Numerical study of the small scale structures in Boussinesq convection

Two-dimensional Boussinesq convection is studied numerically using two different methods: a filtered pseudospectral method and a high order accurate Essentially Nonoscillatory (ENO) scheme. The issue whether finite time singularity occurs for initially smooth flows is investigated. The numerical results suggest that the collapse of the bubble cap is unlikely to occur in resolved calculations. The strain rate corresponding to the intensification of the density gradient across the front saturates at the bubble cap. We also found that the cascade of energy to small scales is dominated by the formulation of thin and sharp fronts across which density jumps

A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow

High order essentially non-oscillatory (ENO) schemes, originally designed for compressible flow and in general for hyperbolic conservation laws, are applied to incompressible Euler and Navier-Stokes equations with periodic boundary conditions. The projection to divergence-free velocity fields is achieved by fourth order central differences through Fast Fourier Transforms (FFT) and a mild high-order filtering. The objective of this work is to assess the resolution of ENO schemes for large scale features of the flow when a coarse grid is used and small scale features of the flow, such as shears and roll-ups, are not fully resolved. It is found that high-order ENO schemes remain stable under such situations and quantities related to large-scale features, such as the total circulation around the roll-up region, are adequately resolved

Effective equations and the inverse cascade theory for Kolmogorov flows

We study the two dimensional Kolmogorov flows in the limit as the forcing frequency goes to infinity. Direct numerical simulation indicates that the low frequency energy spectrum evolves to a universal kappa (exp -4) decay law. We derive effective equations governing the behavior of the large scale flow quantities. We then present numerical evidence that with smooth initial data, the solution to the effective equation develops a kappa (exp -4) type singularity at a finite time. This gives a convenient explanation for the kappa (exp -4) decay law exhibited by the original Kolmogorov flows

Life Tables of Bactrocera cucurbitae (Coquillett) (Diptera: Tephritidae): with a Mathematical Invalidation for Applying the Jackknife Technique to the Net Reproductive Rate

Life table data for the melon fly, Bactrocera cucurbitae (Coquillett), reared on cucumber (Cucumis sativus L.) were collected under laboratory and simulated field conditions. Means and standard errors of life table parameters were estimated for two replicates using the jackknife technique. At 25ºC, the intrinsic rates of increase (_r_) found for the two replicates were 0.1354 and 0.1002 day-1, and the net reproductive rates (_R_~0~) were 206.3 and 66.0 offspring, respectively. When the cucumbers kept under simulated field conditions were covered with leaves, the _r_ and _R_~0~ for the two replicates were 0.0935 and 0.0909 day-1, 17.5 and 11.4 offspring, respectively. However, when similar cucumbers were left uncovered, the _r_ and _R_~0~ for the two replicates were 0.1043 and 0.0904 day-1, and 27.7 and 10.1 offspring, respectively. Our results revealed that considerable variability between replicates in both laboratory and field conditions is possible; this variability should be taken into consideration in data collection and application of life tables. Mathematical analysis has demonstrated that applying the jackknife technique results in unrealistic pseudo-_R_~0~ and overestimation of its variance. We suggest that the jackknife technique should not be used for the estimation of variability of _R_~0~

Spectrum of the Dirac Hamiltonian with the mass-hedgehog in arbitrary dimension

It is shown that the square of the Dirac Hamiltonian with the isotropic mass-hedgehog potential in d dimensions is the number operator of fictitious bosons and fermions over d quantum states. This result allows one to obtain the complete spectrum and degeneracies of the Dirac Hamiltonian with the hedgehog mass configuration in any dimension. The result pertains to low-energy states in the core of a general superconducting or insulating vortex in graphene in two dimensions, and in the superconducting vortex at the topological - trivial insulator interface in three dimensions, for example. The spectrum in d=2 is also understood in terms of the underlying accidental SU(2) symmetry and the supersymmetry of the Hamiltonian.Comment: 6 pages: typos corrected, new section on accidental supersymmetry, added references, many comments, and a figure. Published versio