On the fourth-order accurate compact ADI scheme for solving the unsteady Nonlinear Coupled Burgers' Equations

The two-dimensional unsteady coupled Burgers' equations with moderate to severe gradients, are solved numerically using higher-order accurate finite difference schemes; namely the fourth-order accurate compact ADI scheme, and the fourth-order accurate Du Fort Frankel scheme. The question of numerical stability and convergence are presented. Comparisons are made between the present schemes in terms of accuracy and computational efficiency for solving problems with severe internal and boundary gradients. The present study shows that the fourth-order compact ADI scheme is stable and efficient

Dynamical properties of the unitary Fermi gas: collective modes and shock waves

We discuss the unitary Fermi gas made of dilute and ultracold atoms with an infinite s-wave inter-atomic scattering length. First we introduce an efficient Thomas-Fermi-von Weizsacker density functional which describes accurately various static properties of the unitary Fermi gas trapped by an external potential. Then, the sound velocity and the collective frequencies of oscillations in a harmonic trap are derived from extended superfluid hydrodynamic equations which are the Euler-Lagrange equations of a Thomas-Fermi-von Weizsacker action functional. Finally, we show that this amazing Fermi gas supports supersonic and subsonic shock waves.Comment: 9 pages, 3 figures, invited talk at the International Workshop "Critical Stability 2011" (Erice, October 2011), to be published in the journal Few Body System

From genes to ecosystems: a synthesis of the effects of plant genetic factors across levels of organization

Using two genetic approaches and seven different plant systems, we present findings from a meta-analysis examining the strength of the effects of plant genetic introgression and genotypic diversity across individual, community and ecosystem levels with the goal of synthesizing the patterns to date. We found that (i) the strength of plant genetic effects can be quite high; however, the overall strength of genetic effects on most response variables declined as the levels of organization increased. (ii) Plant genetic effects varied such that introgression had a greater impact on individual phenotypes than extended effects on arthropods or microbes/fungi. By contrast, the greatest effects of genotypic diversity were on arthropods. (iii) Plant genetic effects were greater on above-ground versus below-ground processes, but there was no difference between terrestrial and aquatic environments. (iv) The strength of the effects of intraspecific genotypic diversity tended to be weaker than interspecific genetic introgression. (v) Although genetic effects generally decline across levels of organization, in some cases they do not, suggesting that specific organisms and/or processes may respond more than others to underlying genetic variation. Because patterns in the overall impacts of introgression and genotypic diversity were generally consistent across diverse study systems and consistent with theoretical expectations, these results provide generality for understanding the extended consequences of plant genetic variation across levels of organization, with evolutionary implications