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.     

The origin for tubular growth of TiO2 nanotubes: A fluoride rich layer between tube-walls

High resolution Scanning Auger Electron Spectroscopy (AES) is used to demonstrate the compositional variation across self-organized TiO₂ nanotube layers grown in fluoride containing ethylene glycol electrolytes. The analysis results show a distinct fluoride rich layer in between the TiO₂ nanotubes and particularly in the triple points of the hexagonally ordered nanotubular arrays. AES analysis further revealed that extended e-beam exposure leads to a decrease in the fluoride signal (electron beam induced decomposition of fluoride species). The proof of the existence of a fluoride rich layer located between the tube walls strongly supports fluoride dissolution as the reason for a transition from a porous to a tubular morphology.     

High-pressure phase equilibrium calculations for carbon dioxide + cyclopentane binary system

The phase behavior of the carbon dioxide + cycloalkane mixtures usually receives low attention, though these systems are important for many industries, e.g. the carbon capture and storage. In this paper calculations results for the carbon dioxide + cyclopentane binary system are presented, based on SRK and PR cubic equations of state with classical van der Waals mixing rules. A single set of binary parameters for each model was proposed to predict the global phase behavior of the system in a wide range of pressure and temperature. Albeit the thermodynamic models used are simple, they are able to represent fairly well the phase behavior of the system analyzed in this paper.

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Bi-convexity and bi-martingales

A set in a product spaceX×Y isbi-convex if all itsx- andy-sections are convex. Abi-martingale is a martingale with values inX×Y whosex- andy-coordinates change only one at a time. This paper investigates the limiting behavior of bimartingales in terms of thebi-convex hull of a set — the smallest bi-convex set containing it — and of several related concepts generalizing the concept of separation to the bi-convex case. Research partially supported by NSF grants at the Institute for Mathematical Studies in the Social Sciences, Standford University. The second author has also been partially supported by the Deutche Forschungsgemeinschaft. We thank Andreu Mas-Colell, Jean-Francois Mertens, Abraham Neyman and Lloyd S. Shapley for many useful discussions.