Computer simulation of particles with position-dependent mass

In the present work a dynamical system is investigated, in which the particles’ mass depends on their position in space. The first case study is that of a single point-like particle in one dimension, whose Hamiltonian is numerically integrated with a first-order, energy-conserving algorithm; subsequently, the model is extended to a Lennard-Jones fluid in three dimensions. The features of both setups are examined, and a simple, exact method is devised to obtain, from a system of particles with position-dependent mass, the same equilibrium observables that would be measured in a conventional simulation. The properties of these dynamical systems are explored, with possible applications in the development of efficient sampling strategies.     

LINC-NIRVANA: MCAO toward Extremely Large Telescopes

LINC-NIRVANA is a Fizeau (imaging) interferometer exploiting the full spatial resolution of a 23 m class telescope in the combined beam of the Large Binocular Telescope supported through Multi-Conjugated Adaptive Optics (MCAO). By means of science cases, we show how LINC-NIRVANA takes advantage of the MCAO, increasing the sky coverage of the instrument and the field of view for the Fringe and Flexure tracker. We introduce the MCAO system of LINC-NIRVANA in detail, which in a first step will be installed with two deformable mirrors per arm and has the provision to be upgraded with a third mirror. The MCAO system implements several novel concepts proposed for extremely large telescopes, such as layer oriented MCAO, optical co-adding of guide stars, or Multiple Field of View sensing. LINC-NIRVANA will demonstrate some of the concepts for the first time on sky. To cite this article: W. Gaessler et. al., C. R. Physique 6 (2005).     

Synchronized fluxional motion and cyclometalation of ligands in platinum(II) complexes

Oscillation of the 2,9-dimethyl-1,10-phenanthroline (dmphen) ligand between nonequivalent exchanging sites in [Pt(Me)(dmphen)(P(o-tolyl)3)]+ and phosphane rotation around the Pt-P bond take place at the same rate. Thus, this cationic complex behaves as a molecular gear, exhibiting a fascinating synchronism between two otherwise independent fluxional motions. The process (DeltaG(3330)(#) = 68.5 +/- 0.2 kJ mol(-1)) was found to be unaffected by (i) the nature of various counteranions (X = PF6- 1, SbF6- 2, CF3SO3- 3, BF4- 4, BArf- 5), (ii) the polarity or the electron-donor properties of the solvent and, (iii) the addition of weak nucleophiles. Restricted phosphane rotation around the Pt-P bond impedes free dmphen oscillation in a 14-electron three-coordinate T-shaped intermediate, containing eta1-coordinated dmphen, generated by easy Pt-N bond dissociation from [Pt(Me)(dmphen)(P(o-tolyl)3)]+. 1-5 undergo easy orthoplatination, leading to new [Pt(dmphen){CH2C6H4P(o-tolyl)2-kappaC,P}]X cyclometalated Pt(II) compounds (X = PF6- 1, SbF6- 2, CF3SO3- 3, BF4- 4, BArf- 5). The kinetics of the cyclometalation of 3 and 4 were followed in tetrachloroethane by both 1H NMR and spectrophotometric techniques (kobs = 1.7 x 10-4 s(-1) at 333 K, DeltaH = 59.3 +/- 3 kJ mol(-1), and DeltaS = -141 +/- 8 J K(-1) mol(-1)). Ring opening of dmphen is again a prerequisite for C-H bond activation, which takes place through a multistep oxidative-addition reductive-elimination pathway. The molecular structure of cyclometalated 10 shows a butterfly shape with two o-tolyl rings projected above and below the coordination plane. Variable-temperature 1H NMR spectra revealed hindered rotation around the P-Cipso(o-tolyl) bonds at rather mild temperatures (DeltaG(3330)(#) = 55.2 +/- 0.4 kJ mol(-1)). Dmphen oscillation results very slowly and is dependent on the nature of the counteranions, of the solvents, and is strongly accelerated by the presence of weak nucleophiles that act as catalysts, according to an associative mode of activation.     

Lysozyme Immobilized on Micro-Sized Magnetic Particles: Kinetic Parameters at Wine pH

In order to use lysozyme as an anti-microbial agent during the winemaking process, hen egg-white lysozyme (LYZ) was covalently immobilized on two different micro-size magnetic particles (tosyl-activated and carboxylated, TSA and CA, respectively). A cell suspension of Oenococcus oeni, an oenological strain involved in the winemaking process, was utilized as LYZ substrate. Both a kinetic study and a study of the stability of free and immobilized LYZ were performed in McIlvane buffer at pH 3.2, that is the average minimum pH value in wine. The activity and kinetic parameters measured for the free LYZ at pH 3.2 are lower than those reported at the optimum pH (4.5); however the residual activity at pH 3.2 is sufficient to be of interest for further immobilization and applications in winemaking. All kinetic parameters of both biocatalysts (LYZ-CA and LYZ-TSA) are altered after immobilization, probably due to the structural modifications in the active site caused by covalent attachment to the supports. The half-life calculated at 25 °C was 39 h for free LYZ, while it increased to 280 and 134 h for LYZ-TSA and LYZ-CA, respectively. This result indicates that immobilization improves the enzyme stability and that LYZ can be utilized in wine applications in its immobilized forms. In addition, LYZ-TSA seems to be the best biocatalyst for further applications in winemaking.     

Numerical properties of generalized discrepancies on spheres of arbitrary dimension

Quantifying uniformity of a configuration of points on the sphere is an interesting topic that is receiving growing attention in numerical analysis. An elegant solution has been provided by Cui and Freeden [J. Cui, W. Freeden, Equidistribution on the sphere, SIAM J. Sci. Comput. 18 (2) (1997) 595–609], where a class of discrepancies, called generalized discrepancies   and originally associated with pseudodifferential operators on the unit sphere in R³${\mathbb{R}}^3$, has been introduced. The objective of this paper is to extend to the sphere of arbitrary dimension this class of discrepancies and to study their numerical properties. First we show that generalized discrepancies are diaphonies on the hypersphere. This allows us to completely characterize the sequences of points for which convergence to zero of these discrepancies takes place. Then we discuss the worst-case error of quadrature rules and we derive a result on tractability of multivariate integration on the hypersphere. At last we provide several versions of Koksma–Hlawka type inequalities for integration of functions defined on the sphere.     

Dynamical generalized Hurst exponent as a tool to monitor unstable periods in financial time series

We investigate the use of the Hurst exponent, dynamically computed over a weighted moving time-window, to evaluate the level of stability/instability of financial firms. Financial firms bailed-out as a consequence of the 2007–2008 credit crisis show a neat increase with time of the generalized Hurst exponent in the period preceding the unfolding of the crisis. Conversely, firms belonging to other market sectors, which suffered the least throughout the crisis, show opposite behaviors. We find that the multifractality of the bailed-out firms increase at the crisis suggesting that the multi fractal properties of the time series are changing. These findings suggest the possibility of using the scaling behavior as a tool to track the level of stability of a firm. In this paper, we introduce a method to compute the generalized Hurst exponent which assigns larger weights to more recent events with respect to older ones. In this way large fluctuations in the remote past are less likely to influence the recent past. We also investigate the scaling associated with the tails of the log-returns distributions and compare this scaling with the scaling associated with the Hurst exponent, observing that the processes underlying the price dynamics of these firms are truly multi-scaling.     

Non conventional syntheses of heterocyclic compounds. 2. Synthesis of 1H-4,5-dihydro-1,3,4-benzotriazepine derivatives

Arylazoanils carrying aromatic methyl or ethyl groups in the position ortho to the imine function thermally cyclize to give 1H-4,5-dihydro-1,3,4-benzotriazepine derivatives in fairly good yields. A study of the effect of the substituents on both the aryl rings is reported. The reaction is interpreted as an internal oxo-reduction process.     

(η6-Arene)(η4-cycloocta-1,5-diene)ruthenium(0) complexes as homogeneous hydrogenation catalysts

Ru(η⁶-arene)(η⁴-COD) complexes (COD = cycloocta-1,5-diene) have been found to be catalytic precursors for the homogeneous hydrogenation of α-olefins and cycloolefins under mild conditions (room temperature, P(H₂) 1–20 atm).