Continuation for thin film hydrodynamics and related scalar problems

This chapter illustrates how to apply continuation techniques in the analysis of a particular class of nonlinear kinetic equations that describe the time evolution through transport equations for a single scalar field like a densities or interface profiles of various types. We first systematically introduce these equations as gradient dynamics combining mass-conserving and nonmass-conserving fluxes followed by a discussion of nonvariational amendmends and a brief introduction to their analysis by numerical continuation. The approach is first applied to a number of common examples of variational equations, namely, Allen-Cahn- and Cahn-Hilliard-type equations including certain thin-film equations for partially wetting liquids on homogeneous and heterogeneous substrates as well as Swift-Hohenberg and Phase-Field-Crystal equations. Second we consider nonvariational examples as the Kuramoto-Sivashinsky equation, convective Allen-Cahn and Cahn-Hilliard equations and thin-film equations describing stationary sliding drops and a transversal front instability in a dip-coating. Through the different examples we illustrate how to employ the numerical tools provided by the packages auto07p and pde2path to determine steady, stationary and time-periodic solutions in one and two dimensions and the resulting bifurcation diagrams. The incorporation of boundary conditions and integral side conditions is also discussed as well as problem-specific implementation issues

Transcriptome of Aphanomyces euteiches: New Oomycete Putative Pathogenicity Factors and Metabolic Pathways

Aphanomyces euteiches is an oomycete pathogen that causes seedling blight and root rot of legumes, such as alfalfa and pea. The genus Aphanomyces is phylogenically distinct from well-studied oomycetes such as Phytophthora sp., and contains species pathogenic on plants and aquatic animals. To provide the first foray into gene diversity of A. euteiches, two cDNA libraries were constructed using mRNA extracted from mycelium grown in an artificial liquid medium or in contact to plant roots. A unigene set of 7,977 sequences was obtained from 18,864 high-quality expressed sequenced tags (ESTs) and characterized for potential functions. Comparisons with oomycete proteomes revealed major differences between the gene content of A. euteiches and those of Phytophthora species, leading to the identification of biosynthetic pathways absent in Phytophthora, of new putative pathogenicity genes and of expansion of gene families encoding extracellular proteins, notably different classes of proteases. Among the genes specific of A. euteiches are members of a new family of extracellular proteins putatively involved in adhesion, containing up to four protein domains similar to fungal cellulose binding domains. Comparison of A. euteiches sequences with proteomes of fully sequenced eukaryotic pathogens, including fungi, apicomplexa and trypanosomatids, allowed the identification of A. euteiches genes with close orthologs in these microorganisms but absent in other oomycetes sequenced so far, notably transporters and non-ribosomal peptide synthetases, and suggests the presence of a defense mechanism against oxidative stress which was initially characterized in the pathogenic trypanosomatids