R-process and alpha-elements in the Galactic disk: Kinematic correlations

Recent studies of elemental abundances in the Galactic halo and in the Galactic disk have underscored the possibility to kinematically separate different Galactic subcomponents. Correlations between the galactocentric rotation velocity and various element ratios were found, providing an important means to link different tracers of star formation and metal enrichment to the Galactic components of different origin (collapse vs. accretion). In the present work we determine stellar kinematics for a sample of 124 disk stars, which we derive from their orbits based on radial velocities and proper motions from the the literature. Our stars form a subsample of the Edvardsson et al. (1993) sample and we concentrate on three main tracers: (i) Europium as an r-process element is predominantly produced in Supernovae of type II. (ii) Likewise, alpha-elements, such as Ca, Si, Mg, are synthesised in SNe II, contrary to iron, which is being produced preferentially in SNe Ia. (iii) The s-process element Barium is a measure of the relative contribution of AGB stars to the Galaxy's enrichment history and has been shown to be an indicator for distinguishing between thin and thick disk stars. All such studies reveal, basically, that stars with low galactocentric rotational velocity tend to have high abundances of alpha-elements and Eu, but lower abundances of, e.g., Ba.Comment: 5 pages, 2 figures, Poster contribution to appear in "Planets To Cosmology: Essential Science In Hubble's Final Years", proceedings of the May 2004 STScI Symposium, M. Livio (ed.), (Cambridge University Press

Theory of the Anderson impurity model: The Schrieffer--Wolff transformation re--examined

We apply the method of infinitesimal unitary transformations recently introduced by Wegner to the Anderson single impurity model. It is demonstrated that this method provides a good approximation scheme for all values of the on-site interaction $U$, it becomes exact for $U=0$. We are able to treat an arbitrary density of states, the only restriction being that the hybridization should not be the largest parameter in the system. Our approach constitutes a consistent framework to derive various results usually obtained by either perturbative renormalization in an expansion in the hybridization~$\Gamma$, Anderson's ``poor man's" scaling approach or the Schrieffer--Wolff unitary transformation. In contrast to the Schrieffer--Wolff result we find the correct high--energy cutoff and avoid singularities in the induced couplings. An important characteristic of our method as compared to the ``poor man's" scaling approach is that we continuously decouple modes from the impurity that have a large energy difference from the impurity orbital energies. In the usual scaling approach this criterion is provided by the energy difference from the Fermi surface.Comment: Uuencoded gzipped postscript, 26 pages, 5 postscript figure

Optimal Strong Rates of Convergence for a Space-Time Discretization of the Stochastic Allen-Cahn Equation with multiplicative noise

The stochastic Allen-Cahn equation with multiplicative noise involves the nonlinear drift operator ${\mathscr A}(x) = \Delta x - \bigl(\vert x\vert^2 -1\bigr)x$. We use the fact that ${\mathscr A}(x) = -{\mathcal J}^{\prime}(x)$ satisfies a weak monotonicity property to deduce uniform bounds in strong norms for solutions of the temporal, as well as of the spatio-temporal discretization of the problem. This weak monotonicity property then allows for the estimate $\underset{1 \leq j \leq J}\sup {\mathbb E}\bigl[ \Vert X_{t_j} - Y^j\Vert_{{\mathbb L}^2}^2\bigr] \leq C_{\delta}(k^{1-\delta} + h^2)$ for all small $\delta>0$, where $X$ is the strong variational solution of the stochastic Allen-Cahn equation, while $\big\{Y^j:0\le j\le J\big\}$ solves a structure preserving finite element based space-time discretization of the problem on a temporal mesh $\{ t_j;\, 1 \leq j \leq J\}$ of size $k>0$ which covers $[0,T]$

Dynamic features of successive upwelling events in the Baltic Sea - a numerical case study

Coastal upwelling often reveals itself during the thermal stratification season as an abrupt sea surface temperature (SST) drop. Its intensity depends not only on the magnitude of an upwelling-favourable wind impulse but also on the temperature stratification of the water column during the initial stage of the event. When a "chain" of upwelling events is taking place, one event may play a part in forming the initial stratification for the next one; consequently, SST may drop significantly even with a reduced wind impulse. Two upwelling events were simulated on the Polish coast in August 1996 using a three-dimensional, baroclinic prognostic model. The model results proved to be in good agreement with in situ observations and satellite data. Comparison of the simulated upwelling events show that the first one required a wind impulse of 28000 kg m-1 s-1 to reach its mature, full form, whereas an impulse of only 7500 kg m-1 s-1 was sufficient to bring about a significant drop in SST at the end of the second event. In practical applications like operational modelling, the initial stratification conditions prior to an upwelling event should be described with care in order to be able to simulate the coming event with very good accuracy

Transport across a carbon nanotube quantum dot contacted with ferromagnetic leads: experiment and non-perturbative modeling

We present measurements of tunneling magneto-resistance (TMR) in single-wall carbon nanotubes attached to ferromagnetic contacts in the Coulomb blockade regime. Strong variations of the TMR with gate voltage over a range of four conductance resonances, including a peculiar double-dip signature, are observed. The data is compared to calculations in the "dressed second order" (DSO) framework. In this non-perturbative theory, conductance peak positions and linewidths are affected by charge fluctuations incorporating the properties of the carbon nanotube quantum dot and the ferromagnetic leads. The theory is able to qualitatively reproduce the experimental data.Comment: 14 pages, 13 figure

Multiplicative combinatorial properties of return time sets in minimal dynamical systems

We investigate the relationship between the dynamical properties of minimal topological dynamical systems and the multiplicative combinatorial properties of return time sets arising from those systems. In particular, we prove that for a residual sets of points in any minimal system, the set of return times to any non-empty, open set contains arbitrarily long geometric progressions. Under the separate assumptions of total minimality and distality, we prove that return time sets have positive multiplicative upper Banach density along $\mathbb{N}$ and along multiplicative subsemigroups of $\mathbb{N}$, respectively. The primary motivation for this work is the long-standing open question of whether or not syndetic subsets of the positive integers contain arbitrarily long geometric progressions; our main result is some evidence for an affirmative answer to this question.Comment: 32 page