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.     

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.     

Formation of a grating of submicron nematic layers by photopolymerization of nematic-containing mixtures

A submicron, spatially periodic, structure consisting of a sequence of oriented layers of a nematic liquid crystal (NLC), separated by isotropic polymeric walls, was obtained experimentally. This was accomplished by polymerization induced by the interference pattern of UV laser radiation in a NLC-containing prepolymer mixture. It was established that such a structure occurs when phase separation and nematic ordering are prevented during the polymerization process. These structures are the diffraction elements, whose efficiency is much greater than that of a standard grating of polymer-dispersed liquid crystals [1–4] which is obtained in the same initial mixture. Specifically, a diffraction efficiency of 60–70% was obtained for structures with the period Δ = 0.2 μm, even in mixtures where a grating with Δ < 6 μm cannot be obtained at all by the standard technique.     

Competitive binding exchange between alkali metal ions (K+, Rb+, and Cs+) and Na+ ions bound to the dimeric quadruplex [d(G4T4G4)]2: a 23Na and 1H NMR study

A comparative study of the competitive cation exchange between the alkali metal ions K⁺, Rb⁺, and Cs⁺ and the Na⁺ ions bound to the dimeric quadruplex [d(G₄T₄G₄)]₂ was performed in aqueous solution by a combined use of the ²³Na and ¹H NMR spectroscopy. The titration data confirm the different binding affinities of these ions for the G‐quadruplex and, in particular, major differences in the behavior of Cs⁺ as compared to the other ions were found. Accordingly, Cs⁺ competes with Na⁺ only for the binding sites at the quadruplex surface (primarily phosphate groups), while K⁺ and Rb⁺ are also able to replace sodium ions located inside the quadruplex. Furthermore, the ¹H NMR results relative to the CsCl titration evidence a close approach of Cs⁺ ions to the phosphate groups in the narrow groove of [d(G₄T₄G₄)]₂. Based on a three‐site exchange model, the ²³Na NMR relaxation data lead to an estimate of the relative binding affinity of Cs⁺ versus Na⁺ for the quadruplex surface of 0.5 at 298 K. Comparing this value to those reported in the literature for the surface of the G‐quadruplex formed by 5′‐guanosinemonophosphate and for the surface of double‐helical DNA suggests that topology factors may have an important influence on the cation affinity for the phosphate groups on DNA. Copyright © 2009 John Wiley & Sons, Ltd.     

A necessary and sufficient condition for a lower bound for fourth-order pseudodifferential operators

We give necessary and sufficient conditions for the lower bound {fx55-01} to hold for any compact setK ⊂X, an open set ofR ⁿ , andP =P* ∃ ψ _phg ⁴ (X) with p(x, ξ) ~ q ₂ ² + p₃ + p₂ + ..., q₂ beingtransversally elliptic with respect to the characteristic manifold Σ =q ₂ ^-1 (0).     

Generalized Hessian and External Approximations in Variational Problems of Second Order

We introduce a suitable notion of generalized Hessian and show that it can be used to construct approximations by means of piecewise linear functions to the solutions of variational problems of second order. An important guideline of our argument is taken from the theory of the Γ-convergence. The convergence of the method is proved for integral functionals whose integrand is convex in the Hessian and satisfies standard growth conditions.