Evolution of sexual dimorphism of wing shape in the Drosophila melanogaster subgroup

Background: Sexual dimorphism of body size has been the subject of numerous studies, but few have examined sexual shape dimorphism (SShD) and its evolution. Allometry, the shape change associated with size variation, has been suggested to be a main component of SShD. Yet little is known about the relative importance of the allometric and non-allometric components for the evolution of SShD. Results: We investigated sexual dimorphism in wing shape in the nine species of the Drosophila melanogaster subgroup. We used geometric morphometrics to characterise wing shape and found significant SShD in all nine species. The amount of shape difference and the diversity of the shape changes evolved across the group. However, mapping the divergence of SShD onto the phylogeny of the Drosophila melanogaster subgroup indicated that there is little phylogenetic signal. Finally, allometry accounted for a substantial part of SShD, but did not explain the bulk of evolutionary divergence in SShD because allometry itself was found to be evolutionarily plastic. Conclusion: SShD in the Drosophila wing can evolve rapidly and therefore shows only weak phylogenetic structure. The variable contribution of allometric and non-allometric components to the evolutionary divergence of SShD and the evolutionary plasticity of allometry suggest that SShD and allometry are influenced by a complex interaction of processes

Thermonuclear explosions of rapidly rotating white dwarfs - I. Deflagrations

Context: Turbulent deflagrations of Chandrasekhar mass White Dwarfs are commonly used to model Type Ia Supernova explosions. In this context, rapid rotation of the progenitor star is plausible but has so far been neglected. Aims: The aim of this work is to explore the influence of rapid rotation on the deflagration scenario. Methods: We use three dimensional hydrodynamical simulations to model turbulent deflagrations ignited within a variety of rapidly rotating CO WDs obeying rotation laws suggested by accretion studies. Results: We find that rotation has a significant impact on the explosion. The flame develops a strong anisotropy with a preferred direction towards the stellar poles, leaving great amounts of unburnt matter along the equatorial plane. Conclusions: The large amount of unburnt matter is contrary to observed spectral features of SNe Ia. Thus, rapid rotation of the progenitor star and the deflagration scenario are incompatible in order to explain SNe Ia.Comment: 13 pages, 10 figures, accepted for publication by A&

Computer simulations of electrorheological fluids in the dipole-induced dipole model

We have employed the multiple image method to compute the interparticle force for a polydisperse electrorheological (ER) fluid in which the suspended particles can have various sizes and different permittivites. The point-dipole (PD) approximation being routinely adopted in computer simulation of ER fluids is shown to err considerably when the particles approach and finally touch due to multipolar interactions. The PD approximation becomes even worse when the dielectric contrast between the particles and the host medium is large. From the results, we show that the dipole-induced-dipole (DID) model yields very good agreements with the multiple image results for a wide range of dielectric contrasts and polydispersity. As an illustration, we have employed the DID model to simulate the athermal aggregation of particles in ER fluids both in uniaxial and rotating fields. We find that the aggregation time is significantly reduced. The DID model accounts for multipolar interaction partially and is simple to use in computer simulation of ER fluids.Comment: 22 pages, 7 figures, submitted to Phys. Rev.

An all speed second order well-balanced IMEX relaxation scheme for the Euler equations with gravity

We present an implicit-explicit well-balanced finite volume scheme for the Euler equations with a gravitational source term which is able to deal also with low Mach flows. To visualize the different scales we use the non-dimensionalized equations on which we apply a pressure splitting and a Suliciu relaxation. On the resulting model, we apply a splitting of the flux into a linear implicit and an non-linear explicit part that leads to a scale independent time-step. The explicit step consists of a Godunov type method based on an approximative Riemann solver where the source term is included in the flux formulation. We develop the method for a first order scheme and give an extension to second order. Both schemes are designed to be well-balanced, preserve the positivity of density and internal energy and have a scale independent diffusion. We give the low Mach limit equations for well-prepared data and show that the scheme is asymptotic preserving. These properties are numerically validated by various test cases

ARBITRARY ORDER FINITE VOLUME WELL-BALANCED SCHEMES FOR THE EULER EQUATIONS WITH GRAVITY

This work presents arbitrary high order well balanced finite volume schemes for the Euler equations with a prescribed gravitational field. It is assumed that the desired equilibrium solution is known, and we construct a scheme which is exactly well balanced for that particular equilibrium. The scheme is based on high order reconstructions of the fluctuations from equilibrium of density, velocity, and pressure, and on a well-balanced integration of the source terms, while no assumptions are needed on the numerical flux, beside consistency. This technique also allows one to construct well-balanced methods for a class of moving equilibria. Several numerical tests demonstrate the performance of the scheme on different scenarios, from equilibrium solutions to nonsteady problems involving shocks. The numerical tests are carried out with methods up to fifth order in one dimension, and third order accuracy in two dimensions

Applications of the Gauss-Bonnet theorem to gravitational lensing

In this geometrical approach to gravitational lensing theory, we apply the Gauss-Bonnet theorem to the optical metric of a lens, modelled as a static, spherically symmetric, perfect non-relativistic fluid, in the weak deflection limit. We find that the focusing of the light rays emerges here as a topological effect, and we introduce a new method to calculate the deflection angle from the Gaussian curvature of the optical metric. As examples, the Schwarzschild lens, the Plummer sphere and the singular isothermal sphere are discussed within this framework.Comment: 10 pages, 1 figure, IoP styl

Do cladistic and morphometric data capture common patterns of morphological disparity?

The distinctly non-random diversity of organismal form manifests itself in discrete clusters of taxa that share a common body plan. As a result, analyses of disparity require a scalable comparative framework. The difficulties of applying geometric morphometrics to disparity analyses of groups with vastly divergent body plans are overcome partly by the use of cladistic characters. Character-based disparity analyses have become increasingly popular, but it is not clear how they are affected by character coding strategies or revisions of primary homology statements. Indeed, whether cladistic and morphometric data capture similar patterns of morphological variation remains a moot point. To address this issue, we employ both cladistic and geometric morphometric data in an exploratory study of disparity focussing on caecilian amphibians. Our results show no impact on relative intertaxon distances when different coding strategies for cladistic characters were used or when revised concepts of homology were considered. In all instances, we found no statistically significant difference between pairwise Euclidean and Procrustes distances, although the strength of the correlation among distance matrices varied. This suggests that cladistic and geometric morphometric data appear to summarize morphological variation in comparable ways. Our results support the use of cladistic data for characterizing organismal disparity