Clusterized nuclear matter in the (proto-)neutron star crust and the symmetry energy

Though generally agreed that the symmetry energy plays a dramatic role in determining the structure of neutron stars and the evolution of core-collapsing supernovae, little is known in what concerns its value away from normal nuclear matter density and, even more important, the correct definition of this quantity in the case of unhomogeneous matter. Indeed, nuclear matter traditionally addressed by mean-field models is uniform while clusters are known to exist in the dilute baryonic matter which constitutes the main component of compact objects outer shells. In the present work we investigate the meaning of symmetry energy in the case of clusterized systems and the sensitivity of the proto-neutron star composition and equation of state to the effective interaction. To this aim an improved Nuclear Statistical Equilibrium (NSE) model is developed, where the same effective interaction is consistently used to determine the clusters and unbound particles energy functionals in the self-consistent mean-field approximation. In the same framework, in-medium modifications to the cluster energies due to the presence of the nuclear gas are evaluated. We show that the excluded volume effect does not exhaust the in-medium effects and an extra isospin and density-dependent energy shift has to be considered to consistently determine the composition of subsaturation stellar matter. The symmetry energy of diluted matter is seen to depend on the isovector properties of the effective interaction, but its behavior with density and its quantitative value are strongly modified by clusterization.     

Comparison Between Methyl and Trimethylsilyl Ester Derivatives in the Separation and GC Quantification of Triterpene Acids in Eugenia brasiliensis Leaf Extract

This study details a method to characterize the triterpene acid-rich extract obtained from the defatted leaves of Eugenia brasiliensis (Myrtaceae) via extraction with 2 % NaOH in ethanol at room temperature. The crude extract (yield 2.35 %) was submitted to analysis by gas chromatography coupled to mass spectrometry (GC–MS) confirming ursolic acid as its major compound. The optimal conditions for the separation of oleanolic, betulinic and ursolic acids were assayed by GC with flame ionization detection (GC–FID) using two different columns (DB-5 and DB-17HT) and by applying two distinct derivatizing protocols. The use of a DB-17HT column led to the best results, with a shorter runtime and a better resolution (Rs) between the oleanolic and betulinic signals for both the bis-trimethylsilyl (Rs 2.84) and methyl ester derivatives (Rs 2.47). A DB-5 column also gave satisfactory results for the TMS ester, with a runtime of 30 min and Rs 2.14. Ursolic acid in the crude extract was quantified by comparison to two individual standard curves determined using commercial ursolic as its TMS derivative on the DB-5 column and its methyl ester on the DB-17HT column. Good linearity was achieved in both cases (r ² = 0.9776 and 0.9953, respectively), and the amounts of ursolic acid in the extracts were calculated to be 144.7 and 147.9 mg·g^?1, respectively. These results showed no significant differences when compared using Tukey’s HSD test. Total triterpene acids amounted to 0.52 % in E. brasiliensis dry leaves.     

Fixed Points of Set Functors: How Many Iterations are Needed?

The initial algebra for a set functor can be constructed iteratively via a well-known transfinite chain, which converges after a regular infinite cardinal number of steps or at most three steps. We extend this result to the analogous construction of relatively initial algebras. For the dual construction of the terminal coalgebra Worrell proved that if a set functor is α-accessible, then convergence takes at most α + α steps. But until now an example demonstrating that fewer steps may be insufficient was missing. We prove that the functor of all α-small filters is such an example. We further prove that for β ≤ α the functor of all α-small β-generated filters requires precisely α + β steps and that a certain modified power-set functor requires precisely α steps. We also present an example showing that whether a terminal coalgebra exists at all does not depend solely on the object mapping of the given set functor. (This contrasts with the fact that existence of an initial algebra is equivalent to existence of a mere fixed point.)     

Metal-free and PdII-promoted [2+3] cycloadditions of a cyclic nitrone to phthalonitriles: syntheses of oxadiazolines as well as phthalamide-PdII and dihydropyrrolyl-iminoisoindolinone-PdII complexes with high catalytic activity in Suzuki-Miyaura cross-coupling reactions

The previously unknown reactions between phthalonitriles, 1,2-(CN)2(C6)R1R2R3R4 1 (1 a, R1=R2=R3=R4=H; 1 b, R1=R2=R4=H, R3=CH3; 1 c, R1=R4=H, R2=R3=Cl; 1 d, R1=R2=R3=R4=Cl; 1 e, R1=R2=R3=R4=F), and a cyclic nitrone, -O+N==CHCH2CH2CMe2 2, proceed under heating in a sealed tube to give phthalimides 3, 2-oxadiazolyl-benzonitriles 4 or ortho-bis(oxadiazolyl)tetrafluorobenzene 4 e'. In the presence of palladium(II) chloride, phthalonitriles 1 react with 2 at room temperature, to give bis(pyrrolidin-2-ylidene)phthalamide PdII complexes 5 via metal-promoted rupture of the N--O bond of the oxadiazoline ring. The ketoimine ligands thus generated can be liberated from the metal by displacement with a diphosphine. Although the first [2+3] cycloaddition of 2 to 1 can occur in the absence of the metal to give the mono-cycloadducts 4, the second [2+3] coupling at the still-unreacted cyano group requires its activation by coordination to PdII, affording complexes 6 containing two ligated oxadiazolyl-benzonitriles. These ligands undergo either i) further cycloaddition with 2 to afford ultimately (upon rearrangement) the bis(pyrrolidinylidene)phthalamide complexes 5 or ii) N--O bond cleavage in the oxadiazoline ring with intramolecular attack of the imine nitrogen on the cyano carbon and bridging to a second PdII center to afford dimeric palladium(II) complexes 7, with chloride bridges, that bear a dihydropyrrolyl-iminoisoindolinone, a new type of ligand.The compounds were characterized by IR, 1H, and 13C NMR spectroscopy, ESI MS or FAB+ MS, elemental analyses and, in the case of 4 c, 5 a, 5 c, and 7 c, also by X-ray diffraction analysis. Complexes 5 a and 7 c show high catalytic activity for the Suzuki-Miyaura cross-coupling reaction of bromobenzene and phenylboronic acid and give biphenyl in high yields with turnover frequencies (TOFs) of up to 9.0x10(5) h(-1).     

Spectra of water dimer from a new ab initio potential with flexible monomers

We report the definition and testing of a new ab initio 12-dimensional potential for the water dimer with flexible monomers. Using our recent accurate CCpol-8s rigid water pair potential [W. Cencek, K. Szalewicz, C. Leforestier, R. van Harrevelt, and A. van der Avoird, Phys. Chem. Chem. Phys. 10, 4716 (2008)] as a reference for the undistorted monomers' geometries, a distortion correction has been added, which was taken from a former flexible-monomer ab initio potential. This correction allows us to retrieve the correct binding energy D(e)=21.0 kJ mol(-1), and leads to an equilibrium geometry in close agreement with the one obtained from benchmark calculations. The kinetic energy operator describing the flexible-monomer water dimer has been expressed in terms of Radau coordinates for each monomer and a recent general cluster polyspherical formulation describing their relative motions. Within this formulation, an adiabatic scheme has been invoked in order to decouple fast (intramolecular) modes and slow (intermolecular) ones. Different levels of approximation were tested, which differ in the way in which the residual potential coupling between the intramolecular modes located on different monomers and the dependence of the monomer rotational constants on the dimer geometry are handled. Accurate calculations of the vibration-rotation-tunneling levels of (H(2)O)(2) and (D(2)O)(2) were performed, which show the best agreement with experiments achieved so far for any water potential. Intramolecular excitations of the two monomers were calculated within two limiting cases, to account for the lack of non-adiabatic coupling between intramolecular modes due to the intermolecular motion. In the first model, the excitation was assumed to stay either on the donor or the acceptor molecule, and to hop between the two moieties upon donor-acceptor interchange. In the second model, the excitation remains on the same molecule whatever is the dimer geometry. Marginal frequency differences, less than 2?cm(-1), were obtained for all modes, and the resulting infrared shifts are in good agreement with experiments.     

Resonances in rotationally inelastic scattering of OH(X2Π) with helium and neon

We present detailed calculations on resonances in rotationally and spin-orbit inelastic scattering of OH (X(2)Π, j = 3/2, F(1), f) radicals with He and Ne atoms. We calculate new ab initio potential energy surfaces for OH-He, and the cross sections derived from these surfaces compare well with the recent crossed beam scattering experiment of Kirste et al. [Phys. Rev. A 82, 042717 (2010)]. We identify both shape and Feshbach resonances in the integral and differential state-to-state scattering cross sections, and we discuss the prospects for experimentally observing scattering resonances using Stark decelerated beams of OH radicals.     

Cooperative assistance in bifunctional organocatalysis: enantioselective mannich reactions with aliphatic and aromatic imines

Hold them tight: Guided by X-ray structures, bifunctional thiourea catalysts containing an activating intramolecular hydrogen bond were redesigned. The new catalysts were used to effect a highly enantioselective Mannich reaction between malonates and both aliphatic and aromatic imines (see scheme; Boc=tert-butoxycarbonyl).     

Birkhoff’s variety theorem in many sorts

For many-sorted algebras, Garrett Birkhoff’s characterization of equational classes is proved to generalize in case of finitely many sorts. For infinitely sorted algebras, closure under directed unions needs to be added.     

Laser threshold of Mie resonances

We show that time-independent scattering coefficients calculated from the standard extrapolation of Mie theory to the gain regime have physical meaning up to the laser threshold. The theoretical width of a resonance decreases linearly with increasing gain and becomes zero at the laser threshold. We performed experiments on dielectric microspheres with gain, trapped with optical tweezers. The width of the mode was measured to narrow as a function of the gain up to the lasing threshold, confirming both the validity of the extrapolation of Mie theory to the gain regime below threshold and our interpretation of its point of divergence as the laser threshold.     

Structure of BRIJ-35 nonionic surfactant in water: a reverse Monte Carlo study

There are some contradictions in the literature on the structure of micelles formed by the BRIJ-35 surfactant in water. One can find reasonable differences in the aggregation numbers and micellar sizes, but there is a lack of data on the intermicellar structure. In this study, we reevaluated the small-angle neutron scattering experiments performed previously on the BRIJ-35 surfactant in the concentration range of 5-200 g/dm3 at 20, 40, and 60 degrees C. The data were analyzed with a reverse Monte Carlo-type method developed recently for colloids. The micelles were modeled as spherical cores representing the hydrophobic parts and number of balls put on the cores to mimic the hydrated hydrophilic chains. The simulations provided data on the mean aggregation number and on the extent of hydration of the hydrophilic shell of the micelles. We obtained intermicellar pair-correlation functions indicating different micelle-micelle interactions from the usually assumed hard-sphere ones.