Synchronization of oscillators coupled through an environment

We study synchronization of oscillators that are indirectly coupled through their interaction with an environment. We give criteria for the stability or instability of a synchronized oscillation. Using these criteria we investigate synchronization of systems of oscillators which are weakly coupled, in the sense that the influence of the oscillators on the environment is weak. We prove that arbitrarily weak coupling will synchronize the oscillators, provided that this coupling is of the ‘right’ sign. We illustrate our general results by applications to a model of coupled GnRH neuron oscillators proposed by Khadra and Li [A. Khadra, Y.X. Li, A model for the pulsatile secretion of gonadotropin-releasing hormone from synchronized hypothalamic neurons, Biophys. J. 91 (2006) 74-83.], and to indirectly weakly-coupled λ-ω oscillators.     

Molecular-dynamics simulations of electron-ion temperature relaxation in a classical Coulomb plasma

Molecular-dynamics simulations are used to investigate temperature relaxation between electrons and ions in a fully ionized, classical Coulomb plasma with minimal assumptions. Recombination is avoided by using like charges. The relaxation rate agrees with theory in the weak coupling limit (g identical with potential/kinetic energy < 1), whereas it saturates at g > 1 due to correlation effects. The "Coulomb log" is found to be independent of the ion charge (at constant g) and mass ratio > 25.     

Short range order in anomalous liquid metals

Liquid metals with anomalous physical properties such as increasing sound velocity with temperature or density anomalies, exhibit a complex structure in their one dimensional experimental diffraction patterns. Typically, their radial distribution functions are characterized by an asymmetric first peak and a subsidiary peak or shoulder on the right hand side of the first main peak. It has been hypothesized that the complex structure is associated with short range ordering the liquid. Specifically in the liquid pnictides, it has been proposed that such order may be associated with the underlying solid A7 structure. We present an analysis of the short range order in liquids using a modified quasi-crystalline model of liquid structure. This model is shown to fit the experimental radial distribution function very well and to reproduce the experimentally observed structure factor. Using this model we find that the short range order in the liquid pnictides is dominated by an A7-like structure with two types of bonds, in close agreement with the underlying solid phase. The existence of two bond lengths is necessary within this model to explain the asymmetry in the first peak as well as the change in coordination number along the pnictide series. The quasi-crystalline model is discussed and shown to correlate with the Lindemann melting criterion.     

Separation of nitroimidazoles by reversed-phase high-pressure liquid chromatography

A mixture of eight N-substituted and unsubstituted nitroimidazoles has been separated by high-pressure liquid chromatography with 5% ethanol as the eluent. Compounds with the same capacity ratios were selectively detected electrochemically by differential pulse polarography with a hanging mercury drop electrode. The HMDE detector had higher detection limits than the photometric detector set at 315 nm.     

Efficient asymmetric hydrogenation with rhodium complexes of C(1)-symmetric 2,5-dimethylphospholane-diphenylphosphines

The unsymmetrical, optically active ligands 1,2-C(6)H(4)(PPh(2))((R,R)-2,5-dimethylphospholanyl) and the new 1,1'-Fe(C(5)H(4))(2)(PPh(2))((R,R)-2,5-dimethylphospholanyl) form complexes of the type [PtCl(2)(diphos)] and [Rh(diphos)(diene)][BF(4)]. The crystal structure of reveals that only one quadrant is blocked. Asymmetric hydrogenation of acrylic esters and enamides using and as catalysts show that the phenylene-backboned diphosphine gives a more efficient catalyst in terms of asymmetric induction than the more flexible ferrocene-backboned diphosphine. The best results, which were obtained with and enamide substrates, exceeded those obtained with Duphos catalysts. The rate of hydrogenation of the enamides with was 10 times faster than with [Rh(Duphos)(diene)][BF(4)]. A quadrant diagram can be used to predict the configuration of the major product, provided it is assumed to be derived from the less sterically congested intermediate.     

Reversible Soft Mechanochemical Control of Biaryl Conformations through Crosslinking in a 3D Macromolecular Network

Tuning the dihedral angle (DA) of axially chiral compounds can impact biological activity, catalyst efficiency, molecular motor performance, or chiroptical properties. Herein, we report gradual, controlled, and reversible changes in molecular conformation of a covalently linked binaphthyl moiety within a 3D polymeric network by application of a macroscopic stretching force. We managed direct observation of DA changes by measuring the circular dichroism signal of an optically pure BINOL-crosslinked elastomer network. Stretching the elastomer resulted in a widening of the DA between naphthyl rings when the BINOL was doubly grafted to the elastomer network; no effect was observed when a single naphthyl ring of the BINOL was grafted to the elastomer network. We have determined that ca. 170 % extension of the elastomers led to the transfer of a mechanical force to the BINOL moiety of 2.5 kcal mol⁻¹ Å⁻¹ (ca. 175 pN) in magnitude and results in the opening of the DA of BINOL up to 130°.     

Synthesis and vibrational circular dichroism of enantiopure chiral oxorhenium(V) complexes containing the hydrotris(1-pyrazolyl)borate ligand

The infrared and vibrational circular dichroism (VCD) spectra of six chiral oxorhenium(V) complexes, bearing a hydrotris(1-pyrazolyl)borate (Tp) ligand, have been investigated. These complexes are promising candidates for observation of parity violation (symmetry breaking due to the weak nuclear force). New chiral oxorhenium complexes have been synthesized, namely, [TpReO(eta2-O(CH3)CH2CH2O-O,O)] (4a and 4b) diastereomers and [TpReO(eta2-N(CH3)CH2CH2O-N,O)] (5) and [TpReO(eta2-N(tBu)CH2CH2O-N,O)] (6) enantiomers. All compounds could be obtained in enantiomerically pure form by using either column chromatography or HPLC over chiral columns. VCD spectroscopy of these compounds and of [TpReO(eta2-N(CH3)CH(CH3)CH(Ph)O-N,O)] (2) and [TpReO(eta2-N(CH2)3CHCO2-N,O)] (3) (with chiral bidentate ligands derived, respectively, from ephedrine and proline) were studied. This allowed the absolute configuration determination of all compounds together with their conformational analysis, by comparing calculated and experimental spectra. This is the first VCD study of rhenium complexes which further demonstrates the applicability of VCD spectroscopy in determining the chirality of inorganic complexes.