The PML for rough surface scattering

In this paper we investigate the use of the perfectly matched layer (PML) to truncate a time harmonic rough surface scattering problem in the direction away from the scatterer. We prove existence and uniqueness of the solution of the truncated problem as well as an error estimate depending on the thickness and composition of the layer. This global error estimate predicts a linear rate of convergence (under some conditions on the relative size of the real and imaginary parts of the PML function) rather than the usual exponential rate. We then consider scattering by a half-space and show that the solution of the PML truncated problem converges globally at most quadratically (up to logarithmic factors), providing support for our general theory. However we also prove exponential convergence on compact subsets. We continue by proposing an iterative correction method for the PML truncated problem and, using our estimate for the PML approximation, prove convergence of this method. Finally we provide some numerical results in 2D.(C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.

An analysis of arithmetic averaging in approximate Riemann solvers with an application to steady, supercritical flows

An analysis of various arithmetic averaging procedures for approximate Riemann solvers is made with a specific emphasis on efficiency and a jump capturing property. The various alternatives discussed are intended for future work, as well as the more immediate problem of steady, supercritical free-surface flows. Numerical results are shown for two test problems.

Chaos of Wolbachia Sequences Inside the Compact Fig Syconia of Ficus benjamina (Ficus: Moraceae)

Figs and fig wasps form a peculiar closed community in which the Ficus tree provides a compact syconium (inflorescence) habitat for the lives of a complex assemblage of Chalcidoid insects. These diverse fig wasp species have intimate ecological relationships within the closed world of the fig syconia. Previous surveys of Wolbachia, maternally inherited endosymbiotic bacteria that infect vast numbers of arthropod hosts, showed that fig wasps have some of the highest known incidences of Wolbachia amongst all insects. We ask whether the evolutionary patterns of Wolbachia sequences in this closed syconium community are different from those in the outside world. In the present study, we sampled all 17 fig wasp species living on Ficus benjamina, covering 4 families, 6 subfamilies, and 8 genera of wasps. We made a thorough survey of Wolbachia infection patterns and studied evolutionary patterns in wsp (Wolbachia Surface Protein) sequences. We find evidence for high infection incidences, frequent recombination between Wolbachia strains, and considerable horizontal transfer, suggesting rapid evolution of Wolbachia sequences within the syconium community. Though the fig wasps have relatively limited contact with outside world, Wolbachia may be introduced to the syconium community via horizontal transmission by fig wasps species that have winged males and visit the syconia earlier.

On the parameterization of turbulent surface fluxes over heterogeneous sea ice surfaces

Turbulent surface fluxes of momentum and sensible and latent heat as well as surface temperature, air temperature, air humidity, and wind speed were measured by the German Falcon research aircraft over the marginal ice zone (MIZ) of the northern Baltic Sea and the Fram Strait. Applying the bulk formulas and the stability functions to the measurements, the roughness lengths for momentum z0, sensible heat zT, and latent heat zq were calculated. As mean values over a wide range of sea ice conditions, we obtain z0 = 5 � 10�4 m, zT = 1 � 10�8 m, and zq = 1 � 10�7 m. These correspond to the following mean values (± standard deviations) of neutral transfer coefficients reduced to 10 m height, CDN10 = (1.9 ± 0.8) � 10�3, CHN10 = (0.9 ± 0.3) � 10�3, and CEN10 = (1.0 ± 0.2) � 10�3. An average ratio of z0/zT � 104 was observed over the range of 10�6 m < z0 < 10�2 m and differs from previously published results over compact sea ice (10�1 < z0/zT < 103). Other observational results over heterogeneous sea ice do not exist. However, our z0/zT ratio approximately agrees with observations over heterogeneous land surfaces. Flux parameterizations based on commonly used roughness lengths ratios (z0 = zT = zq) overestimate the surface heat fluxes compared to our measurements by more than 100%.