Euler-Poincaré Approaches to Nematodynamics

Nematodynamics is the orientation dynamics of flowless liquid-crystals. We show how Euler-Poincaré reduction produces a unifying framework for various theories, including Ericksen-Leslie, Luhiller-Rey, and Eringen??s micropolar theory. In particular, we show that these theories are all compatible with each other and some of them allow for more general configurations involving a non vanishing disclination density. All results are also extended to flowing liquid crystals.     

A Generalization of Hörmander's Inequality-I

We give sufficient conditions to generalize Hörmander's inequality to the case of operators with multiple characteristics of order higher than two     

Full Bandwidth Measurement of Supercontinuum Spectral Phase Coherence in Long Pulse Regime

Abstract

This article reports that spectral phase coherence in the supercontinuum in long pulse regime can be measured simply and effectively by using an interference technique with the help of a Mach–Zehnder interferometer. It is also demonstrated that chromatic dispersion on the fringe visibility of interference spectral patterns is overcome in the setup. The technique is applied to characterize supercontinuum spectral phase coherence in a highly non-linear optical fiber with different input conditions: unseeded, coherent seeded, and incoherent seeded picosecond pumps. The results confirm the phase coherence characteristic predicted theoretically in previous studies.     

Reduction theory for symmetry breaking with applications to nematic systems

We formulate Euler–Poincaré and Lagrange–Poincaré equations for systems with broken symmetry. We specialize the general theory to present explicit equations of motion for nematic systems, ranging from single nematic molecules to biaxial liquid crystals. The geometric construction applies to order parameter spaces consisting of either unsigned unit vectors (directors) or symmetric matrices (alignment tensors). On the Hamiltonian side, we provide the corresponding Poisson brackets in both Lie–Poisson and Hamilton–Poincaré formulations. The explicit form of the helicity invariant for uniaxial nematics is also presented, together with a whole class of invariant quantities (Casimirs) for two-dimensional incompressible flows.     

A local-MP2 approach to the ab initio study of electron correlation in crystals and to the simulation of vibrational spectra: the case of Ice XI

Wave-function-based computational techniques for describing electron correlation effects in periodic systems have a long history. Among early attempts, the method proposed by Colle and Salvetti (Theor Chim Acta 37:329, 1975) more than 30 years ago is noteworthy for its simplicity, power, and far-reaching consequences. The renewed interest in this topic is due to the well-known failure of techniques based on Density Functional Theory when it comes to obtaining very accurate estimates of some important quantities. Here we present the essential features of an ab initio code, ( CRYSCOR ) recently implemented (Phys Rev B 76: 075101, 075102, 2007), which solves the MP2 equations for crystals by adopting a local-correlation approach and using as a reference the Hartree-Fock solution provided by the CRYSTAL program. As an example of application, we discuss the MP2 corrections to the frequency of some vibrational modes in a proton-ordered structure of water ice (Ice XI).     

Charge renormalization in planar and spherical charged lipidic aqueous interfaces

The charge renormalization in planar and spherical charged lipidic aqueous interfaces has been investigated by means of thermodynamic and electrokinetic measurements. We analyzed the behavior of mixed DOTAP/DOPE monolayers at the air-electrolyte solution interface and DOTAP/DOPE liposomes 100 nm in size dispersed in an aqueous phase of varying ionic strength. For the two systems, we have compared the "effective" surface charge derived from the measurements of surface potential and zeta-potential to the "bare" charge based on the stoichiometry of the lipid mixture investigated. The results confirm that a strong charge renormalization occurs, whose strength depends on the geometry of the mesoscopic system. The dependence of the "effective" charge on the "bare" charge is discussed in light of an analytical approximation based on the Poisson-Boltzmann equation recently proposed.     

One-pot synthesis of macrocycles by a tandem three-component reaction and intramolecular [3+2] cycloaddition

By combining three appropriately designed simple substrates, a programmed sequence involving an alpha-isocyano acetamide-based three-component reaction followed by a copper-catalyzed intramolecular [3+2] cycloaddition of alkyne and azide took place to afford complex macrocycles in moderate to good yields. One macrocycle and two heterocycles were produced with concurrent formation of five chemical bonds in this operationally simple process.     

Enantioselective determination of the novel antidepressant mirtazapine and its active demethylated metabolite in human plasma by means of capillary electrophoresis

Mirtazapine is a recent noradrenergic and specific serotonergic antidepressant drug. A capillary electrophoretic method has been developed for the enantioseparation and analysis of mirtazapine and its main active metabolite, N-desmethylmirtazapine, in human plasma. For method optimisation several experimental parameters were investigated, such as type and concentration of the chiral selector, buffer pH and capillary temperature. Baseline enantioseparation of the analytes was achieved in 2.5 min in a fused silica capillary (50 microm i.d.; 48.5 cm total length; 8.5 cm effective length) using carboxymethyl-beta-cyclodextrin, dissolved in a background electrolyte consisting of 50 mM phosphate buffer at pH 2.5, as the chiral selector. UV detection was set at 205 nm. A careful pre-treatment of plasma samples was developed, using solid-phase extraction with hydrophilic-lipophilic balance cartridges (60 mg, 3 mL), eluting the sample with methanol, then concentrating it 37.5 times before injection. Extraction yield values are very satisfactory, being the average 89% for mirtazapine and 73% for N-desmethylmirtazapine. Application of the method to some human plasma samples has given satisfactory results.