In situ fabrication of waveguide-compatible glass-embedded silver nanoparticle patterns by masked ion-exchange process

We report a study on the properties of silver nanoparticles formed in glass using a masked silver–sodium ion-exchange technique, a process that has been used to fabricate patterned optical waveguides. Characterizations reveal that spherical nanoparticles with a diameter of 5–10 nm are concentrated below the mask edge at a depth of 50–100 nm from the surface. The amount of nanoparticles and the wavelength of the associated localized surface plasmon resonance can be controlled by the spacing between adjacent mask openings. After gentle etching, the surface morphology of the sample shows well-defined nanoparticle patterns. These closely packed nanoparticles embedded in the glass surface have a potential to be used for high-sensitivity surface enhanced spectroscopy, in a glass waveguide device.     

Study of M4,5N4,5N4,5 auger energy shifts of Cs and I in free CsI molecules

High-resolution electron beam excited M_4,5N_4,5N_4,5 Auger electron spectra of Cs and I have been measured from CsI vapour. The Auger energies of both Cs and I observed from gaseous CsI are higher than the corresponding free-atom energies due to extra-atomic relaxation. The molecular Auger results have been compared with corresponding photoelectron measurements and free-atom data. Estimates for extra-atomic relaxation energies have been extracted from the changes of the Auger parameter between molecular and atomic species and from the difference between experimental energies and energies calculated with a relativistic Dirac-Fock program, applying the point-charge model for the CsI molecule.     

Passive Systems with a Normal Main Operator and Quasi-selfadjoint Systems

Passive systems with and as an input and output space and as a state space are considered in the case that the main operator on the state space is normal. Basic properties are given and a general unitary similarity result involving some spectral theoretic conditions on the main operator is established. A passive system with is said to be quasi-selfadjoint if ran . The subclass of the Schur class is the class formed by all transfer functions of quasi-selfadjoint passive systems. The subclass is characterized and minimal passive quasi-selfadjoint realizations are studied. The connection between the transfer function belonging to the subclass and the Q-function of T is given. Received: December 16, 2007., Accepted: March 4, 2008.     

A new,facile synthesis of the 3-methyl-2(5H)-furanoid structural unit from ketones

The 3-methyl-2(5H)-furanoid structural unit is prepared from ketones via 1,4-rearrangement of siloxyalkenes on peroxidation and via oxetene rearrangement of 1-diethylaminopropyne in 53–58% overall yield.     

Trace Element Determination in Diesel Particulates by Total-Reflection X-Ray Fluorescence Analysis

 Particulate matter of Diesel emissions collected from diluted exhaust during standard test runs with two Diesel fuels of different sulfur content was analysed by total-reflection X-ray fluorescence (TXRF). The trace elements determined were S, Ca, Cr, Mn, Fe, Ni, Cu, Zn and Pb. Additionally, some filter materials were tested with respect to their applicability for sample collection. Quartz fibre filters were found to be most suitable, both from a technical and a chemical point of view. A clear reduction of total particulate emissions during the whole test was observed when the fuel with very low sulfur content was used. In addition, it was found that the wear metal content of particulate matter emitted by a cold engine was higher than that observed during normal engine working temperature. Received September 10, 1998. Revision March 2, 1999     

Chaos in the one-dimensional gravitational three-body problem

We have investigated the appearance of chaos in the one-dimensional Newtonian gravitational three-body system (three masses on a line with -1/r pairwise potential). In the center of mass coordinates this system has two degrees of freedom and can be conveniently studied using Poincare sections. We have concentrated in particular on how the behavior changes when the relative masses of the three bodies change. We consider only the physically more interesting case of negative total energy. For two mass choices we have calculated 18 000 full orbits (with initial states on a 100x180 lattice on the Poincare section) and obtained dwell time distributions. For 105 mass choices we have calculated Poincare maps for 10x18 starting points. Our results show that the Poincare section (and hence the phase space) divides into three well defined regions with orbits of different characteristics: (1) There is a region of fast scattering, with a minimum of pairwise collisions. This region consists of 'scallops' bordering the E=0 line, within a scallop the orbits vary smoothly. The number of the scallops increases as the mass of the central particle decreases. (2) In the chaotic scattering region the interaction times are longer, and both the interaction time and the final state depend sensitively on the starting point on the Poincare section. For both (1) and (2) the initial and final states consist of a binary + single particle. (3) The third region consists of quasiperiodic orbits where the three masses are bound together forever. At the center of the quasiperiodic region there is a periodic orbit discovered (numerically) by Schubart in 1956. The stability of the Schubart orbit turns out to correlate strongly with the global behavior.     

Nevanlinna Functions,Perturbation Formulas,and Triplets of Hilbert Spaces

Let S be a closed symmetric operator with defect numbers (1,1) in a Hilbert space ?? and let A be a selfadjoint operator extension of S in ??. Then S is necessarily a graph restriction of A and the selfadjoint extensions of S can be considered as graph perturbations of A, cf. [8]. Only when S is not densely defined and, in particular, when S is bounded, 5 is given by a domain restriction of A and the graph perturbations reduce to rank one perturbations in the sense of [23]. This happens precisely when the Q - function of S and A belongs to the subclass No of Nevanlinna functions. In this paper we show that by going beyond the Hilbert space ?? the graph perturbations can be interpreted as compressions of rank one perturbations. We present two points of view: either the Hilbert space ?? is given a one-dimensional extension, or the use of Hilbert space triplets associated with A is invoked. If the Q - function of S and A belongs to the subclass N₁ of Nevanlinna functions, then it is convenient to describe the selfadjoint extensions of S including its generalized Friedrichs extension (see [6]) by interpolating the original triplet, cf. [5]. For the case when A is semibounded, see also [4]. We prove some invariance properties, which imply that such an interpolation is independent of the (nonexceptional) extension.     

Double diffusive convection in the diffusive regime

Numerical solutions to convection of a fluid which is heated, and to which salt is introduced from the bottom, have been obtained. Although different in boundary conditions from the conditions in the study of Huppert and Moore, qualitatively the flow investigated here has many features the same as theirs. The differences are discussed and solutions are given for two fluids whose Prandtl numbers are 1 and 7 and ratio of molecular and thermal diffusivities is 0.1. The fields of temperature and salinity, and the stream patterns are shown in contour plots. The saline and thermal Nusselt numbers are given as functions of the thermal Rayleigh number.Nomenclature A aspect ratio of the enclosure - g gravitational acceleration - H the height of the enclosure - k _S molecular diffusivity of salt - k _T molecular diffusivity of heat - N _S averaged saline Nusselt number - N _T averaged thermal Nusselt number - P transported variable of temperature, salinity, or vorticity - p pressure above its hydrostatic value - Pr Prandtl number - velocity vector - R _S saline Rayleigh number - R _T thermal Rayleigh number - S salinity - S slainity difference between the top and the bottom - S ₀ salinity at the top surface - S _r salinity at the reference state=S₀+S/2 - T temperature - T temperature difference between the top and and the bottom - T ₀ temperature at the top surface - T _r temperature at the reference state=T₀+T/2 - t time - u velocity component in the horizontal direction - transport velocity - v velocity component in the vertical direction - W the width of the enclosure - x horizontal coordinate - x mesh size in the horizontal direction - y vertical coordinate Greek Letters coefficient of thermal expansion - coefficient of volumetric expansion produced by salt - kinematic viscosity - ratio of diffusivities - vorticity - density - _r density at the reference state - density difference between the top and the bottom - streamfunction