Diffusion-induced vortex filament instability in 3-dimensional excitable media

We studied the stability of linear vortex filaments in 3-dimensional (3D) excitable media, using both analytical and numerical methods. We found an intrinsic 3D instability of vortex filaments that is diffusion-induced, and is due to the slower diffusion of the inhibitor. This instability can result either in a single helical filament or in chaotic scroll breakup, depending on the specific kinetic model. When the 2-dimensional dynamics were in the chaotic regime, filament instability occurred via on-off intermittency, a failure of chaos synchronization in the third dimension.Comment: 5 pages, 5 figures, to appear in PRL (September, 1999

Zonal image analysis of tumour vascular perfusion, hypoxia, and necrosis

A number of laboratories are utilising both hypoxia and perfusion markers to spatially quantify tumour oxygenation and vascular distributions, and scientists are increasingly turning to automated image analysis methods to quantify such interrelationships. In these studies, the presence of regions of necrosis in the immunohistochemical sections remains a potentially significant source of error. In the present work, frozen MCa-4 mammary tumour sections were used to obtain a series of corresponding image montages. Total vessels were identified using CD31 staining, perfused vessels by DiOC7 staining, hypoxia by EF5/Cy3 uptake, and necrosis by haematoxylin and eosin staining. Our goal was to utilise image analysis techniques to spatially quantitate hypoxic marker binding as a function of distance from the nearest blood vessel. Several refinements to previous imaging methods are described: (1) hypoxia marker images are quantified in terms of their intensity levels, thus providing an analysis of the gradients in hypoxia with increasing distances from blood vessels, (2) zonal imaging masks are derived, which permit spatial sampling of images at precisely defined distances from blood vessels, as well as the omission of necrotic artifacts, (3) thresholding techniques are applied to omit holes in the tissue sections, and (4) distance mapping is utilised to define vascular spacing

Scroll waves in isotropic excitable media : linear instabilities, bifurcations and restabilized states

Scroll waves are three-dimensional analogs of spiral waves. The linear stability spectrum of untwisted and twisted scroll waves is computed for a two-variable reaction-diffusion model of an excitable medium. Different bands of modes are seen to be unstable in different regions of parameter space. The corresponding bifurcations and bifurcated states are characterized by performing direct numerical simulations. In addition, computations of the adjoint linear stability operator eigenmodes are also performed and serve to obtain a number of matrix elements characterizing the long-wavelength deformations of scroll waves.Comment: 30 pages 16 figures, submitted to Phys. Rev.

The dune effect on sand-transporting winds on Mars

Wind on Mars is a significant agent of contemporary surface change, yet the absence of in situ meteorological data hampers the understanding of surface–atmospheric interactions. Airflow models at length scales relevant to landform size now enable examination of conditions that might activate even small-scale bedforms (ripples) under certain contemporary wind regimes. Ripples have the potential to be used as modern ‘wind vanes’ on Mars. Here we use 3D airflow modelling to demonstrate that local dune topography exerts a strong influence on wind speed and direction and that ripple movement likely reflects steered wind direction for certain dune ridge shapes. The poor correlation of dune orientation with effective sand-transporting winds suggests that large dunes may not be mobile under modelled wind scenarios. This work highlights the need to first model winds at high resolution before inferring regional wind patterns from ripple movement or dune orientations on the surface of Mars today

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

Coupling Experiment and Simulation in Electromagnetic Forming Using Photon Doppler Velocimetry

Modeling electromagnetic forming processes is in many ways simpler than modeling traditional metal forming processes. In electromagnetic forming the problem is often dominated by inertial acceleration by a magnetic field. This is a much better posed problem than the more traditional ones that are often dominated by complex three dimensional constitutive behavior and frictional effects. However, important aspects of the problem are dominated by the constitutive properties of the material, and often electromagnetic forming is performed in a regime where there is little reliable material strength data. Strain rates are often high (102 to 104 s-1 is the typical range for electromagnetic forming). Also, heat is generated both by ohmic heating as well as by plastic deformation, and peak temperatures can be quite high. Also, while hightemperature, high-strain-rate data is scarce, there is little or no data in cases where temperature rises significantly over very short times (tens of micro-seconds) as happens in electromagnetic metal forming. This rapid temperature rise is very important to the material response because the short time scales largely preclude the material from recovery and recrystallization processes and precipitates cannot dissolve as they normally would in an age-hardening alloy in these time scales. This presentation will show how advanced instrumentation, particularly the Photon Doppler Velocimeter (PDV) can be coupled with electromagnetic forming and provide both avenues to characterize material as well as to provide very critical tests of numerical models of the process

Nonlinear Magneto-Optical Response of ss- and dd-Wave Superconductors

The nonlinear magneto-optical response of $s$- and $d$-wave superconductors is discussed. We carry out the symmetry analysis of the nonlinear magneto-optical susceptibility in the superconducting state. Due to the surface sensitivity of the nonlinear optical response for systems with bulk inversion symmetry, we perform a group theoretical classification of the superconducting order parameter close to a surface. For the first time, the mixing of singlet and triplet pairing states induced by spin-orbit coupling is systematically taken into account. We show that the interference of singlet and triplet pairing states leads to an observable contribution of the nonlinear magneto-optical Kerr effect. This effect is not only sensitive to the anisotropy of the gap function but also to the symmetry itself. In view of the current discussion of the order parameter symmetry of High-T$_c$ superconductors, results for a tetragonal system with bulk singlet pairing for various pairing symmetries are discussed.Comment: 21 pages (REVTeX) with 8 figures (Postscript

Reproducibility of species recognition in modern planktonic foraminifera and its implications for analyses of community structure

Applications of planktonic foraminifera in Quaternary palaeoceanographic and palaeobiological studies require consistency in species identification. Yet the degree of taxonomic consistency among the practitioners and the effects of any potential deviations on community structure metrics have never been quantitatively assessed. Here we present the results of an experiment in taxonomic consistency involving 21 researchers representing a range of experience and taxonomic schools from around the world. Participants were asked to identify the same two sets of 300 specimens from a modern subtropical North Atlantic sample, one sieved at  &gt; 125&thinsp;µm and one at  &gt;  150&thinsp;µm. The identification was carried out either on actual specimens (slide test) or their digital images (digital test). The specimens were fixed so the identifications could be directly compared. In all tests, only between one-quarter and one-eighth of the specimens achieved absolute agreement. Therefore, the identifications across the participants were used to determine a consensus ID for each specimen. Since no strict consensus ( &gt; 50&thinsp;% agreement) could be achieved for 20–30&thinsp;% of the specimens, we used a soft consensus based on the most common identification. The average percentage agreement relative to the consensus of the slide test was 77&thinsp;% in the  &gt; 150&thinsp;µm and 69&thinsp;% in the  &gt; 125&thinsp;µm test. These values were 7&thinsp;% lower for the digital analyses. We find that taxonomic consistency is enhanced when researchers have been trained within a taxonomic school and when they regularly perform community analyses. There is an almost negligible effect of taxonomic inconsistency on sea surface temperature estimates based on transfer function conversion of the census counts, indicating the temperature signal in foraminiferal assemblages is correctly represented even if only two-thirds of the assemblage is consistently identified. The same does not apply to measures of diversity and community structure within the assemblage, and here we advise caution in using compound datasets for such studies. The decrease in the level of consistency when specimens are identified from digital images is significant and species-specific, with implications for the development of training sets for automated identification systems.</p

Software defect prediction: do different classifiers find the same defects?

Open Access: This article is distributed under the terms of the Creative Commons Attribution 4.0 International License CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.During the last 10 years, hundreds of different defect prediction models have been published. The performance of the classifiers used in these models is reported to be similar with models rarely performing above the predictive performance ceiling of about 80% recall. We investigate the individual defects that four classifiers predict and analyse the level of prediction uncertainty produced by these classifiers. We perform a sensitivity analysis to compare the performance of Random Forest, Naïve Bayes, RPart and SVM classifiers when predicting defects in NASA, open source and commercial datasets. The defect predictions that each classifier makes is captured in a confusion matrix and the prediction uncertainty of each classifier is compared. Despite similar predictive performance values for these four classifiers, each detects different sets of defects. Some classifiers are more consistent in predicting defects than others. Our results confirm that a unique subset of defects can be detected by specific classifiers. However, while some classifiers are consistent in the predictions they make, other classifiers vary in their predictions. Given our results, we conclude that classifier ensembles with decision-making strategies not based on majority voting are likely to perform best in defect prediction.Peer reviewedFinal Published versio