Remarks on the instability of black Dp-branes

We show that for black D$p$-branes having charge $Q$ and Hawking temperature $T$, the product $QT^{7-p}$ is bounded from above for $p\leq 5$ and is unbounded for $p=6$. While the maximum occurs at some finite value of a parameter for $p \leq 4$, it occurs at infinity of the parameter for $p=5$. As a consequence, for fixed charge, there are two black D$p$-branes (for $p\leq 4$) at any given temperature less than its maximum value, and when the temperature is maximum there is one black D$p$-brane. For $p=5$, there is only one black D5-brane at a given temperature less than its maximum value, whereas, for $p=6$, since there is no bound for the temperature, there is always a black D6-brane solution at a given temperature. Of the two black D$p$-branes (for $p\leq 4$), one is large which is shown to be thermodynamically unstable and the other is small which is stable. But for $p=5,6$, the black D$p$-branes are always thermodynamically unstable. The stable, small black D$p$-brane, however, under certain conditions, can become unstable quantum mechanically and decay either to a BPS D$p$-brane or to a Kaluza-Klein "bubble of nothing" through closed string tachyon condensation. The small D5, D6 branes, although classically unstable, have the same fate under similar conditions.Comment: 12 pages, LaTeX, 1 figure, v2: minor clarifications added, v3: added free energy calculation, version to appear in Phys. Lett.

Linking Aboveground Traits to Root Traits and Local Environment: Implications of the Plant Economics Spectrum.

The plant economics spectrum proposes that ecological traits are functionally coordinated and adapt along environmental gradients. However, empirical evidence is mixed about whether aboveground and root traits are consistently linked and which environmental factors drive functional responses. Here we measure the strength of relationships between aboveground and root traits, and examine whether community-weighted mean trait values are adapted along gradients of light and soil fertility, based on the seedling censuses of 57 species in a subtropical forest. We found that aboveground traits were good predictors of root traits; specific leaf area, dry matter, nitrogen and phosphorus content were strongly correlated with root tissue density and specific root length. Traits showed patterns of adaptation along the gradients of soil fertility and light; species with fast resource-acquisitive strategies were more strongly associated with high soil phosphorus, potassium, openness, and with low nitrogen, organic matter conditions. This demonstrates the potential to estimate belowground traits from known aboveground traits in seedling communities, and suggests that soil fertility is one of the main factors driving functional responses. Our results extend our understanding of how ecological strategies shape potential responses of plant communities to environmental change

Alkyl-Alkyl Suzuki Cross-Coupling of Unactivated Secondary Alkyl Chlorides

No such thing as a problem substrate! In a reaction designed specifically for the title substrates C-C coupling with alkyl boranes occurred in good yield at room temperature with commercially available catalyst components (see scheme). This versatile method is also suitable for Suzuki reactions of secondary and primary alkyl bromides and iodides, as well as primary alkyl chlorides.National Institute of General Medical Sciences (U.S.) (Grant R01-GM62871)Eli Lilly and Company (Fellowship)Martin Family Society of Fellows for Sustainability (Fellowship)Merck Research LaboratoriesNovartis (Firm