Sharp thresholds between finite spread and uniform convergence for a reaction–diffusion equation with oscillating initial data

International audienceWe investigate the large-time dynamics of solutions of multi-dimensional reaction-diffusion equations with ignition type nonlinearities. We consider solutions which are in some sense locally persistent at large time and initial data which asymptotically oscillate around the ignition threshold. We show that, as time goes to infinity, any solution either converges uniformly in space to a constant state, or spreads with a finite speed uniformly in all directions. Furthermore, the transition between these two behaviors is sharp with respect to the period vector of the asymptotic profile of the initial data. We also show the convergence to planar fronts when the initial data are asymptotically periodic in one direction

Modelling planar cell polarity in Drosophila melanogaster

During development, polarity is a common feature of many cell types. One example is the polarisation of whole fields of epithelial cells within the plane of the epithelium, a phenomenon called planar cell polarity (PCP). It is widespread in nature and plays important roles in development and physiology. Prominent examples include the epithelial cells of external structures of insects like the fruit fly Drosophila melanogaster, polarised tissue morphogenesis in vertebrates and sensory hair cells in the vertebrate ear. In this work we focus on the wing and the abdomen of Drosophila, where PCP becomes obvious in the alignment of hairs and bristles. The underlying dynamics are not fully understood yet, but two distinct protein networks centred around the transmembrane proteins Frizzled and Dachsous, respectively, have been shown to play essential roles. We will present and analyse five models for different aspects of the process of planar cell polarisation. The first two models assess the nature of PCP in a generic setting, ensuring that the results are valid for whole classes of PCP models. Models three and four are existing more complex models that include detailed assumptions about the underlying protein interactions of the Frizzled system in the Drosophila wing. Model five considers the Dachsous system in the Drosophila abdomen. We describe the features of the different types of mechanisms and determine the conditions under which they can yield polarity. All five models can establish wild-type polarity for a wide range of parameter values. We find, however, that for model one, three and four an inhomogeneous pattern exists for the same parameter values as the polarised state. Therefore, in these cases either specific initial conditions, which are unlikely in nature, or a global bias are necessary to ensure correct polarisation. Furthermore, we present the effects of clonal clusters of cells on the polarity of the surrounding cells in our models and relate them to the phenotypes observed in experiments. Model one and five show the largest discrepance between the numerical and the experimental results. We discuss the biological relevance of these findings and indicate outstanding questions

Abstracts on Radio Direction Finding (1899 - 1995)

The files on this record represent the various databases that originally composed the CD-ROM issue of "Abstracts on Radio Direction Finding" database, which is now part of the Dudley Knox Library's Abstracts and Selected Full Text Documents on Radio Direction Finding (1899 - 1995) Collection. (See Calhoun record https://calhoun.nps.edu/handle/10945/57364 for further information on this collection and the bibliography). Due to issues of technological obsolescence preventing current and future audiences from accessing the bibliography, DKL exported and converted into the three files on this record the various databases contained in the CD-ROM. The contents of these files are: 1) RDFA_CompleteBibliography_xls.zip [RDFA_CompleteBibliography.xls: Metadata for the complete bibliography, in Excel 97-2003 Workbook format; RDFA_Glossary.xls: Glossary of terms, in Excel 97-2003 Workbookformat; RDFA_Biographies.xls: Biographies of leading figures, in Excel 97-2003 Workbook format]; 2) RDFA_CompleteBibliography_csv.zip [RDFA_CompleteBibliography.TXT: Metadata for the complete bibliography, in CSV format; RDFA_Glossary.TXT: Glossary of terms, in CSV format; RDFA_Biographies.TXT: Biographies of leading figures, in CSV format]; 3) RDFA_CompleteBibliography.pdf: A human readable display of the bibliographic data, as a means of double-checking any possible deviations due to conversion