On the energy deposited by a quark moving in an N=4 SYM plasma

We evaluate the energy momentum tensor of a massive quark as it moves through an N=4 SYM quark gluon plasma at constant velocity. We find that in the near-quark region, where the dynamics is expected to be dominated by dissipative behavior, the energy density may be quantitatively characterized by a transient at velocities above the speed of sound of the plasma.Comment: 19 pages, 1 figure; Typos corrected, references adde

Principal bundle structure of matrix manifolds

In this paper, we introduce a new geometric description of the manifolds of matrices of fixed rank. The starting point is a geometric description of the Grassmann manifold $\mathbb{G}_r(\mathbb{R}^k)$ of linear subspaces of dimension $r<k$ in $\mathbb{R}^k$ which avoids the use of equivalence classes. The set $\mathbb{G}_r(\mathbb{R}^k)$ is equipped with an atlas which provides it with the structure of an analytic manifold modelled on $\mathbb{R}^{(k-r)\times r}$. Then we define an atlas for the set $\mathcal{M}_r(\mathbb{R}^{k \times r})$ of full rank matrices and prove that the resulting manifold is an analytic principal bundle with base $\mathbb{G}_r(\mathbb{R}^k)$ and typical fibre $\mathrm{GL}_r$, the general linear group of invertible matrices in $\mathbb{R}^{k\times k}$. Finally, we define an atlas for the set $\mathcal{M}_r(\mathbb{R}^{n \times m})$ of non-full rank matrices and prove that the resulting manifold is an analytic principal bundle with base $\mathbb{G}_r(\mathbb{R}^n) \times \mathbb{G}_r(\mathbb{R}^m)$ and typical fibre $\mathrm{GL}_r$. The atlas of $\mathcal{M}_r(\mathbb{R}^{n \times m})$ is indexed on the manifold itself, which allows a natural definition of a neighbourhood for a given matrix, this neighbourhood being proved to possess the structure of a Lie group. Moreover, the set $\mathcal{M}_r(\mathbb{R}^{n \times m})$ equipped with the topology induced by the atlas is proven to be an embedded submanifold of the matrix space $\mathbb{R}^{n \times m}$ equipped with the subspace topology. The proposed geometric description then results in a description of the matrix space $\mathbb{R}^{n \times m}$, seen as the union of manifolds $\mathcal{M}_r(\mathbb{R}^{n \times m})$, as an analytic manifold equipped with a topology for which the matrix rank is a continuous map

The European Commission’s decision on Visa’s interchange fees

Debit cards ; Credit cards

Age, growth, and spawning season of red bream (Beryx decadactylus) off the southeastern United States

Red bream (Beryx decadactylus) is a commercially important deep-sea benthopelagic fish with a circumglobal distribution on insular and continental slopes and seamounts. In the United States, small numbers are caught incidentally in the wreckfish (Polyprion americanus) fishery which operates off the southeastern coast, but no biological information exists for the management of the U.S. red bream population. For this study, otoliths (n=163) and gonads (n=161) were collected from commercially caught red bream between 2003 and 2008 to determine life history parameters. Specimens ranged in size from 410 to 630 mm fork length and were all determined to be mature by histological examination of the gonads. Females in spawning condition were observed from June through September, and reproductively active males were found year-round. Sectioned otoliths were difficult to interpret, but maximum age estimates were much higher than the 15 years previously reported for this species from the eastern North Atlantic based on whole-otolith analysis. Estimated ages ranged from 8 to 69 years, and a minimum lifespan of 49 years was validated by using bomb radiocarbon dating. Natural mortality was estimated at 0.06/yr. This study shows that red bream are longer lived and more vulnerable to overfishing than previously assumed and should be managed carefully to prevent overexploitation

Tropical wetlands and REDD+: Three unique scientific challenges for policy

The carbon sequestration and storage value of terrestrial habitats is now increasingly appreciated, and is the basis for Payment for Ecosystem Service (PES) policies such as REDD+. Tropical wetlands may be suitable for inclusion in such schemes because of the disproportionately large volume of carbon they are able to store. However, tropical wetlands offer a number of unique challenges for carbon management and policy compared to terrestrial forest systems: 1) Tropical wetlands are dynamic and subject to a wide range of physical and ecological processes that affect their long-term carbon storage potential – thus, such systems can quickly become a carbon source instead of a sink; 2) Carbon dynamics in tropical wetlands often operate over longer time-scales than are currently covered by REDD+ payments; and 3) Much of the carbon in a tropical wetland is stored in the soil, so monitoring, reporting and verification (MRV) needs to adequately encapsulate the entire ecosystem and not just the vegetative component. This paper discusses these physical and biological concepts, and highlights key legal, management and policy questions that must be considered when constructing a policy framework to conserve these crucial ecosystems