Thermodynamic stabilities of ternary metal borides: An ab initio guide for synthesizing layered superconductors

Density functional theory calculations have been used to identify stable layered Li-$M$-B crystal structure phases derived from a recently proposed binary metal-sandwich (MS) lithium monoboride superconductor. We show that the MS lithium monoboride gains in stability when alloyed with electron-rich metal diborides; the resulting ordered Li$_{2(1-x)}M_x$B$_2$ ternary phases may form under normal synthesis conditions in a wide concentration range of $x$ for a number of group-III-V metals $M$. In an effort to pre-select compounds with the strongest electron-phonon coupling we examine the softening of the in-plane boron phonon mode at $\Gamma$ in a large class of metal borides. Our results reveal interesting general trends for the frequency of the in-plane boron phonon modes as a function of the boron-boron bond length and the valence of the metal. One of the candidates with a promise to be an MgB$_2$-type superconductor, Li$_2$AlB$_4$, has been examined in more detail: according to our {\it ab initio} calculations of the phonon dispersion and the electron-phonon coupling $\lambda$, the compound should have a critical temperature of $\sim4$ K.Comment: 10 pages, 9 figures, submitted to PR

The debris disk - terrestrial planet connection

The eccentric orbits of the known extrasolar giant planets provide evidence that most planet-forming environments undergo violent dynamical instabilities. Here, we numerically simulate the impact of giant planet instabilities on planetary systems as a whole. We find that populations of inner rocky and outer icy bodies are both shaped by the giant planet dynamics and are naturally correlated. Strong instabilities -- those with very eccentric surviving giant planets -- completely clear out their inner and outer regions. In contrast, systems with stable or low-mass giant planets form terrestrial planets in their inner regions and outer icy bodies produce dust that is observable as debris disks at mid-infrared wavelengths. Fifteen to twenty percent of old stars are observed to have bright debris disks (at wavelengths of ~70 microns) and we predict that these signpost dynamically calm environments that should contain terrestrial planets.Comment: Contribution to proceedings of IAU 276: Astrophysics of Planetary System

Theoretical study of metal borides stability

We have recently identified metal-sandwich (MS) crystal structures and shown with ab initio calculations that the MS lithium monoboride phases are favored over the known stoichiometric ones under hydrostatic pressure [Phys. Rev. B 73, 180501(R) (2006)]. According to previous studies synthesized lithium monoboride tends to be boron-deficient, however the mechanism leading to this phenomenon is not fully understood. We propose a simple model that explains the experimentally observed off-stoichiometry and show that compared to such boron-deficient phases the MS-LiB compounds still have lower formation enthalpy under high pressures. We also investigate stability of MS phases for a large class of metal borides. Our ab initio results suggest that MS noble metal borides are less unstable than the corresponding AlB$_2$-type phases but not stable enough to form under equilibrium conditions.Comment: 14 pages, 15 figure

Spectra of Discrete Schr\"odinger Operators with Primitive Invertible Substitution Potentials

We study the spectral properties of discrete Schr\"odinger operators with potentials given by primitive invertible substitution sequences (or by Sturmian sequences whose rotation angle has an eventually periodic continued fraction expansion, a strictly larger class than primitive invertible substitution sequences). It is known that operators from this family have spectra which are Cantor sets of zero Lebesgue measure. We show that the Hausdorff dimension of this set tends to $1$ as coupling constant $\lambda$ tends to $0$. Moreover, we also show that at small coupling constant, all gaps allowed by the gap labeling theorem are open and furthermore open linearly with respect to $\lambda$. Additionally, we show that, in the small coupling regime, the density of states measure for an operator in this family is exact dimensional. The dimension of the density of states measure is strictly smaller than the Hausdorff dimension of the spectrum and tends to $1$ as $\lambda$ tends to $0$

Symbolic approach and induction in the Heisenberg group

We associate a homomorphism in the Heisenberg group to each hyperbolic unimodular automorphism of the free group on two generators. We show that the first return-time of some flows in "good" sections, are conjugate to niltranslations, which have the property of being self-induced.Comment: 18 page

Super-Earths: A New Class of Planetary Bodies

Super-Earths, a class of planetary bodies with masses ranging from a few Earth-masses to slightly smaller than Uranus, have recently found a special place in the exoplanetary science. Being slightly larger than a typical terrestrial planet, super-Earths may have physical and dynamical characteristics similar to those of Earth whereas unlike terrestrial planets, they are relatively easier to detect. Because of their sizes, super-Earths can maintain moderate atmospheres and possibly dynamic interiors with plate tectonics. They also seem to be more common around low-mass stars where the habitable zone is in closer distances. This article presents a review of the current state of research on super-Earths, and discusses the models of the formation, dynamical evolution, and possible habitability of these objects. Given the recent advances in detection techniques, the detectability of super-Earths is also discussed, and a review of the prospects of their detection in the habitable zones of low-mass stars is presented.Comment: A (non-technical) review of the literature on the current state ofresearch on super-Earths. The topics include observation, formation, dynamical evolution, habitability, composition, interior dynamics, magnetic field, atmosphere, and propsect of detection. The article has 44 pages, 27 figures, and 203 references. It has been accepted for publication in the journal Contemporary Physics (2011

The Impact of Water on Ru-Catalyzed Olefin Metathesis: Potent Deactivating Effects Even at Low Water Concentrations

Ruthenium catalysts for olefin metathesis are widely viewed as water-tolerant. Evidence is presented, however, that even low concentrations of water cause catalyst decomposition, severely degrading yields. Of 11 catalysts studied, fast-initiating examples (e.g., the Grela catalyst RuCl2(H2IMes)(═CHC6H4-2-OiPr-5-NO2) were most affected. Maximum water tolerance was exhibited by slowly initiating iodide and cyclic (alkyl)(amino)carbene (CAAC) derivatives. Computational investigations indicated that hydrogen bonding of water to substrate can also play a role, by retarding cyclization relative to decomposition. These results have important implications for olefin metathesis in organic media, where water is a ubiquitous contaminant, and for aqueous metathesis, which currently requires superstoichiometric “catalyst” for demanding reactions.publishedVersio

Geometric representation of interval exchange maps over algebraic number fields

We consider the restriction of interval exchange transformations to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and study its relationships with a geometrical quantity that we call the drift vector. We exhibit some examples of renormalizable interval exchange maps with zero and non-zero drift vector, and carry out some investigations of their properties. In particular, we look for evidence of the finite decomposition property: each lattice is the union of finitely many orbits.Comment: 34 pages, 8 postscript figure