Conservative Space and Time Regularizations for the ICON Model

In this article, we consider two modified (regularized) versions of the shallow water equations which are of potential interest for the construction of global oceanic and atmospheric models. The first modified system is the Lagrangian averaged shallow water system, which involves the use of a regularized advection velocity and which has been recently proposed as a turbulence parametrization for ocean models in order to avoid an excessive damping of the computed solution. The second modified system is the pressure regularized shallow water system, which provides an alternative to traditional semi-implicit time integration schemes and which results in larger freedom in the design of the time integrator and in a better treatment of nearly geostrophic flows. The two modified systems are both nondissipative, in that they do not result in an increase of the overall dissipation of the flow. We first show how the numerical discretization of the two regularized equation sets can be constructed in a natural way within the finite difference formulation adopted for the ICON general circulation model currently under developed at the Max Planck Institute for Meteorology and at the German Weather Service. The resulting scheme is then validated on a set of idealized tests in both planar and spherical geometry, and the effects of the considered regularizations on the computed solution are analyzed concerning: stability properties and maximum allowable time steps, similarities and differences in the behavior of the solutions, discrete conservation of flow invariants such as total energy and enstrophy. Our analysis should be considered as a first step toward the use of the regularization ideas in the simulation of more complex and more realistic flows

Lieb-Thirring inequalities for geometrically induced bound states

We prove new inequalities of the Lieb-Thirring type on the eigenvalues of Schr\"odinger operators in wave guides with local perturbations. The estimates are optimal in the weak-coupling case. To illustrate their applications, we consider, in particular, a straight strip and a straight circular tube with either mixed boundary conditions or boundary deformations.Comment: LaTeX2e, 14 page

Temporal profiling of the heat-stable proteome during late maturation of Medicago truncatula seeds identifies a restricted subset of late embryogenesis abundant proteins associated with longevity

Developing seeds accumulate late embryogenesis abundant (LEA) proteins, a family of intrinsically disordered and hydrophilic proteins that confer cellular protection upon stress. Many different LEA proteins exist in seeds, but their relative contribution to seed desiccation tolerance or longevity (duration of survival) is not yet investigated. To address this, a reference map of LEA proteins was established by proteomics on a hydrophilic protein fraction from mature Medicago truncatula seeds and identified 35 polypeptides encoded by 16 LEA genes. Spatial and temporal expression profiles of the LEA polypeptides were obtained during the long maturation phase during which desiccation tolerance and longevity are sequentially acquired until pod abscission and final maturation drying occurs. Five LEA polypeptides, representing 6% of the total LEA intensity, accumulated upon acquisition of desiccation tolerance. The gradual 30-fold increase in longevity correlated with the accumulation of four LEA polypeptides, representing 35% of LEA in mature seeds, and with two chaperone-related polypeptides. The majority of LEA polypeptides increased around pod abscission during final maturation drying. The differential accumulation profiles of the LEA polypeptides suggest different roles in seed physiology, with a small subset of LEA and other proteins with chaperone-like functions correlating with desiccation tolerance and longevity

Inferring statistics of planet populations by means of automated microlensing searches

(abridged) The study of other worlds is key to understanding our own, and not only provides clues to the origin of our civilization, but also looks into its future. Rather than in identifying nearby systems and learning about their individual properties, the main value of the technique of gravitational microlensing is in obtaining the statistics of planetary populations within the Milky Way and beyond. Only the complementarity of different techniques currently employed promises to yield a complete picture of planet formation that has sufficient predictive power to let us understand how habitable worlds like ours evolve, and how abundant such systems are in the Universe. A cooperative three-step strategy of survey, follow-up, and anomaly monitoring of microlensing targets, realized by means of an automated expert system and a network of ground-based telescopes is ready right now to be used to obtain a first census of cool planets with masses reaching even below that of Earth orbiting K and M dwarfs in two distinct stellar populations, namely the Galactic bulge and disk. The hunt for extra-solar planets acts as a principal science driver for time-domain astronomy with robotic-telescope networks adopting fully-automated strategies. Several initiatives, both into facilities as well as into advanced software and strategies, are supposed to see the capabilities of gravitational microlensing programmes step-wise increasing over the next 10 years. New opportunities will show up with high-precision astrometry becoming available and studying the abundance of planets around stars in neighbouring galaxies becoming possible. Finally, we should not miss out on sharing the vision with the general public, and make its realization to profit not only the scientists but all the wider society.Comment: 10 pages in PDF format. White paper submitted to ESA's Exo-Planet Roadmap Advisory Team (EPR-AT); typos corrected. The embedded figures are available from the author on request. See also "Towards A Census of Earth-mass Exo-planets with Gravitational Microlensing" by J.P. Beaulieu, E. Kerins, S. Mao et al. (arXiv:0808.0005

Upper and lower limits on the number of bound states in a central potential

In a recent paper new upper and lower limits were given, in the context of the Schr\"{o}dinger or Klein-Gordon equations, for the number $N_{0}$ of S-wave bound states possessed by a monotonically nondecreasing central potential vanishing at infinity. In this paper these results are extended to the number $N_{\ell}$ of bound states for the $\ell$-th partial wave, and results are also obtained for potentials that are not monotonic and even somewhere positive. New results are also obtained for the case treated previously, including the remarkably neat \textit{lower} limit $N_{\ell}\geq \{\{[\sigma /(2\ell+1)+1]/2\}\}$ with $V(r)| ^{1/2}]$ (valid in the Schr\"{o}dinger case, for a class of potentials that includes the monotonically nondecreasing ones), entailing the following \textit{lower} limit for the total number $N$ of bound states possessed by a monotonically nondecreasing central potential vanishing at infinity: N\geq \{\{(\sigma+1)/2\}\} {(\sigma+3)/2\} \}/2 (here the double braces denote of course the integer part).Comment: 44 pages, 5 figure

On non-local variational problems with lack of compactness related to non-linear optics

We give a simple proof of existence of solutions of the dispersion manage- ment and diffraction management equations for zero average dispersion, respectively diffraction. These solutions are found as maximizers of non-linear and non-local vari- ational problems which are invariant under a large non-compact group. Our proof of existence of maximizer is rather direct and avoids the use of Lions' concentration compactness argument or Ekeland's variational principle.Comment: 30 page