Some fundamental transmission properties of impedance transitions

Reflection and transmission of waves by impedance transitions from a constant input to a constant output characteristic impedence are considered. Several fundamental properties are explored, primarily for impedance transitions with piece-wise constant characteristic impedance in an arbitrary number N of intervals of equal length. For example, the following properties are shown: (i) The relative momentum transmission depends only on the ratio of output to input characteristic impedance. (ii) For a given impedance transition there are at most, and generally exactly, 2^N different transitions, including the original one, with identical transmission properties. (iii) For monotoneous impedance transitions the efficiency of energy transmission is minimized by one with an abrupt change in characteristic impedance. (iv) There exists an optimal impedance transition, with a certain antisymmetry, which maximizes the efficiency of energy transmission for a given incident wave of finite duration and energy. Several of the results can be extended to more general classes of impedence transitions. Simple illustrative examples are given.     

Construction of compactp-wavelets

In [D1] the method for construction of compact wavelets, based on a decimation by 2, was introduced. In [CW] and [A] decimation by an integer different from 2 is discussed but construction for a generalp is not completely treated. Here we review some of the elements of that construction and give an approach that generalizes to thep>2 case in a concrete fashion which requires some new ideas.     

Solution behavior of sulfonate ionomer interpolymer complexes

The interaction of metal sulfonate ionomers with polymers containing low levels of amines has been investigated in solution. For example, zinc sulfo EPDM and a styrene/vinyl pyridine copolymer form such complexes over broad concentration ranges. The resultant solutions offer enhanced viscosities at dilute polymer concentrations. At high polymer levels solutions based on these complexes are lower in viscosity than the ionomer alone. These interpolymer complexes have been shown to exhibit an improved property/rheology balance in bulk systems. In solution, polymer complexes provide control of hydrocarbon solution viscosity not available with conventional polymers. Reduced viscosity-concentration studies suggest that these polymer complexes are a result of the amine-containing polymer interacting with intramolecular-associated ionomer coils, which at higher concentrations form a pseudonetwork.     

Parametric Excitation of Electromagnetic Fields by two Pump Waves

A collisionless plasma in the presence of two monochromatic electric fields is considered. By means of a kinetic analysis, a dispersion relation that governs the excitation of transverse electromagnetic fluctuations is derived and analysed.     

Lactone polymers. II. Hydrodynamic properties and unperturbed dimensions of poly-ε-caprolactone

Poly-ε-caprolactone prepared by a dibutylzinc-catalyzed bulk polymerization process was fractionated, and the solution properties of the fractions were studied in benzene and in dimethylformamide. In these solvents at 30°C the Mark-Houwink relations were [η] = 9.94 × 10^?5 M and [η] = 1.91 × 10^?4 M , respectively. The value of K_Θ was found to vary from 1.1 to 1.2 × 10^?3 when determined by three known extrapolation techniques. Poly-ε-caprolactone chains appear to be quite flexible in solution, and the steric hindrance parameter σ had the low value of 1.37. Root-mean-square end-to-end dimensions were approximated from the experimental data and calculated from the Debye-Bueche and the Kirkwood-Riseman theories.     

Cost and sensitivity of restricted active‐space calculations of metal L‐edge X‐ray absorption spectra

The restricted active‐space (RAS) approach can accurately simulate metal L‐edge X‐ray absorption spectra of first‐row transition metal complexes without the use of any fitting parameters. These characteristics provide a unique capability to identify unknown chemical species and to analyze their electronic structure. To find the best balance between cost and accuracy, the sensitivity of the simulated spectra with respect to the method variables has been tested for two models, [FeCl₆]^3– and [Fe(CN)₆]^3–. For these systems, the reference calculations give deviations, when compared with experiment, of ≤1 eV in peak positions, ≤30% for the relative intensity of major peaks, and ≤50% for minor peaks. When compared with these deviations, the simulated spectra are sensitive to the number of final states, the inclusion of dynamical correlation, and the ionization potential electron affinity shift, in addition to the selection of the active space. The spectra are less sensitive to the quality of the basis set and even a double‐ζ basis gives reasonable results. The inclusion of dynamical correlation through second‐order perturbation theory can be done efficiently using the state‐specific formalism without correlating the core orbitals. Although these observations are not directly transferable to other systems, they can, together with a cost analysis, aid in the design of RAS models and help to extend the use of this powerful approach to a wider range of transition metal systems. © 2015 Wiley Periodicals, Inc.     

Self-assembly of cationic surfactants that contain thioether groups in the hydrophobic tails

Self-assembly in aqueous solutions of cationic surfactants that carry thioether groups in their hydrophobic tails has been investigated. Of particular interest was the identification of possible changes in the aggregate structure due to the presence of sulfur atoms. Solutions of four different compounds [CH(3)CH(2)S(CH(2))(10)N(CH(3))(3)(+)Br(-) (2-10), CH(3)(CH(2))(5)S(CH(2))(6)N(CH(3))(3)(+)Br(-) (6-6), CH(3)(CH(2))(7)S(CH(2))(6)N(CH(3))(3)(+)Br(-) (8-6), and CH(3)(CH(2))(7)S(CH(2))(8)N(CH(3))(3)(+)Br(-) (8-8)] were characterized by (1)H NMR, (13)C NMR, NMR diffusometry, and conductivity measurements. In addition to investigating aqueous solutions containing each of the thioethers present as the sole solute, mixtures of 2-10 or 6-6 with dodecyltrimethylammonium bromide (DTAB) were studied. The addition of a sulfide group to the hydrophobic tail causes an increase in the critical micelle concentration but has a limited effect on the aggregate structure. Micelles are formed at a well-defined concentration for all of the investigated surfactants and surfactant mixtures. However, a comparison of the behavior of concentrated solutions of 8-8 to that of solutions of hexadecyltrimethylammonium bromide (CTAB) of similar concentrations suggests that the presence of a sulfur atom decreases the tendency for micellar growth. This may be a consequence of a slightly higher preference for the micellar surface of a sulfur atom as compared to that of a methylene group in a similar position, an idea that is also supported by results for the surfactant mixtures.