Indefinite Kasparov Modules and Pseudo-Riemannian Manifolds

We present a definition of indefinite Kasparov modules, a generalisation of unbounded Kasparov modules modelling non-symmetric and non-elliptic (e.g. hyperbolic) operators. Our main theorem shows that to each indefinite Kasparov module we can associate a pair of (genuine) Kasparov modules, and that this process is reversible. We present three examples of our framework: the Dirac operator on a pseudo-Riemannian spin manifold (i.e. a manifold with an indefinite metric); the harmonic oscillator; and the construction via the Kasparov product of an indefinite spectral triple from a family of spectral triples. This last construction corresponds to a foliation of a globally hyperbolic spacetime by spacelike hypersurfaces.     

Photochromism Emergence in N‐Salicylidene p‐Aminobenzenesulfonate Diallylammonium Salts

N‐Salicylidene p‐aminobenzenesulfonate salts were prepared by in situ condensation of p‐aminobenzenesulfonate diallylammonium salt and salicylaldehyde. Modulation of thermo‐ and photochromism was achieved by varying the alkyl chain length of the diallylammonium counter‐cation. A structural–optical properties investigation reveals that both crystal packing and dihedral angle between aromatic rings of the N‐salicylidene aniline switch are not sufficient to predict the occurrence of photochromism in the solid state. The available free space around the N‐salicylidene p‐aminobenzenesulfonate, in addition to the flexibility of the nearby environment, is shown to be of major importance for the cis→trans isomerisation to occur as well as for the stabilisation of the trans‐keto form. Emergence of photochromic properties was determined from the diallylhexylammonium cation within the series of investigated counter‐cations. High stability is observed for the trans‐keto form of one polymorph of N‐salicylidene p‐aminobenzenesulfonate diallylhexylammonium salt (k=2.4×10^?7 s^?1).     

Modelling of Unsteady Transition in Low-Pressure Turbine Blade Flows with Two Dynamic Intermittency Equations

A transition model for describing wake-induced transition is presented based on the SST turbulence model by Menter and two dynamic equations for intermittency: one for near-wall intermittency and one for free-stream intermittency. In the Navier-Stokes equations, the total intermittency factor, which is the sum of the two, multiplies the turbulent viscosity computed by the turbulence model. The quality of the transition model is illustrated on the T106A test cascade for two Reynolds numbers, using experimental results by Stieger and Hodson for transition mainly due to kinematic wake impact on a separation bubble. The quality of the model is also revealed on the T106D test cascade using experimental results from Hilgenfeld, Stadtmuller and Fottner for wake turbulence induced transition. The test cases differ in pitch to chord ratio, Reynolds number and inlet free-stream turbulence intensity, causing different transition mechanisms. The unsteady results are presented in space-time diagrams of shape factor and wall shear stress on the suction side. The results show the capability of the model to capture the physics of unsteady transition in separated state. Inevitable shortcomings are revealed as well.     

An easily accessible isoindigo-based polymer for high-performance polymer solar cells

A new, low-band-gap alternating copolymer consisting of terthiophene and isoindigo has been designed and synthesized. Solar cells based on this polymer and PC(71)BM show a power conversion efficiency of 6.3%, which is a record for polymer solar cells based on a polymer with an optical band gap below 1.5 eV. This work demonstrates the great potential of isoindigo moieties as electron-deficient units for building donor-acceptor-type polymers for high-performance polymer solar cells.     

Spin transition charted in a fluorophore-tagged thermochromic dinuclear iron(II) complex

The first crystal structures of a dinuclear iron(II) complex with three N1,N2-1,2,4-triazole bridges in the high-spin and low-spin states are reported. Its sharp spin transition, which was probed using X-ray, calorimetric, magnetic, and (57)Fe Mossbauer analyses, is also delineated in the crystalline state by variable-temperature fluorimetry for the first time.     

Thermal and optical behaviour of octa-alkoxy substituted phthalocyaninatovanadyl complexes

This paper deals with the synthesis of vanadyl phthalocyanines substituted with eight alkoxy chains in the peripheral (2, 3, 9, 10, 16, 17, 23, 24) positions. The alkoxy chain length was varied, and octa-octyloxy (C₈H₁₇O), octa-dodecyloxy (C₁₂H₂₅O) and octa-hexadecyloxy (C₁₆H₃₃O) substituted vanadyl phthalocyanine complexes were prepared. Studies by polarizing optical microscopy and small angle X-ray diffraction (XRD) revealed that all the complexes are liquid crystalline and that these metallomesogens exhibit a columnar phase. The symmetry of the 2D lattice is rectangular, with a ^c 2 ^mm space group, as determined by the indexation of the XRD reflections; hence a rectangular columnar phase (Col_r) was assigned. A double periodicity, although weak, along the axis of the columns was found, which indicates some degree of pairing or dimerization. A tentative explanation based on an antiferroelectric stacking is given. Transition enthalpies were determined by differential scanning calorimetry. The compounds start to decompose above 250°C before reaching the clearing temperatures. A significant bathochromic shift of the Q-band in the UV/Vis spectra of the vanadyl complexes compared with the metal-free ligands and other metallophthalocyanines (M=Co^II, Ni^II, Cu^II, Zn^II) was also observed.     

Mesophase behaviour and thermal stability of octa-alkoxy substituted phthalocyaninatocobalt (II) complexes

Cobalt (II) phthalocyanines substituted with eight alkoxy chains in the peripheral (2, 3, 9, 10, 16, 17, 23, 24) positions were prepared. The alkoxy chain length was varied between n-butyloxy (C₄H₉O) and n-octadecyloxy (C₁₈H₃₇O). Studies by polarizing optical microscopy and high temperature X-ray diffraction revealed that all the complexes are liquid crystalline and that they exhibit a hexagonal columnar mesophase (Col_h). Transition enthalpies were determined by differential scanning calorimetry. The clearing point could only be observed for compounds with a chain length longer than C₁₃H₂₇O. Both the melting and clearing points decrease with increasing chain length. The transition temperatures of these discotic metallomesogens are higher than those of the corresponding metal-free phthalocyanines, but are comparable with those of the corresponding copper (II) compounds. The thermal decomposition of the compounds was studied by thermogravimetry.     

Trimetallic Nickel–Lanthanum and Nickel–Gadolinium Metallomesogens

Adducts were formed between a mesomorphic Ni(salen) complex [salen=2,2′-N,N′-bis(salicylidene)ethylenediamine] with six terminal alkoxy chains and a lanthanide nitrate (Ln=La, Gd). Different alkoxy chain lengths were used: OC¹²H²⁵, OC¹⁴H²⁹, OC¹⁶H³³ and OC¹⁸H³⁷. Trinuclear nickel–lanthanum and nickel–gadolinium complexes [Ln(NO³)³{Ni(salen)}²] were obtained. The compounds exhibit a wide-temperature-range hexagonal columnar mesophase (Col^H) with rather low melting points. The mesophase stability ranges of both the parent nickel complexes and the nickel–lanthanide complexes decrease with increasing chain length. A decrease in the mesophase stability range over the lanthanide series was also observed. The results are compared with those of similar copper–lanthanide complexes. A marked difference is the higher thermal stability of the nickel–lanthanide complexes in comparison with the copper–lanthanide complexes.     

Reactivity of Cobalt-Fullerene Complexes towards Deuterium

The adsorption of molecular deuterium (D₂) onto charged cobalt-fullerene-complexes Co_nC₆₀⁺ (n=1–8) is measured experimentally in a few-collision reaction cell. The reactivity is strongly size-dependent, hinting at clustering of the transition metal atoms on the fullerenes. Formation and desorption rate constants are obtained from the pressure-dependent deuterogenation curves. DFT calculations indeed find that this transition metal clustering is energetically more favorable than decorating the fullerene. For n=1, D₂ is predicted to bind molecularly and for n=2 dissociative and molecular configurations are quasi-isoenergetic. For n=3–8, dissociation of D₂ is thermodynamically preferred. However, reaching the ground state configuration with dissociated deuterium on the timescale of the experiment may be hindered by dissociation barriers.     

Relative Energies for Non-Gibbsian States

We investigate the suggestion of R.L. Dobrushin, that for many examples of non-Gibbsian measures, a well-defined interaction potential can still be derived. Such an interaction cannot be absolutely summable, uniformly in all configurations. Rather there will exist a typical set of configurations on which the interaction decays sufficiently fast. We show how to construct an interaction, using quite elementary methods, for example of the restriction of the Ising pure phases to one layer of the lattice. We sketch a general setup, showing that there is an intimate relation between the problem treated here and the decay of correlations in certain disordered systems. Received: 27 March 1996 / Accepted: 29 July 1996