and its spectral index beta can cause significant systematic errors in mass estimates. These are mainly multiplicative and leave the slope of the mass spectrum intact, unless cores with very high optical depth are included. Temperature variations bias colour temperature estimates and, in quiescent cores with optical depths higher than for normal stable cores, masses can be underestimated by up to one order of magnitude. When heated by internal radiation sources the observations recover the true mass spectra. The shape, although not the position, of the mass spectrum is reliable against observational errors and biases introduced in the analysis. This changes only if the cores have optical depths much higher than expected for basic hydrostatic equilibrium conditions. Observations underestimate the value of beta whenever there are temperature variations along the line of sight. A bias can also be observed when the true beta varies with wavelength. Internal heating sources produce an inverse correlation between colour temperature and beta that may be difficult to separate from any intrinsic beta(T) relation of the dust grains. This suggests caution when interpreting the observed mass spectra and the spectral indices.Comment: Revised version, 17 pages, 17 figures, submitted to A&

Order Parameter Equations for Front Transitions: Planar and Circular Fronts

Near a parity breaking front bifurcation, small perturbations may reverse the propagation direction of fronts. Often this results in nonsteady asymptotic motion such as breathing and domain breakup. Exploiting the time scale differences of an activator-inhibitor model and the proximity to the front bifurcation, we derive equations of motion for planar and circular fronts. The equations involve a translational degree of freedom and an order parameter describing transitions between left and right propagating fronts. Perturbations, such as a space dependent advective field or uniform curvature (axisymmetric spots), couple these two degrees of freedom. In both cases this leads to a transition from stationary to oscillating fronts as the parity breaking bifurcation is approached. For axisymmetric spots, two additional dynamic behaviors are found: rebound and collapse.Comment: 9 pages. Aric Hagberg: http://t7.lanl.gov/People/Aric/; Ehud Meron: http://www.bgu.ac.il/BIDR/research/staff/meron.htm

Sub-millimeter to centimeter excess emission from the Magellanic Clouds. I. Global spectral energy distribution

In order to reconstruct the global SEDs of the Magellanic Clouds over eight decades in spectral range, we combined literature flux densities representing the entire LMC and SMC respectively, and complemented these with maps extracted from the WMAP and COBE databases covering the missing the 23--90 GHz (13--3.2 mm) and the poorly sampled 1.25--250 THz (240--1.25 micron). We have discovered a pronounced excess of emission from both Magellanic Clouds, but especially the SMC, at millimeter and sub-millimeter wavelengths. We also determined accurate thermal radio fluxes and very low global extinctions for both LMC and SMC. Possible explanations are briefly considered but as long as the nature of the excess emission is unknown, the total dust masses and gas-to-dust ratios of the Magellanic Clouds cannot reliably be determined.Comment: Accepted for publication by A&

Effects of dust abundance on the far-infrared colours of blue compact dwarf galaxies

We investigate the FIR properties of a sample of BCDs observed by AKARI. By utilizing the data at wavelengths of $\lambda =65 \mu$m, 90 $\mu$m, and 140 $\mu$m, we find that the FIR colours of the BCDs are located at the natural high-temperature extension of those of the Milky Way and the Magellanic Clouds. This implies that the optical properties of dust in BCDs are similar to those in the Milky Way. Indeed, we explain the FIR colours by assuming the same grain optical properties, which may be appropriate for amorphous dust grains, and the same size distribution as those adopted for the Milky Way dust. Since both interstellar radiation field and dust optical depth affect the dust temperature, it is difficult to distinguish which of these two physical properties is responsible for the change of FIR colours. Then, in order to examine if the dust optical depth plays an important role in determining the dust temperature, we investigate the correlation between FIR colour (dust temperature) and dust-to-gas ratio. We find that the dust temperature tends to be high as the dust-to-gas ratio decreases but that this trend cannot be explained by the effect of dust optical depth. Rather, it indicates a correlation between dust-to-gas ratio and interstellar radiation field. Although the metallicity may also play a role in this correlation, we suggest that the dust optical depth could regulate the star formation activities, which govern the interstellar radiation field. We also mention the importance of submillimetre data in tracing the emission from highly shielded low-temperature dust.Comment: 12 pages, 8 figures, accepted for publication in MNRA

Fitting the integrated Spectral Energy Distributions of Galaxies

Fitting the spectral energy distributions (SEDs) of galaxies is an almost universally used technique that has matured significantly in the last decade. Model predictions and fitting procedures have improved significantly over this time, attempting to keep up with the vastly increased volume and quality of available data. We review here the field of SED fitting, describing the modelling of ultraviolet to infrared galaxy SEDs, the creation of multiwavelength data sets, and the methods used to fit model SEDs to observed galaxy data sets. We touch upon the achievements and challenges in the major ingredients of SED fitting, with a special emphasis on describing the interplay between the quality of the available data, the quality of the available models, and the best fitting technique to use in order to obtain a realistic measurement as well as realistic uncertainties. We conclude that SED fitting can be used effectively to derive a range of physical properties of galaxies, such as redshift, stellar masses, star formation rates, dust masses, and metallicities, with care taken not to over-interpret the available data. Yet there still exist many issues such as estimating the age of the oldest stars in a galaxy, finer details ofdust properties and dust-star geometry, and the influences of poorly understood, luminous stellar types and phases. The challenge for the coming years will be to improve both the models and the observational data sets to resolve these uncertainties. The present review will be made available on an interactive, moderated web page (sedfitting.org), where the community can access and change the text. The intention is to expand the text and keep it up to date over the coming years.Comment: 54 pages, 26 figures, Accepted for publication in Astrophysics & Space Scienc

Involvement of Iron in Biofilm Formation by Staphylococcus aureus

Staphylococcus aureus is a human pathogen that forms biofilm on catheters and medical implants. The authors' earlier study established that 1,2,3,4,6-penta-O-galloyl-β-D-glucopyranose (PGG) inhibits biofilm formation by S. aureus by preventing the initial attachment of the cells to a solid surface and reducing the production of polysaccharide intercellular adhesin (PIA). Our cDNA microarray and MALDI-TOF mass spectrometric studies demonstrate that PGG treatment causes the expression of genes and proteins that are normally expressed under iron-limiting conditions. A chemical assay using ferrozine verifies that PGG is a strong iron chelator that depletes iron from the culture medium. This study finds that adding FeSO4 to a medium that contains PGG restores the biofilm formation and the production of PIA by S. aureus SA113. The requirement of iron for biofilm formation by S. aureus SA113 can also be verified using a semi-defined medium, BM, that contains an iron chelating agent, 2, 2′-dipyridyl (2-DP). Similar to the effect of PGG, the addition of 2-DP to BM medium inhibits biofilm formation and adding FeSO4 to BM medium that contains 2-DP restores biofilm formation. This study reveals an important mechanism of biofilm formation by S. aureus SA113

Genetic Dissection of an Exogenously Induced Biofilm in Laboratory and Clinical Isolates of E. coli

Microbial biofilms are a dominant feature of many human infections. However, developing effective strategies for controlling biofilms requires an understanding of the underlying biology well beyond what currently exists. Using a novel strategy, we have induced formation of a robust biofilm in Escherichia coli by utilizing an exogenous source of poly-N-acetylglucosamine (PNAG) polymer, a major virulence factor of many pathogens. Through microarray profiling of competitive selections, carried out in both transposon insertion and over-expression libraries, we have revealed the genetic basis of PNAG-based biofilm formation. Our observations reveal the dominance of electrostatic interactions between PNAG and surface structures such as lipopolysaccharides. We show that regulatory modulation of these surface structures has significant impact on biofilm formation behavior of the cell. Furthermore, the majority of clinical isolates which produced PNAG also showed the capacity to respond to the exogenously produced version of the polymer

Spiral-Wave Turbulence and Its Control in the Presence of Inhomogeneities in Four Mathematical Models of Cardiac Tissue

Regular electrical activation waves in cardiac tissue lead to the rhythmic contraction and expansion of the heart that ensures blood supply to the whole body. Irregularities in the propagation of these activation waves can result in cardiac arrhythmias, like ventricular tachycardia (VT) and ventricular fibrillation (VF), which are major causes of death in the industrialised world. Indeed there is growing consensus that spiral or scroll waves of electrical activation in cardiac tissue are associated with VT, whereas, when these waves break to yield spiral- or scroll-wave turbulence, VT develops into life-threatening VF: in the absence of medical intervention, this makes the heart incapable of pumping blood and a patient dies in roughly two-and-a-half minutes after the initiation of VF. Thus studies of spiral- and scroll-wave dynamics in cardiac tissue pose important challenges for in vivo and in vitro experimental studies and for in silico numerical studies of mathematical models for cardiac tissue. A major goal here is to develop low-amplitude defibrillation schemes for the elimination of VT and VF, especially in the presence of inhomogeneities that occur commonly in cardiac tissue. We present a detailed and systematic study of spiral- and scroll-wave turbulence and spatiotemporal chaos in four mathematical models for cardiac tissue, namely, the Panfilov, Luo-Rudy phase 1 (LRI), reduced Priebe-Beuckelmann (RPB) models, and the model of ten Tusscher, Noble, Noble, and Panfilov (TNNP). In particular, we use extensive numerical simulations to elucidate the interaction of spiral and scroll waves in these models with conduction and ionic inhomogeneities; we also examine the suppression of spiral- and scroll-wave turbulence by low-amplitude control pulses. Our central qualitative result is that, in all these models, the dynamics of such spiral waves depends very sensitively on such inhomogeneities. We also study two types of control schemes that have been suggested for the control of spiral turbulence, via low amplitude current pulses, in such mathematical models for cardiac tissue; our investigations here are designed to examine the efficacy of such control schemes in the presence of inhomogeneities. We find that a local pulsing scheme does not suppress spiral turbulence in the presence of inhomogeneities; but a scheme that uses control pulses on a spatially extended mesh is more successful in the elimination of spiral turbulence. We discuss the theoretical and experimental implications of our study that have a direct bearing on defibrillation, the control of life-threatening cardiac arrhythmias such as ventricular fibrillation