Approximation of stationary solutions of Gaussian driven stochastic differential equations

We study sequences of empirical measures of Euler schemes associated to some non-Markovian SDEs: SDEs driven by Gaussian processes with stationary increments. We obtain the functional convergence of this sequence to a stationary solution to the SDE. Then, we end the paper by some specific properties of this stationary solution. We show that, in contrast to Markovian SDEs, its initial random value and the driving Gaussian process are always dependent. However, under an integral representation assumption, we also obtain that the past of the solution is independent of the future of the underlying innovation process of the Gaussian driving process.     

Forms of Lepage type and the balance systems

In this work we apply infinitesimal variational calculus to the systems of balance equations. We determine a class of the exterior $n+(n+1)$-forms Θ on the jet bundle of infinite order over a configurational bundle $\pi :Y^{n+m}\to X^n$ similar to the class of Lepage n-forms. Systems of differential equations obtained in the way similar to one used in the Lagrangian field theory, include the Euler–Lagrange equations corresponding to a Lagrangian functions as well as arbitrary regular systems of balance equations. For a balance system with a symmetry group G we present the Noether balance laws corresponding to the generators of the Lie algebra of the group G.     

Optimal control of the Stokes equations: conforming and non-conforming finite element methods under reduced regularity

This paper deals with a control-constrained linear-quadratic optimal control problem governed by the Stokes equations. It is concerned with situations where the gradient of the velocity field is not bounded. The control is discretized by piecewise constant functions. The state and the adjoint state are discretized by finite element schemes that are not necessarily conforming. The approximate control is constructed as projection of the discrete adjoint velocity in the set of admissible controls. It is proved that under certain assumptions on the discretization of state and adjoint state this approximation is of order 2 in L ²(Ω). As first example a prismatic domain with a reentrant edge is considered where the impact of the edge singularity is counteracted by anisotropic mesh grading and where the state and the adjoint state are approximated in the lower order Crouzeix-Raviart finite element space. The second example concerns a nonconvex, plane domain, where the corner singularity is treated by isotropic mesh grading and state and adjoint state can be approximated by a couple of standard element pairs.     

Quantitative impact of small angle forward scatter on whole blood oximetry using a Beer-Lambert absorbance model

It is well known that red blood cell scattering has an impact on whole blood oximetry as well as in vivo retinal oxygen saturation measurements. The goal of this study was to quantify the impact of small angle forward scatter on whole blood oximetry for scattering angles found in retinal oximetry light paths. Transmittance spectra of whole blood were measured in two different experimental setups: one that included small angle scatter in the transmitted signal and one that measured the transmitted signal only, at absorbance path lengths of 25, 50, 100, 250 and 500 μm. Oxygen saturation was determined by multiple linear regression in the 520-600 nm wavelength range and compared between path lengths and experimental setups. Mean calculated oxygen saturation differences between setups were greater than 10% at every absorbance path length. The deviations to the Beer-Lambert absorbance model had different spectral dependences between experimental setups, with the highest deviations found in the 520-540 nm range when scatter was added to the transmitted signal. These results are consistent with other models of forward scatter that predict different spectral dependences of the red blood cell scattering cross-section and haemoglobin extinction coefficients in this wavelength range.     

First identification of dimethoxycinnamic acids in human plasma after coffee intake by liquid chromatography-mass spectrometry

There is a substantial amount of published literature on the bioavailability of various coffee components including the most abundant metabolites, caffeic and ferulic acids. Surprisingly, to date, the appearance of dimethoxycinnamic acid derivatives in humans has not been reported despite the fact that methylated form of catechol-type polyphenols could help maintain, modify or even improve their biological activities. This study reports an LC-MS method for the detection of dimethoxycinnamic acid in human plasma after treatment with an esterase. Liquid chromatography, including the combination of methanol and acetonitrile as organic eluent, was optimized to resolve all interferences and enable reliable detection and identification of 3,4-dimethoxycinnamic and 3,4-dimethoxy-dihydrocinnamic acids. In addition to the good mass accuracy achieved (better than 5 ppm), tandem mass spectrometric and co-chromatography experiments further confirmed the identity of the compounds. The optimized method was applied to analyze samples obtained immediately, 1 and 10 h after coffee ingestion. The results show that in particular 3,4-dimethoxycinnamic acid appears in high abundance (～380 nM at 60 min) in plasma upon coffee intake, indicating that it is important to consider these derivatives in future bioavailability and bioefficacy studies.     

Description of the response of a fiber optic velocity sensor applied to capillary gas chromatography

This paper explores the response of a novel fiber optics sensor allowing real-time determination of the migration rate of vapor zones in capillary gas chromatography. The sensitivity is related to the gradient of the vapor zone distribution in the capillary and it is highest when vapor zones show steep variations in concentration. The expected linearity between the height of the velocity peaks and the response of a thermal conductivity detector is demonstrated experimentally. The sensor can be used to infer an approximate value of the analyte diffusion coefficient from the time response. Finally, the time evolution of the envelope of the optical signal is explained with experimental evidences.     

Synthesis, magnetic properties, and magnetic structure of a natrochalcite structural variant, KM(II)2D3O2(MoO4)2 (M = Mn, Fe, or Co)

We report the syntheses, crystal structures, and magnetic properties of KMn(2)(H(3)O(2))(MoO(4))(2) (MnH), KMn(2)(D(3)O(2))(MoO(4))(2) (MnD), KFe(2)(H(3)O(2))(MoO(4))(2) (FeH), KFe(2)(D(3)O(2))(MoO(4))(2) (FeD), KCo(2)(H(3)O(2))(MoO(4))(2) (CoH), and KCo(2)(D(3)O(2))(MoO(4))(2) (CoD), and the magnetic structures of MnD and FeD. They belong to the structural variant (space group I2/m) of the mineral natrochalcite NaCu(2)(H(3)O(2))(SO(4))(2) (space group C2/m) where the diagonal within the ac-plane of the latter become one axis of the former. The structure of MnD, obtained from Rietveld refinement of a high-resolution neutron pattern taken at 300 K, consists of chains of edge-sharing octahedra bridged by MoO(4) and D(3)O(2) to form layers, which are connected to K through the oxygen atoms to form the three-dimensional (3D)-network. The X-ray powder diffraction patterns of the other two compounds were found to belong to the same space group with similar parameters. The magnetic susceptibilities of MnH and FeH exhibit long-range ordering of the moments at a Ne?el temperature of 8 and 11 K, respectively, which are accompanied by additional strong Bragg reflections in the neutron diffraction in the ordered state, consistent with antiferromagnetism. Analyses of the neutron data for MnD and FeD reveal the presence of both long- and short-range orderings and commensurate magnetic structures with a propagation vector of (?, 0, ?). The moments are antiferromagnetically ordered within the chains with alternation between chains to generate four nonequivalent nuclear unit cells. For MnD the moments are perpendicular to the chain axis (b-axis) while for FeD they are parallel to the b-axis. The overall total is a fully compensated magnetic structure with zero moment in each case. Surprisingly, for KCo(2)(D(3)O(2))(MoO(4))(2) neither additional peaks nor increase of the nuclear peaks' intensities were observed in the neutron diffraction patterns below the magnetic anomaly at 12 K which was identified to originate from a small quantity of a ferromagnetic compound, Co(2)(OH)(2)MoO(4).     

Effect of mixed solvents on PCDTBT:PC70BM based solar cells

We investigated the effect of solvents on the morphology, charge transport and device performance of poly[N-9″-hepta-decanyl-2,7-carbazole-alt-5,5-(4′,7′-di-2-thienyl-2′,1′,3′-benzothiadiazole)] (PCDTBT) and [6,6]-phenyl C71-butyric acid methyl ester (PC₇₀BM) based solar cells. To carry out this investigation, chloroform and 1,2-dichlorobenzene were chosen as good solvents of the two compounds. Films prepared with chloroform exhibit larger domains than those prepared with 1,2-dichlorobenzene and their size increases with the amount of PC₇₀BM. Fine tuning of the domain size was realized by using a solvent of mixed chloroform and 1,2-dichlorobenzene. At a mixing ratio of 50%:50%, a power conversion efficiency of 6.1% was achieved on PCDTBT:PC₇₀BM (1:3) devices with an active area of 1 cm², under air mass 1.5 global (AM 1.5 G) irradiation at 100 mW/cm².     

Three-dimensional imaging of sulfides in silicate rocks at submicron resolution with multiphoton microscopy

We report the first application of multiphoton microscopy (MPM) to generate three-dimensional (3D) images of natural minerals (micron-sized sulfides) in thick (～120 μm) rock sections. First, reflection mode (RM) using confocal laser scanning microscopy (CLSM), combined with differential interference contrast (DIC), was tested on polished sections. Second, two-photon fluorescence (TPF) and second harmonic signal (SHG) images were generated using a femtosecond-laser on the same rock section without impregnation by a fluorescent dye. CSLM results show that the silicate matrix is revealed with DIC and RM, while sulfides can be imaged in 3D at low resolution by RM. Sulfides yield strong autofluorescence from 392 to 715 nm with TPF, while SHG is only produced by the embedding medium. Simultaneous recording of TPF and SHG images enables efficient discrimination between different components of silicate rocks. Image stacks obtained with MPM enable complete reconstruction of the 3D structure of a rock slice and of sulfide morphology at submicron resolution, which has not been previously reported for 3D imaging of minerals. Our work suggests that MPM is a highly efficient tool for 3D studies of microstructures and morphologies of minerals in silicate rocks, which may find other applications in geosciences.