Dynamics of Small-scale topographic heterogeneity in European sandy salt marshes

Heterogeneity can boost biodiversity, as well as increase the resilience of an ecosystem to changing environmental conditions; therefore, it is important to understand how topographic heterogeneity in ecosystems is formed. Sandy tidal marshes have a repetitive pattern of higher elevated hummocks surrounded by lower elevated depressions, representing topographic heterogeneity at the scale of a few square meters. The aims of this study were to determine when this topographic heterogeneity forms, how it is structured, and whether it persists during marsh development. The soil topography of marshes consists of coarse-grained sediment formed before marsh vegetation development, with an overlaying fine-grained sediment layer formed after initial marsh development. To gain insight into the formation of topographic heterogeneity, we studied the underlying soil topography of four European sandy marshes, where topographic heterogeneity at a scale of a few square meters was present. The differences in elevation between hummocks and depressions can either be caused by heterogeneity in the coarse-grained sediment or by heterogeneity in the top layer containing the fine-grained sediment. Our results showed that the largest percentage of elevational differences between hummocks and depressions could be attributed to heterogeneity in the underlying coarse-grained substratum. Therefore, we conclude that the patterns in all four marshes were primarily formed before marsh development, before fine-grained sediment was deposited on top of the coarse-grained sediment. However, a smaller percentage of the elevational difference between hummocks and depressions can also be explained by the presence of thicker fine-grained sediment layers on top of hummocks compared with depressions. This implies that marsh accretion rates were higher on hummocks compared with depressions. However, this result was limited to very early stages of marsh development, as marsh accretion rates estimated on marshes ranging between 15- and 120-years-old showed that depressions actually accreted sediments at a significantly faster rate than hummocks. Eventually, the patterns of heterogeneity stabilized and we found similar marsh accretion rates on hummocks and in depressions in the 120-year-old marsh, which resulted in the persistency of these topographic patterns

Classical transport equation in non-commutative QED at high temperature

We show that the high temperature behavior of non-commutative QED may be simply obtained from Boltzmann transport equations for classical particles. The transport equation for the charge neutral particle is shown to be characteristically different from that for the charged particle. These equations correctly generate, for arbitrary values of the non-commutative parameter theta, the leading, gauge independent hard thermal loops, arising from the fermion and the gauge sectors. We briefly discuss the generating functional of hard thermal amplitudes.Comment: 11 page

Hard-Loop Effective Action for Anisotropic Plasmas

We generalize the hard-thermal-loop effective action of the equilibrium quark-gluon plasma to a non-equilibrium system which is space-time homogeneous but for which the parton momentum distribution is anisotropic. We show that the manifestly gauge-invariant Braaten-Pisarski form of the effective action can be straightforwardly generalized and we verify that it then generates all n-point functions following from collisionless gauge-covariant transport theory for a homogeneous anisotropic plasma. On the other hand, the Taylor-Wong form of the hard-thermal-loop effective action has a more complicated generalization to the anisotropic case. Already in the simplest case of anisotropic distribution functions, it involves an additional term that is gauge invariant by itself, but nontrivial also in the static limit.Comment: 12 pages. Version 3: typo in (15) corrected, note added discussing metric conventions use

A remark on non-Abelian classical kinetic theory

It is known that non-Abelian classical kinetic theory reproduces the Hard Thermal/Dense Loop (HTL/HDL) effective action of QCD, obtained after integrating out the hardest momentum scales from the system, as well as the first higher dimensional operator beyond the HTL/HDL level. We discuss here its applicability at still higher orders, by comparing the exact classical effective action obtained in the static limit, with the 1-loop quantum effective potential. We remark that while correct types of operators arise, the classical colour algebra reproduces correctly the prefactor of the 4-point function $tr A_0^4$ only for matter in asymptotically high dimensional colour representations.Comment: 6 page

Transport equation for the photon Wigner operator in non-commutative QED

We derive an exact quantum equation of motion for the photon Wigner operator in non-commutative QED, which is gauge covariant. In the classical approximation, this reduces to a simple transport equation which describes the hard thermal effects in this theory. As an example of the effectiveness of this method we show that, to leading order, this equation generates in a direct way the Green amplitudes calculated perturbatively in quantum field theory at high temperature.Comment: 13 pages, twocolumn revtex4 styl