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.     

A C^r trivariate macro-element based on the Worsey–Farin split of a tetrahedron

We construct trivariate $C^r$ macro-elements for any $r\ge 1$ over the Worsey–Farin refinement of any tetrahedral partition. This extends the construction of $C^1$ cubic Worsey–Farin elements and $C^2$ elements of degree nine to the $C^r$ situation with $r>2$ . We also show that the degree of polynomials used for our macro-elements is the lowest.     

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.

     

Derivations and spectral triples on quantum domains II: Quantum annulus

Science China Mathematics - Continuing our study of spectral triples on quantum domains, we look at unbounded invariant and covariant derivations in the quantum annulus. In particular, we...     

Synthesis,physicochemical characterization,and self‐assembly of linear,dibranched, and miktoarm semifluorinated triphilic polymers

Linear, dibranched, and miktoarm amphiphiles containing both hydrophobic and fluorophilic moieties were synthesized and characterized in an attempt to elucidate the relationship between semifluorinated amphiphile structure and aggregate behavior in aqueous solution. For the linear and dibranched amphiphiles, there was an exponential decrease in critical aggregation concentration (CMC) and a logarithmic increase in core microviscosity with increasing length of the fluorocarbon segments; while the miktoarm architecture produced no notable trend in microviscosity or CMC. Furthermore, the linear and dibranched surfactants showed enhanced kinetic stability, dissociating more slowly in the presence of human serum than did either the dibranched or miktoarm amphiphiles. Finally, encapsulation studies with the hydrophobic drug paclitaxel (PTX) showed that the ability to solubilize and retain PTX increased with the presence and with the increasing size of the fluorocarbon moiety for both the linear and dibranched amphiphiles, while no such trend was observed for the miktoarm amphiphiles. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 3324–3336     

Further studies on the application of vinylogous amides and β-halovinylaldehydes to the regiospecific synthesis of unsymmetrical,polyfunctionalized 2,3,4- and 1,2,3,4- substituted pyrroles

Highly functionalized pyrroles with appropriate regiochemical functionality represent an important class of marine natural products and potential drug candidates. We describe herein a detailed study of the reaction of α-aminoacid esters with vinylogous amides and also β-halovinylaldehydes for the regiospecific synthesis of 2,3,4-trisubstituted and 1,2,3,4-tetrasubstituted pyrroles. Since the vinylogous amides and β-halovinylaldehydes are readily available precursors, rapid access to a wide variety of unsymmetrically substituted pyrroles is accomplished via this methodology.