FTIR spectroscopy study of CO adsorption on Pt-Na-mordenite

Different carbonyls are formed after CO adsorption at ambient temperature on a Pt-Na-mordenite (Pt-Na-MOR) sample. Pt(3+)(CO)(2) dicarbonyls (nu(s) at 2205 cm(-1) and nu(as) at 2167 cm(-1)) are decomposed without formation of monocarbonyls. The respective mixed-ligand species, Pt(3+)((12)CO)((13)CO), formed after (12)CO-(13)CO coadsorption, display bands at 2192 and 2131 cm(-1), in excellent agreement with the theoretically calculated values. Pt(2+)-CO species absorb at 2145 cm(-1) and are not able to accept a second CO molecule. Pt(+)-CO carbonyls are characterized by a band at 2111 cm(-1). Under CO equilibrium pressure, these species are converted into dicarbonyls (nu(s) at 2135 cm(-1) and nu(as) at 2101 cm(-1)). The respective mixed-ligand species, Pt(+)((12)CO)((13)CO), manifest bands at 2123 and 2069 cm(-1), in good agreement again with the theory. Different carbonyls of metallic platinum are observed below 2100 cm(-)(1). In addition, weakly adsorbed CO was registered as Na(+)-CO complexes (2177 and 2165 cm(-1)) and Na(+)-OC-Na(+) species (2138 cm(-1)). It was found that during desorption of CO platinum was reduced, ultimately to metal. However, heating in a NO + O(2) mixture leads to reoxidation of the metal particles and restoration of the initial state of the sample.     

Identically conserved currents and their charges

We examine, at a classical level, the features that distinguish dynamically conserved currents from identically conserved ones. Then we prove that, in four spacetime dimensions, the quantum charges corresponding to identically conserved currents always annihilate the vacuum state. We illustrate our discussion with several examples.     

Exponential dichotomies of evolution operators in Banach spaces

This paper considers three dichotomy concepts (exponential dichotomy, uniform exponential dichotomy and strong exponential dichotomy) in the general context of non-invertible evolution operators in Banach spaces. Connections between these concepts are illustrated. Using the notion of Green function, we give necessary conditions and sufficient ones for strong exponential dichotomy. Some illustrative examples are presented to prove that the converse of some implication type theorems are not valid.     

Generalizations of a Theorem of Datko and Pazy

This note gives necessary and sufficient conditions for exponential stability of semigroups of linear operators in Banach spaces. Generalizations of a well-known result due to Datko, Pazy and Neerven are obtained for the case of semigroups of operators that are not strongly continuous.     

Numerical solution of the steady incompressible Navier—Stokes equations for the flow past a sphere by a multigrid defect correction technique

A nested non-linear multigrid algorithm is developed to solve the Navier–Stokes equations which describe the steady incompressible flow past a sphere. The vorticity–streamfunction formulation of the Navier–Stokes equations is chosen. The continuous operators are discretized by an upwind finite difference scheme. Several algorithms are tested as smoothing steps. The multigrid method itself provides only a first-order-accurate solution. To obtain at least second-order accuracy, a defect correction iteration is used as outer iteration. Results are reported for Re = 50, 100, 400 and 1000.     

Surface plasmon polariton assisted optical pulling force

We demonstrate both analytically and numerically the existence of optical pulling forces acting on particles located near plasmonic interfaces. Two main factors contribute to the appearance of this negative recoil force. The interference between the incident and reflected waves induces a rotating dipole with an asymmetric scattering pattern, while the directional excitation of surface plasmon polaritons (SPPs) enhances the linear momentum of scattered light. The strongly asymmetric SPP excitation is determined by spin–orbit coupling of the rotating dipole and surface plasmon polariton. As a result of the total momentum conservation, the force acting on the particle points in a direction opposite to the incident wave propagation. We derive analytical expressions for the force acting on dipolar particles placed in the proximity of plasmonic surfaces. Analytical expressions for this pulling force are derived within the dipole approximation and are in excellent agreement with results of electromagnetic numerical calculations. The forces acting on larger particles are analyzed numerically, beyond the dipole approximation.

     

The Structure of Multiplicative Tilings of the Real Line

Journal of Fourier Analysis and Applications - Suppose $$\Omega , A \subseteq \mathbb {R}\backslash {\left\{ {0}\right\} }$$ are two sets, both of mixed sign, that $$\Omega $$ is Lebesgue...