Finite-dimensional model for defect-trapped light in planar periodic nonlinear structures

We study the dynamics of 2D gap solitons (GSs) in Bragg resonant nonlinear (photonic) gratings in the presence of localized defects. Previous work [Stud. Appl. Math.115, 209 (2005)] explains the mechanism of trapping the GS-carried energy at a defect via a resonant energy transfer from the GS into defect modes. We derive a finite-dimensional model that describes the evolution of the defect-trapped state as an interaction of linear defect modes and show that this model approximates the full dynamics very well in the regime when moderate amounts of GS energy are trapped.     

Simultaneous determination of eight biologically active thiol compounds using gradient elution-liquid chromatography with Coul-Array detection

The most active form of sulfur in biomolecules is the thiol group, present in a number of biologically active compounds. Here we present a comprehensive study of thiol analysis using flow injection analysis/HPLC with electrochemical detection. The effect of different potentials of working electrodes, of organic solvent contents in the mobile phase, and of isocratic and gradient elution on simultaneous determination of thiol compounds (cysteine, cystine, N-acetylcysteine, homocysteine, reduced and oxidised glutathione, desglycinephytochelatin, and phytochelatins) are described and discussed. These thiol compounds were well separated and detected under optimised HPLC-electrochemical detection conditions (mobile phase: 80 mM trifluoroacetic acid and methanol with a gradient profile starting at 97:3 (TFA:methanol), kept constant for the first 8 min, then decreasing to 85:15 during one minute, kept constant for 8 min, and finally increasing linearly up to 97:3 from 17 to 18 min; the flow rate was 0.8 mL/min, column and detector temperature 25 degrees C, and the electrode potential 900 mV). We were able to determine tens of femtomoles (3 S/N) of the thiols per injection (5 microL), except for phytochelatin5 whose detection limit was 2.1 pmole. This technique was consequently used for simultaneous determination of compounds of interest in biological samples (maize tissue and human blood serum).     

Low-threshold lasing eigenmodes of an infinite periodic chain of quantum wires

We study the lasing eigenvalue problems for a periodic open optical resonator made of an infinite grating of circular dielectric cylinders standing in free space, in the E- and H-polarization modes. If possessing a "negative-absorption" refractive index, such cylinders model a chain of quantum wires made of the gain material under pumping. The initial-guess values for the lasing frequencies are provided by the plane-wave scattering problems. We demonstrate a new effect: the existence of specific grating eigenmodes that have a low threshold of lasing even if the wires are optically very thin.     

A note on generating <Emphasis Type="Italic">P</Emphasis>-matrices

We prove that for any \({A,B\in\mathbb{R}^{n\times n}}\) such that each matrix S satisfying min(A, B) ≤ S ≤ max(A, B) is nonsingular, all four matrices A ^?1 B, AB ^?1, B ^?1 A and BA ^?1 are P-matrices. A practical method for generating P-matrices is drawn from this result.     

Self-assembled molecular rafts at liquid|liquid interfaces for four-electron oxygen reduction

The self-assembly of the oppositely charged water-soluble porphyrins, cobalt tetramethylpyridinium porphyrin (CoTMPyP(4+)) and cobalt tetrasulphonatophenyl porphyrin (CoTPPS(4-)), at the interface with an organic solvent to form molecular "rafts", provides an excellent catalyst to perform the interfacial four-electron reduction of oxygen by lipophilic electron donors such as tetrathiafulvalene (TTF). The catalytic activity and selectivity of the self-assembled catalyst toward the four-electron pathway was found to be as good as that of the Pacman type cofacial cobalt porphyrins. The assembly has been characterized by UV-visible spectroscopy, Surface Second Harmonic Generation, and Scanning Electron Microscopy. Density functional theory calculations confirm the possibility of formation of the catalytic CoTMPyP(4+)/ CoTPPS(4-) complex and its capability to bind oxygen.     

Binary and ternary recombination of para-H3(+) and ortho-H3(+) with electrons: state selective study at 77-200 K

Measurements in H(3)(+) afterglow plasmas with spectroscopically determined relative abundances of H(3)(+) ions in the para-nuclear and ortho-nuclear spin states provide clear evidence that at low temperatures (77-200 K) para-H(3)(+) ions recombine significantly faster with electrons than ions in the ortho state, in agreement with a recent theoretical prediction. The cavity ring-down absorption spectroscopy used here provides an in situ determination of the para/ortho abundance ratio and yields additional information on the translational and rotational temperatures of the recombining ions. The results show that H(3)(+) recombination with electrons occurs by both binary recombination and third-body (helium) assisted recombination, and that both the two-body and three-body rate coefficients depend on the nuclear spin states. Electron-stabilized (collisional-radiative) recombination appears to make only a small contribution.     

Modeling nonlinear ultrasound propagation in heterogeneous media with power law absorption using a k-space pseudospectral method

The simulation of nonlinear ultrasound propagation through tissue realistic media has a wide range of practical applications. However, this is a computationally difficult problem due to the large size of the computational domain compared to the acoustic wavelength. Here, the k-space pseudospectral method is used to reduce the number of grid points required per wavelength for accurate simulations. The model is based on coupled first-order acoustic equations valid for nonlinear wave propagation in heterogeneous media with power law absorption. These are derived from the equations of fluid mechanics and include a pressure-density relation that incorporates the effects of nonlinearity, power law absorption, and medium heterogeneities. The additional terms accounting for convective nonlinearity and power law absorption are expressed as spatial gradients making them efficient to numerically encode. The governing equations are then discretized using a k-space pseudospectral technique in which the spatial gradients are computed using the Fourier-collocation method. This increases the accuracy of the gradient calculation and thus relaxes the requirement for dense computational grids compared to conventional finite difference methods. The accuracy and utility of the developed model is demonstrated via several numerical experiments, including the 3D simulation of the beam pattern from a clinical ultrasound probe.     

Weak signal detection in SPC

Changes in the behavior of dynamic systems are detected based on changes in the monitored quantities or their characteristics. This detection usually takes place by monitoring the time evolution of a variable and detecting the change at the time when a predetermined threshold is exceeded. This threshold is determined on the basis of the detection scheme requirements, in particular, the probability of false alarms and the detection rate for the actual change. In some cases, however, a change does not come suddenly, but certain “hints” in the system behavior can be observed that may indicate a future change. For example, an increasing frequency of outliers can result in a sudden permanent change in the signal. The occurrence of some “unusual” frequencies often indicates an imminent change. For example, an increasing correlation value indicates an undesired process status. Detection of these “subliminal” hints can often improve the characteristics of the detection scheme, especially the detection rate for the actual change. In this paper, we will deal with the detection of weak signals in statistical process monitoring using a control chart with adaptive control limits.     

Calculation and analysis of vibrational spectra of PbCl2-Sb2O3-TeO2 glass from first principles

Ternary PbCl₂-Sb₂O₃-TeO₂ system provides promising materials for photonic applications. Glasses in this system are thermally stable, their refraction index is about 2.2 and they are transparent from 400 nm up to 6 μm. The ab initio molecular dynamics (MD) simulations of xPbCl₂-10SbO_3/2−(90-x)TeO₂ glasses (x = 10, 20, 30, 40, and 50) were carried out using density functionals, the plane-wave basis set expansion, and the projector-augment waves (PAW). The resulting glassy structures were analyzed with the help of partial radial distribution functions (RDF) and partial coordination numbers. Good agreement with the available experimental data was confirmed. The axial and equatorial oxygen atoms of TeO₄ trigonal bi-pyramids were distinguished. Vibrational frequencies and their corresponding eigen-modes were found by diagonalization of the dynamical matrix. The simulated vibrational spectra were decomposed to determine the contributions from individual atomic species and some more complex structural features and compared with experimental Raman spectra. The spectral decomposition was carried out by projecting vibrational displacement vectors onto various normal modes of typical symmetric structural units. The method proved to be able to successfully interpret the experimental Raman spectra.     

A residual existence theorem for linear equations

A residual existence theorem for linear equations is proved: if ${A \in \mathbb{R}^{m\times n}}$ , ${b \in \mathbb{R}^{m}}$ and if X is a finite subset of ${\mathbb{R}^{n}}$ satisfying ${{\rm max}_{x \in X}p^T(Ax-b) \geq 0}$ for each ${p \in \mathbb{R}^{m}}$ , then the system of linear equations Ax = b has a solution in the convex hull of X. An application of this result to unique solvability of the absolute value equation Ax + B|x| = b is given.