Affine T-varieties of complexity one and locally nilpotent derivations

Let X=spec A be a normal affine variety over an algebraically closed field k of characteristic 0 endowed with an effective action of a torus T of dimension n. Let also D be a homogeneous locally nilpotent derivation on the normal affine Z^n-graded domain A, so that D generates a k_+-action on X that is normalized by the T-action. We provide a complete classification of pairs (X,D) in two cases: for toric varieties (n=\dim X) and in the case where n=\dim X-1. This generalizes previously known results for surfaces due to Flenner and Zaidenberg. As an application we compute the homogeneous Makar-Limanov invariant of such varieties. In particular we exhibit a family of non-rational varieties with trivial Makar-Limanov invariant.Comment: 31 pages. Minor changes in the structure. Fixed some typo

On Proper Polynomial Maps of C2.\mathbb{C}^2.

Two proper polynomial maps $f_1, f_2 \colon \mathbb{C}^2 \longrightarrow \mathbb{C}^2$ are said to be \emph{equivalent} if there exist $\Phi_1, \Phi_2 \in \textrm{Aut}(\mathbb{C}^2)$ such that $f_2=\Phi_2 \circ f_1 \circ \Phi_1$. We investigate proper polynomial maps of arbitrary topological degree $d \geq 2$ up to equivalence. Under the further assumption that the maps are Galois coverings we also provide the complete description of equivalence classes. This widely extends previous results obtained by Lamy in the case $d=2$.Comment: 15 pages. Final version, to appear in Journal of Geometric Analysi

Structure Factor and Electronic Structure of Compressed Liquid Rubidium

We have applied the quantal hypernetted-chain equations in combination with the Rosenfeld bridge-functional to calculate the atomic and the electronic structure of compressed liquid-rubidium under high pressure (0.2, 2.5, 3.9, and 6.1 GPa); the calculated structure factors are in good agreement with experimental results measured by Tsuji et al. along the melting curve. We found that the Rb-pseudoatom remains under these high pressures almost unchanged with respect to the pseudoatom at room pressure; thus, the effective ion-ion interaction is practically the same for all pressure-values. We observe that all structure factors calculated for this pressure-variation coincide almost into a single curve if wavenumbers are scaled in units of the Wigner-Seitz radius $a$ although no corresponding scaling feature is observed in the effective ion-ion interaction.This scaling property of the structure factors signifies that the compression in liquid-rubidium is uniform with increasing pressure; in absolute Q-values this means that the first peak-position ($Q_1$) of the structure factor increases proportionally to $V^{-1/3}$ ($V$ being the specific volume per ion), as was experimentally observed by Tsuji et al.Comment: 18 pages, 11 figure

Evidence of two viscous relaxation processes in the collective dynamics of liquid lithium

New inelastic X-ray scattering experiments have been performed on liquid lithium in a wide wavevector range. With respect to the previous measurements, the instrumental resolution, improved up to 1.5 meV, allows to accurately investigate the dynamical processes determining the observed shape of the the dynamic structure factor, $S(Q,\omega)$. A detailed analysis of the lineshapes shows the co-existence of relaxation processes with both a slow and a fast characteristic timescales, and therefore that pictures of the relaxation mechanisms based on a simple viscoelastic model must be abandoned.Comment: 5 pages, 4 .PS figure

Evidence of short time dynamical correlations in simple liquids

We report a molecular dynamics (MD) study of the collective dynamics of a simple monatomic liquid -interacting through a two body potential that mimics that of lithium- across the liquid-glass transition. In the glassy phase we find evidences of a fast relaxation process similar to that recently found in Lennard-Jones glasses. The origin of this process is ascribed to the topological disorder, i.e. to the dephasing of the different momentum $Q$ Fourier components of the actual normal modes of vibration of the disordered structure. More important, we find that the fast relaxation persists in the liquid phase with almost no temperature dependence of its characteristic parameters (strength and relaxation time). We conclude, therefore, that in the liquid phase well above the melting point, at variance with the usual assumption of {\it un-correlated} binary collisions, the short time particles motion is strongly {\it correlated} and can be described via a normal mode expansion of the atomic dynamics.Comment: 7 pages, 7 .eps figs. To appear in Phys. Rev.

Geography-dependent horizontal gene transfer from vertebrate predators to their prey

Horizontal transfer (HT) of genes between multicellular animals, once thought to be extremely rare, is being more commonly detected, but its global geographic trend and transfer mechanism have not been investigated. We discovered a unique HT pattern of Bovine-B (BovB) LINE retrotransposons in vertebrates, with a bizarre transfer direction from predators (snakes) to their prey (frogs). At least 54 instances of BovB HT were detected, which we estimate to have occurred across time between 85 and 1.3 Ma. Using comprehensive transcontinental sampling, our study demonstrates that BovB HT is highly prevalent in one geographical region, Madagascar, suggesting important regional differences in the occurrence of HTs. We discovered parasite vectors that may plausibly transmit BovB and found that the proportion of BovB-positive parasites is also high in Madagascar where BovB thus might be physically transported by parasites to diverse vertebrates, potentially including humans. Remarkably, in two frog lineages, BovB HT occurred after migration from a non-HT area (Africa) to the HT hotspot (Madagascar). These results provide a novel perspective on how the prevalence of parasites influences the occurrence of HT in a region, similar to pathogens and their vectors in some endemic diseases

Nucleus-Electron Model for States Changing from a Liquid Metal to a Plasma and the Saha Equation

We extend the quantal hypernetted-chain (QHNC) method, which has been proved to yield accurate results for liquid metals, to treat a partially ionized plasma. In a plasma, the electrons change from a quantum to a classical fluid gradually with increasing temperature; the QHNC method applied to the electron gas is in fact able to provide the electron-electron correlation at arbitrary temperature. As an illustrating example of this approach, we investigate how liquid rubidium becomes a plasma by increasing the temperature from 0 to 30 eV at a fixed normal ion-density $1.03 \times 10^{22}/cm^3$. The electron-ion radial distribution function (RDF) in liquid Rb has distinct inner-core and outer-core parts. Even at a temperature of 1 eV, this clear distinction remains as a characteristic of a liquid metal. At a temperature of 3 eV, this distinction disappears, and rubidium becomes a plasma with the ionization 1.21. The temperature variations of bound levels in each ion and the average ionization are calculated in Rb plasmas at the same time. Using the density-functional theory, we also derive the Saha equation applicable even to a high-density plasma at low temperatures. The QHNC method provides a procedure to solve this Saha equation with ease by using a recursive formula; the charge population of differently ionized species are obtained in Rb plasmas at several temperatures. In this way, it is shown that, with the atomic number as the only input, the QHNC method produces the average ionization, the electron-ion and ion-ion RDF's, and the charge population which are consistent with the atomic structure of each ion for a partially ionized plasma.Comment: 28 pages(TeX) and 11 figures (PS

Inelastic X-ray scattering study of the collective dynamics in liquid sodium

Inelastic X-ray scattering data have been collected for liquid sodium at T=390 K, i.e. slightly above the melting point. Owing to the very high instrumental resolution, pushed up to 1.5 meV, it has been possible to determine accurately the dynamic structure factor, $S(Q,\omega)$, in a wide wavevector range, $1.5 \div 15$ nm$^{-1}$, and to investigate on the dynamical processes underlying the collective dynamics. A detailed analysis of the lineshape of $S(Q,\omega)$, similarly to other liquid metals, reveals the co-existence of two different relaxation processes with slow and fast characteristic timescales respectively. The present data lead to the conclusion that: i) the picture of the relaxation mechanism based on a simple viscoelastic model fails; ii) although the comparison with other liquid metals reveals similar behavior, the data do not exhibit an exact scaling law as the principle of corresponding state would predict.Comment: RevTex, 7 pages, 6 eps figures. Accepted by Phys. Rev.

Dynamical properties of liquid Al near melting. An orbital-free molecular dynamics study

The static and dynamic structure of liquid Al is studied using the orbital free ab-initio molecular dynamics method. Two thermodynamic states along the coexistence line are considered, namely T = 943 K and 1323 K for which X-ray and neutron scattering data are available. A new kinetic energy functional, which fulfills a number of physically relevant conditions is employed, along with a local first principles pseudopotential. In addition to a comparison with experiment, we also compare our ab-initio results with those obtained from conventional molecular dynamics simulations using effective interionic pair potentials derived from second order pseudopotential perturbation theory.Comment: 15 pages, 12 figures, 2 tables, submitted to PR