Mean Extinction Time in Predator-Prey Model

A basic predator-prey (Lotka-Volterra) system exhibits marginal stability on the deterministic level. Intrinsic demographic stochasticity destroys this stability and drives the system toward extinction of one or both species. We analytically calculate the mean extinction time of such a system and investigate its scaling with the system’s parameters. This mean extinction time, measured in number of population cycles, scales as the square root of the size of the smaller population and as the minus three halves power of the size of the larger population. The analytic results are fully confirmed by Monte-Carlo simulations.     

Iterated ultrapowers for the masses

We present a novel, perspicuous framework for building iterated ultrapowers. Furthermore, our framework naturally lends itself to the construction of a certain type of order indiscernibles, here dubbed tight indiscernibles, which are shown to provide smooth proofs of several results in general model theory.     

Naturalness in an emergent analogue spacetime

Effective field theories (EFTs) have been widely used as a framework in order to place constraints on the Planck suppressed Lorentz violations predicted by various models of quantum gravity. There are, however, technical problems in the EFT framework when it comes to ensuring that small Lorentz violations remain small--this is the essence of the "naturalness" problem. Herein we present an "emergent" spacetime model, based on the "analogue gravity" program, by investigating a specific condensed-matter system. Specifically, we consider the class of two-component BECs subject to laser-induced transitions between the components, and we show that this model is an example for Lorentz invariance violation due to ultraviolet physics. Furthermore, our model explicitly avoids the naturalness problem, and makes specific suggestions regarding how to construct a physically reasonable quantum gravity phenomenology.     

Raman spectroscopy of smithsonite

Raman spectroscopy at both 298 and 77 K has been used to study a series of selected natural smithsonites from different origins. An intense sharp band at 1092 cm⁻¹ is assigned to the CO₃²⁻ symmetric stretching vibration. Impurities of hydrozincite are identified by a band around 1060 cm⁻¹. An additional band at 1088 cm⁻¹ which is observed in the 298 K spectra but not in the 77 K spectra is attributed to a CO₃²⁻ hot band. Raman spectra of smithsonite show a single band in the 1405–1409 cm⁻¹ range assigned to the ν₃ (CO₃)²⁻ antisymmetric stretching mode. The observation of additional bands for the ν₃^g modes for some smithsonites is significant in that it shows distortion of the ZnO₆ octahedron. No ν₂ bending modes are observed for smithsonite. A single band at 730 cm⁻¹ is assigned to the ν₄ in phase bending mode. Multiple bands be attributed to the structural distortion are observed for the carbonate ν₄ in phase bending modes in the Raman spectrum of hydrozincite with bands at 733, 707 and 636 cm⁻¹. An intense band at 304 cm⁻¹ is attributed to the ZnO symmetric stretching vibration. Copyright © 2007 John Wiley & Sons, Ltd.     

Ring Opening Polymerization of Lactide under Solvent‐Free Conditions Catalyzed by a Chlorotitanium Calix[4]arene Complex

A novel chlorotitanium calix[4]arene complex was synthesized and tested, without activator, as catalyst for the polymerization of L ‐ and rac‐lactide under solvent‐free conditions. The catalyst displayed high activity, which depended on the monomer‐to‐catalyst molar ratio, and led to highly isotactic PLLA. Despite concomitant transesterification during the polymerization, polylactide formation was well‐controlled, the molar mass distribution indexes remaining in the restricted range of 1.2–1.4.

     

Dimers of boroglycine and methylamine boronic acid: a computational comparison of the relative importance of dative versus hydrogen bonding

Boronic acids are widely used in materials science, pharmacology, and the synthesis of biologically active compounds. In this Article, geometrical structures and relative energies of dimers of boroglycine, H2N-CH2-B(OH)2, and its constitutional isomer H3C-NH-B(OH)2, were computed using second-order M?ller-Plesset perturbation theory and density functional theory; Dunning-Woon correlation-consistent cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, and aug-cc-pVTZ basis sets were employed for the MP2 calculations, and the Pople 6-311++G(d,p) basis set was employed for a majority of the DFT calculations. Effects of an aqueous environment were incorporated into the results using PCM and COSMO-RS methodology. The lowest-energy conformer of the H2N-CH2-B(OH)2 dimer was a six-membered ring structure (chair conformation; Ci symmetry) with two intermolecular B:N dative-bonds; it was 14.0 kcal/mol lower in energy at the MP2/aug-cc-pVDZ computational level than a conformer with the classic eight-centered ring structure (Ci symmetry) in which the boroglycine monomers are linked by a pair of H-O...H bonds. Compared to the results of MP2 calculations with correlation-consistent basis sets, DFT calculations using the PBE1PBE and TPSS functionals with the 6-311++G(d,p) basis set were significantly better at predicting relative conformational energies of the H2N-CH2-B(OH)2 and H3C-NH-B(OH)2 dimers than corresponding calculations using the BLYP, B3LYP, OLYP, and O3LYP functionals, particularly with respect to dative-bonded structures.