Formation of singularities for wave equations including the nonlinear vibrating string

Under very general assumptions, the authors prove that smooth solutions of quasilinear wave equations with small-amplitude periodic initial data always develop singularities in the second derivatives in finite time. One consequence of these results is the fact that all solutions of the classical nonlinear vibrating string equation satisfying either Dirichlet or Neumann boundary conditions and with sufficiently small nontriviai initial data necessarily develop singularities. In particular, there are no nontrivial smooth small-amplitude time-periodic solutions.     

Effects of peripheral substituents and axial ligands on the electronic structure and properties of iron phthalocyanine

The effects of peripheral substituents and axial ligands on the electronic structure and properties of iron phthalocyanine, H(16)PcFe, have been investigated using a DFT method. Substitution by electron-withdrawing fluorinated groups alters the ground state of H(16)PcFe and gives rise to large changes in the ionization potentials and electron affinity. For the six-coordinate adducts with acetone, H(2)O, and pyridine, the axial coordination of two weak-field ligands leads to an intermediate-spin ground state, while the strong-field ligands make the system diamagnetic. The electronic configuration of a ligated iron phthalocyanine is determined mainly by the axial ligand-field strength but can also be affected by peripheral substituents. Axial ligands also exert an effect on ionization potentials and electron affinity and can, as observed experimentally, even change the site of oxidation/reduction.     

Distinguishing between abstraction and addition as the first step in the reaction of a nitroxyl radical with cyclohexene

An unambiguous method for distinguishing between abstraction-addition and addition-abstraction mechanisms (and mixtures thereof) in the reaction of 4-hydroxy-2,2,6,6-tetramethylpiperidine-N-oxyl with a specifically deuterated cyclohexene, 1,2-dideuteriocyclohexene, is demonstrated.     

Synthesis, structure, and magnetic properties of heterometallic dicyanamide-bridged Cu-Na and Cu-Gd one-dimensional polymers

The monometallic precursors L1Cu and L2Cu (L1H2 standing for 1,3-bis((3-ethoxysalicylidene)amino) propane and L2H2 standing for 1,2-bis((3-methoxysalicylidene)amino) ethane) react with sodium dicyanamide (dca) (NaN3C2), a mixture of gadolinium nitrate, and sodium dicyanamide to yield heterodinuclear L2CuNa(NCNCN) and L1CuGd(NO3)(NCNCN)2 entities. The structural determination shows that two Cu-Na entities are linked by dca with an original mu1,1 coordination mode, evidenced here for the first time, to yield tetranuclear complexes. Two hydrogen bonds operate between the water molecule coordinated to one of the sodium ions and the free nitrogen atoms of two dca ligands, yielding infinite zigzag chains. The structural determination of the Cu-Gd entities indicates that they are held together by two dca ligands, bridging alternately Cu to Gd and Gd to Gd cations, in the more common mu1,5 mode to yield a one-dimensional (1D) network. The dca ligands are not able to transmit interaction between the magnetically active centers in these chains, which are the unique example of structurally characterized Cu-Gd complexes involving dca ligands.     

Long‐time convergence of solutions to a phase‐field system

We prove that any global bounded solution of a phase field model tends to a single equilibrium state for large times though the set of equilibria may contain a nontrivial continuum of stationary states. The problem has a partial variational structure, specifically, only the elliptic part of the first equation represents an Euler–Lagrange equation while the second does not. This requires some modifications in comparison with standard methods used to attack this kind of problems. Copyright © 2001 John Wiley & Sons, Ltd.     

A study of energy dissipation and critical speed of granular flow in a rotating cylinder

Tuned vibration absorbers may improve the safety of flexible structures which are prone to excessive oscillation magnitudes under dynamic loads. A novel absorber design proposes sloshing of granular material in a rotating cylinder where the granular material is the energy dissipating agent. As the conventional dissipative elements require maintenance due to the nature of their function, the new design may represent a virtually maintenance free alternative.     

Bergman and Calderón Projectors for Dirac Operators

For a Dirac operator $D_{\bar{g}}$ over a spin compact Riemannian manifold with boundary $(\bar{X},\bar{g})$ , we give a new construction of the Calderón projector on $\partial\bar{X}$ and of the associated Bergman projector on the space of L ² harmonic spinors on $\bar{X}$ , and we analyze their Schwartz kernels. Our approach is based on the conformal covariance of $D_{\bar{g}}$ and the scattering theory for the Dirac operator associated with the complete conformal metric $g=\bar{g}/\rho^{2}$ where ρ is a smooth function on $\bar{X}$ which equals the distance to the boundary near $\partial\bar{X}$ . We show that $\frac{1}{2}(\operatorname{Id}+\tilde{S}(0))$ is the orthogonal Calderón projector, where $\tilde{S}(\lambda)$ is the holomorphic family in {?(λ)≥0} of normalized scattering operators constructed in Guillarmou et al. (Adv. Math., 225(5):2464–2516, 2010), which are classical pseudo-differential of order 2λ. Finally, we construct natural conformally covariant odd powers of the Dirac operator on any compact spin manifold.     

Conductivity of anodic TiO2 nanotubes: Influence of annealing conditions

The present work reports on the resistivity of anodic TiO₂ nanotubes as function of annealing temperature and atmosphere. Significant effects of several orders of magnitude are observed and explained by different crystallinity and self‐doping level. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synthesis of new 10,11-dihydrodibenzo[a,d]cycloheptene S-thiocarbamate derivatives via a benzylic Newman–Kwart rearrangement

New S-thiocarbamates possessing a 10,11-dihydro-5H-dibenzo[a,d]cycloheptene moiety were obtained unexpectedly in the process of preparing new O-thiocarbamates starting from 5-dibenzosuberol (10,11-dihydro-5H-dibenzo[a,d]cyclohepten-5-ol) and aroyl-isothiocyanates. These compounds were obtained via a benzylic Newman–Kwart rearrangement mechanism. The structures of the new thiocarbamates were confirmed by elemental analysis, IR, and NMR spectroscopy and by X-ray crystallography.