Trotter derivation of algorithms for Brownian and dissipative particle dynamics

This paper focuses on the temporal discretization of the Langevin dynamics, and on different resulting numerical integration schemes. Using a method based on the exponentiation of time dependent operators, we carefully derive a numerical scheme for the Langevin dynamics, which we found equivalent to the proposal of Ermak and Buckholtz [J. Comput. Phys. 35, 169 (1980)] and not simply to the stochastic version of the velocity-Verlet algorithm. However, we checked on numerical simulations that both algorithms give similar results, and share the same "weak order two" accuracy. We then apply the same strategy to derive and test two numerical schemes for the dissipative particle dynamics. The first one of them was found to compare well, in terms of speed and accuracy, with the best currently available algorithms.     

Towards comprehensive hydrocarbons analysis of middle distillates by LC-GCxGC

The detailed characterization of middle distillates is essential for a better understanding of reactions involved in refining processes. Owing to a higher resolution power and an enhanced sensitivity, but especially to a group-type ordering in the chromatographic plane, comprehensive two-dimensional gas chromatography (GCxGC) offers unsurpassed characterization possibilities for petroleum samples. However, GCxGC fails to totally discriminate naphthenes from unsaturates occurring in hydrotreated diesel samples. This article aims at promoting the implementation of LC-GCxGC for the quantitative determination of hydrocarbon distribution in middle distillates, including naphthenes. In this configuration, liquid chromatography (LC) enables the separation of hydrocarbons into two fractions (viz., saturated and unsaturated) before the subsequent analysis of each fraction by GCxGC. In this paper, the choice of GCxGC conditions in order to achieve the separation and identification of hydrocarbons by chemical class is discussed; under these conditions, naphthenes are separated according to the number of saturated rings. For the first time, the presence of di-, tri-, and tetra-naphthenes resulting from the hydroconversion of aromatics can clearly be evidenced. A quantitative procedure for the determination of the distribution of hydrocarbons, including the distribution of naphthenes according to the number of saturated rings, is also proposed and discussed in detail. LC-GCxGC is found to provide an unequalled degree of information that will widely contribute to a better understanding of hydroconversion processes.     

Measurement of hold-up volumes in reverse-phase liquid chromatography Definition and comparison between static and dynamic methods

The hold-up volumes, V(M) of two series of RPLC adsorbents were measured using three different approaches. The first method is based on the difference between the volumes of the empty column tube (150x4.6mm) and of the material packed inside the column. It is considered as giving the correct value of V(M). This method combines the results of the BET characterization of the adsorbent before packing (giving the specific pore volume), of carbon element analysis (giving the mass fraction of silica and alkyl bonded chains), of Helium pycnometry (providing silica density), and of inverse size exclusion chromatography (ISEC) performed on the packed column (yielding the interparticle volume). The second method is static pycnometry, which consists in weighing the masses of the chromatographic column filled with two distinct solvents of different densities. The last method is based on the thermodynamic definition of the hold-up volume and uses the dynamic minor disturbance method (MDM) with binary eluents. The experimental results of these three non-destructive methods are compared. They exhibit significant, systematic differences. Pycnometry underestimates V(M) by a few percent for adsorbents having a high carbon content. The results of the MDM method depend strongly on the choice of the binary solution used and may underestimate or overestimate V(M). The hold-up volume V(M) of the RPLC adsorbents tested is best measured by the MDM method using a mixture of ethanol and water.     

Surface energy of talc and chlorite: Comparison between electronegativity calculation and immersion results

The surface energies of talc and chlorite is computed using a simple model, which uses the calculation of the electrostatic energy of the crystal. It is necessary to calculate the atomic charges. We have chosen to follow Henry's model of determination of partial charges using scales of electronegativity and hardness. The results are in correct agreement with a determination of the surface energy obtained from an analysis of the heat of immersion data. Both results indicate that the surface energy of talc is lower than the surface energy of chlorite, in agreement with observed behavior of wettability. The influence of Al and Fe on this phenomenon is discussed. Surface energy of this type of solids seems to depend more strongly on the geometry of the crystal than on the type of atoms pointing out of the surface; i.e., the surface energy depends more on the physics of the system than on its chemistry.     

Practical stereoselective synthesis of an alpha-trifluoromethyl-alpha-alkyl epoxide via a diastereoselective trifluoromethylation reaction

A practical stereoselective synthesis is reported for an alpha-trifluoromethyl-alpha-alkyl epoxide (1), which is an important pharmaceutical intermediate. The key step involves a chiral auxiliary-controlled asymmetric trifluoromethylation reaction for the introduction of the unique trifluoromethyl-substituted tertiary alcohol stereogenic center in the target molecule. The fluoride-initiated CF3 addition to chiral keto ester 6a proceeded with a diastereoselectivity up to 86:14. The major diastereomer was readily obtained with a >99.5:0.5 dr through a simple crystallization of the crude product mixture.     

Organometallic methods for the synthesis and functionalization of azaindoles

Azaindoles (also called pyrrolopyridines) constitute essential subunits in many pharmaceutically important compounds. The synthesis of azaindoles has been a great synthetic challenge for chemists. Many classical methods for indole synthesis (such as Fischer and Madelung cyclizations) often cannot be effectively applied to the synthesis of the corresponding azaindoles. In recent years, advances in organometallic chemistry have enabled a number of novel and efficient methodologies for azaindole formation as well as for the further functionalization of azaindole templates. In this tutorial review, we have surveyed the recent development of organometallic chemistry-based methods for azaindole synthesis.     

Analytical model of a self-complementary connected antenna array on high impedance surface

This paper presents an analytical model to design a self-complementary connected antenna array above artificial materials like high impedance surfaces (HIS). The objective of this model is to perform parametric studies to facilitate deeper understanding of a complex antenna array with a significantly shorter computation time than with electromagnetic simulators. The model of the complete structure has been designed in receiving mode when structure is illuminated with a plane wave and using transmission line model and ABCD matrix. By applying an interesting property which gives equivalence between the input impedance in transmit mode and the surface impedance in receiving mode, the impedance match of the self-complementary connected antenna array can be quickly calculated. It is also simple to evaluate the influence of the incidence angle on the reflection coefficient of a self-complementary connected antenna array above perfect electric conductor (PEC) or HIS. PEC or artificial materials can modify the antenna array behavior by either increasing the bandwidth or by adding additional bandwidths. All these results have been verified to be accurate by numerical simulations done with Ansys HFSS.     

Adiabatic self-focusing in media with spatially variable nonlinearity

An optical medium whose nonlinearity can be spatially adjusted is considered to study beam reshaping. The concept is applied to perform adiabatic self-focusing of broad beams. Experimental results are obtained in a photorefractive lithium niobate crystal where the self-focusing nonlinearity is controlled over propagation by a temperature gradient. As a demonstration, gradual self-focusing is shown to transform an incoming beam into an output circular spot 10 times smaller over a 2 cm long crystal submitted to a 30 °C temperature gradient. Once formed, the adiabatic self-focused beam has inscribed a funnel waveguide in the crystal.     

Perelman’s Entropy and Doubling Property on Riemannian Manifolds

The purpose of this work is to study some monotone functionals of the heat kernel on a complete Riemannian manifold with nonnegative Ricci curvature. In particular, we show that on these manifolds, the gradient estimate of Li and Yau (Acta Math. 156, 153–201, 1986), the gradient estimate of Ni (J. Geom. Anal. 14(1), 87–100, 2004), the monotonicity of the Perelman’s entropy and the volume doubling property are all consequences of an entropy inequality recently discovered by Baudoin and Garofalo, , 2009. The latter is a linearized version of a logarithmic Sobolev inequality that is due to D. Bakry and M. Ledoux (Rev. Mat. Iberoam. 22, 683–702, 2006).