Ruthenium(II)-CO complexes of N-[(2-pyridyl)methyliden]-alpha(or beta)-aminonaphthalene: Synthesis, spectral studies, crystal structure, redox properties and DFT calculation

The characterization and properties of trans-(X)-[RuX2(CO)(2)(alpha/beta-NaiPy)] (1, 2) (alpha-NaiPy (a), beta-NaiPy (b); X = Cl (1), I (2)) are described in this work. The structures are confirmed by single crystal X-ray diffraction studies. Reaction of these compounds with Me3NO in MeCN has isolated monocarbonyl trans-(X)-RuX2(CO)(MeCN)(alpha/beta-NaiPy)] (3, 4). The complexes show intense emission properties. Quantum yields of 1 and 2 (phi= 0.02-0.08) are higher than 3 and 4 (phi = 0.006-0.015). Voltammogram shows higher Ru(III)/Ru(II) (1.3-1.5 V) potential of 1 and 2 than that of 3 and 4 (0.8-0.9 V) that may be due to coordination of two pi-acidic CO groups in former. The electronic spectra and redox properties of the complexes are compared with the results obtained by density functional theory (DFT) and time-dependent density functional theory (TD-DFT) using polarizable continuum model (CPCM).

Energy identities in water wave theory for free-surface boundary condition with higher-order derivatives

A modified form of Green's integral theorem is employed to derive the energy identity in any water wave diffraction problem in a single-layer fluid for free-surface boundary condition with higher-order derivatives. For a two-layer fluid with free-surface boundary condition involving higher-order derivatives, two forms of energy identities involving transmission and reflection coefficients for any wave diffraction problem are also derived here by the same method. Based on this modified Green's theorem, hydrodynamic relations such as the energy-conservation principle and modified Haskind–Hanaoka relation are derived for radiation and diffraction problems in a single as well as two-layer fluid.

Hanle-Zeeman redistribution matrix. I. Classical theory expressions in the laboratory frame

Polarized scattering in spectral lines is governed by a 4; 4 matrix that describes how the Stokes vector is scattered and redistributed in frequency and direction. Here we develop the theory for this redistribution matrix in the presence of magnetic fields of arbitrary strength and direction. This general magnetic field case is called the Hanle- Zeeman regime, since it covers both of the partially overlapping weak- and strong- field regimes in which the Hanle and Zeeman effects dominate the scattering polarization. In this general regime, the angle-frequency correlations that describe the so-called partial frequency redistribution (PRD) are intimately coupled to the polarization properties. We develop the theory for the PRD redistribution matrix in this general case and explore its detailed mathematical properties and symmetries for the case of a J = 0 -> 1 -> 0 scattering transition, which can be treated in terms of time-dependent classical oscillator theory. It is shown how the redistribution matrix can be expressed as a linear superposition of coherent and noncoherent parts, each of which contain the magnetic redistribution functions that resemble the well- known Hummer- type functions. We also show how the classical theory can be extended to treat atomic and molecular scattering transitions for any combinations of quantum numbers.

Theory of the unusual doping and temperature dependence of photoemission spectra in manganites

A recent, major, puzzle in the core-level photoemission spectra of doped manganites is the observation of a 1–2 eV wide shoulder with intensity varying with temperature T as the square of the magnetization over a T scale of order 200 K, an order of magnitude less than electronic energies. This is addressed and resolved here, by extending a recently proposed two-fluid polaron–mobile electron model for these systems to include core-hole effects. The position of the shoulder is found to be determined by Coulomb and Jahn-Teller energies, while its spectral weight is determined by the mobile electron energetics which is strongly T and doping dependent, due to annealed disorder scattering from the polarons and the t2g core spins. Our theory accounts quantitatively for the observed T dependence of the difference spectra, and furthermore, explains the observed correspondence between spectral changes due to increasing doping and decreasing T.

A nonlinear theory of wake development

A simple new series, using an expansion of the velocity profile in parabolic cylinder functions, has been developed to describe the nonlinear evolution of a steady, laminar, incompressible wake from a given arbitrary initial profile. The first term in this series is itself found to provide a very satisfactory prediction of the decay of the maximum velocity defect in the wake behind a flat plate or aft of the recirculation zone behind a symmetric blunt body. A detailed analysis, including higher order terms, has been made of the flat plate wake with a Blasius profile at the trailing edge. The same method yields, as a special case, complete results for the development of linearized wakes with arbitrary initial profile under the influence of arbitrary pressure gradients. Finally, for purposes of comparison, a simple approximate solution is obtained using momentum integral methods, and found to predict satisfactorily the decay of the maximum velocity defect. © 1970 Wolters-Noordhoff Publishing.

Wave propagation analysis in carbon nanotube embedded composite using wavelet based spectral finite elements

In this paper, elastic wave propagation is studied in a nanocomposite reinforced with multiwall carbon nanotubes (CNTs). Analysis is performed on a representative volume element of square cross section. The frequency content of the exciting signal is at the terahertz level. Here, the composite is modeled as a higher order shear deformable beam using layerwise theory, to account for partial shear stress transfer between the CNTs and the matrix. The walls of the multiwall CNTs are considered to be connected throughout their length by distributed springs, whose stiffness is governed by the van der Waals force acting between the walls of nanotubes. The analyses in both the frequency and time domains are done using the wavelet-based spectral finite element method (WSFEM). The method uses the Daubechies wavelet basis approximation in time to reduce the governing PDE to a set of ODEs. These transformed ODEs are solved using a finite element (FE) technique by deriving an exact interpolating function in the transformed domain to obtain the exact dynamic stiffness matrix. Numerical analyses are performed to study the spectrum and dispersion relations for different matrix materials and also for different beam models. The effects of partial shear stress transfer between CNTs and matrix on the frequency response function (FRF) and the time response due to broadband impulse loading are investigated for different matrix materials. The simultaneous existence of four coupled propagating modes in a double-walled CNT-composite is also captured using modulated sinusoidal excitation.

Infrared Spectra of Dimethylquinolines in the Gas Phase: Experiment and Theory

Infrared spectra of atmospherically important dimethylquinolines (DMQs), namely 2,4-DMQ, 2,6-DMQ, 2,7-DMQ, and 2,8-DMQ in the gas phase at 80 degrees C were recorded using a long variable path-length cell. DFT calculations were carried out to assign the bands in the experimentally observed spectra at the B3LYP/6-31G* level of theory. The spectral assignments particularly for the C-H stretching modes could not be made unambiguously using calculated anharmonic or scaled harmonic frequencies. To resolve this problem, a scaled force field method of assignment was used. Assignment of fundamental modes was confirmed by potential energy distributions (PEDs) of the normal modes derived by the scaled force fields using a modified version of the UMAT program in the QCPE package. We demonstrate that for large molecules such as the DMQs, the scaling of the force field is more effective in arriving at the correct assignment of the fundamentals for a quantitative vibrational analysis. An error analysis of the mean deviation of the calculated harmonic, anharmonic, and force field fitted frequencies from the observed frequency provides strong evidence for the correctness of the assignment.

Gauge theory of a group of diffeomorphisms. III. The fiber bundle description

A new fiber bundle approach to the gauge theory of a group G that involves space‐time symmetries as well as internal symmetries is presented. The ungauged group G is regarded as the group of left translations on a fiber bundle G(G/H,H), where H is a closed subgroup and G/H is space‐time. The Yang–Mills potential is the pullback of the Maurer–Cartan form and the Yang–Mills fields are zero. More general diffeomorphisms on the bundle space are then identified as the appropriate gauged generalizations of the left translations, and the Yang–Mills potential is identified as the pullback of the dual of a certain kind of vielbein on the group manifold. The Yang–Mills fields include a torsion on space‐time.

Eigenvalues of kinematical conservation laws (KCL) based 3-D weakly nonlinear ray theory (WNLRT)

System of kinematical conservation laws (KCL) govern evolution of a curve in a plane or a surface in space, even if the curve or the surface has singularities on it. In our recent publication K. R. Arun, P. Prasad, 3-D kinematical conservation laws (KCL): evolution of a surface in R-3-in particular propagation of a nonlinear wavefront, Wave Motion 46 (2009) 293-311] we have developed a mathematical theory to study the successive positions and geometry of a 3-D weakly nonlinear wavefront by adding an energy transport equation to KCL. The 7 x 7 system of equations of this KCL based 3-D weakly nonlinear ray theory (WNLRT) is quite complex and explicit expressions for its two nonzero eigenvalues could not be obtained before. In this short note, we use two different methods: (i) the equivalence of KCL and ray equations and (ii) the transformation of surface coordinates, to derive the same exact expressions for these eigenvalues. The explicit expressions for nonzero eigenvalues are important also for checking stability of any numerical scheme to solve 3-D WNLRT. (C) 2010 Elsevier Inc. All rights reserved.

Spectral Invariance of SG Pseudo-Differential Operators on L-P(R-n)

We prove the spectral invariance of SG pseudo-differential operators on L-P(R-n), 1 < p < infinity, by using the equivalence of ellipticity and Fredholmness of SG pseudo-differential operators on L-p(R-n), 1 < p < infinity. A key ingredient in the proof is the spectral invariance of SC pseudo-differential operators on L-2(R-n).

On the Nash-Williams′ Lemma in Graph Reconstruction Theory

A generalization of Nash-Williams′ lemma is proved for the Structure of m-uniform null (m − k)-designs. It is then applied to various graph reconstruction problems. A short combinatorial proof of the edge reconstructibility of digraphs having regular underlying undirected graphs (e.g., tournaments) is given. A type of Nash-Williams′ lemma is conjectured for the vertex reconstruction problem.