Singularity dynamics in curvature collapse and jet eruption on a fluid surface

Finite-time singularities--local divergences in the amplitude or gradient of a physical observable at a particular time--occur in a diverse range of physical systems. Examples include singularities capable of damaging optical fibres and lasers in nonlinear optical systems, and gravitational singularities associated with black holes. In fluid systems, the formation of finite-time singularities cause spray and air-bubble entrainment, processes which influence air-sea interaction on a global scale. Singularities driven by surface tension have been studied in the break-up of pendant drops and liquid sheets. Here we report a theoretical and experimental study of the generation of a singularity by inertial focusing, in which no break-up of the fluid surface occurs. Inertial forces cause a collapse of the surface that leads to jet formation; our analysis, which includes surface tension effects, predicts that the surface profiles should be describable by a single universal exponent. These theoretical predictions correlate closely with our experimental measurements of a collapsing surface singularity. The solution can be generalized to apply to a broad class of singular phenomena.     

Genome sequence, comparative analysis and haplotype structure of the domestic dog

Here we report a high-quality draft genome sequence of the domestic dog (Canis familiaris), together with a dense map of single nucleotide polymorphisms (SNPs) across breeds. The dog is of particular interest because it provides important evolutionary information and because existing breeds show great phenotypic diversity for morphological, physiological and behavioural traits. We use sequence comparison with the primate and rodent lineages to shed light on the structure and evolution of genomes and genes. Notably, the majority of the most highly conserved non-coding sequences in mammalian genomes are clustered near a small subset of genes with important roles in development. Analysis of SNPs reveals long-range haplotypes across the entire dog genome, and defines the nature of genetic diversity within and across breeds. The current SNP map now makes it possible for genome-wide association studies to identify genes responsible for diseases and traits, with important consequences for human and companion animal health.