On the diffusion equation and diffusion wavelets on flat cylinders and the n‐torus

In this paper we study the solutions to the diffusion equation on some conformally flat cylinders and on the n‐torus. Using the Clifford algebra calculus with an appropriate Witt basis, the solutions can be expressed as multiperiodic eigensolutions to the parabolic Dirac operator. We study their fundamental properties, give representation formulas of all these solutions and develop some integral representation formulas. In particular we set up a Green type formula for the solutions to the homogeneous diffusion equation on cylinders and tori. Then we also treat the inhomogeneous diffusion equation diffusion with prescribed boundary conditions in Lipschitz domains on these manifolds. As main application, we construct well localized diffusion wavelets on this class of cylinders and tori by means of multiperiodic eigensolutions to the parabolic Dirac operator. We round off with presenting some concrete numerical simulations for the three dimensional case. Copyright © 2010 John Wiley & Sons, Ltd.     

Design for Minimum Stress Concentration by Finite Elements and Linear Programming

The problem of design for minimum stress concentration is highly nonlinear and must be solved iteratively. Each iteration (redesign) involves three steps: an analysis of the stresses for a design, a sensitivity analysis corresponding to possible changes in this design, and the decision of redesign. For stress analysis, the FEM is a unified approach which is applied in the present paper to axisymmetric solids that are also subjected to nonaxisymmetric loads. The decision of redesign is a linear programming problem and can thus be solved with the Simplex algorithm. The introduction of move-limits to the formulation is of major importance. The optimization approach is described in general, but most of the paper concentrates on a specific example and shows optimum shapes of a shoulder fillet in a stepped bar. Loads are bending, tension, or torsion, and the stress concentrations are considerably reduced.     

Base-assisted one-pot synthesis of N,N',N"-triaryltriazatriangulenium dyes: enhanced fluorescence efficiency by steric constraints

In this paper we report the first synthesis of cationic N,N',N"-triaryltriazatriangulenium dyes (Ar(3)-TATA(+)). Previously, only alkyl-substituted triazatriangulenium derivatives (R(3)-TATA(+)) were known, a consequence of the low reactivity of anilines in the aromatic nucleophilic substitution reaction leading to the formation of the TATA(+) core. The synthesis of Ar(3)-TATA(+) was achieved by heating the tris(2,6-dimethoxyphenyl)methylium ion (DMP(3)C(+)) in various anilines in the presence of NaH. In the solvent-free reaction all three aryl substituents could be introduced despite the low reactivity of the anilines. The symmetric Ar(3)-TATA(+) derivatives with Ar = phenyl (2), 4-methoxyphenyl (3), and 4-bromophenyl (4) were synthesized. Single crystal structures of 2 and 4 were obtained as BF(4)(-) salts, where torsional angles larger than 80° were observed between the TATA(+) chromophore and the aryl substituents. The photophysical properties were studied in solution and in thin films. The results show that the Ar(3)-TATA(+) dyes have a surprising 3-fold increase in fluorescence quantum yields when compared to the parent alkyl-substituted R(3)-TATA(+) salts. With a high quantum yield (>50%) and emission in the red (λ(fl) = 560 nm) the Ar(3)-TATA(+) dyes represent a promising new addition to the family of superstable cationic triangulenium dyes. Additionally, the synthesized tribromo derivative 4 is shown to be a potential triagonal synthon for polymers and other macromolecules.     

Molecular junctions based on SAMs of cruciform oligo(phenylene ethynylene)s

Cruciform oligo(phenylene ethynylene)s (OPEs) with an extended tetrathiafulvalene (TTF) donor moiety (OPE5-TTF and OPE3-TTF) and their simple analogues (OPE5-S and OPE3) without conjugated substituents were used to form high-quality self-assembled monolayers (SAMs) on ultraflat gold substrates. Molecular junctions based on these SAMs were investigated using conducting-probe atomic force microscopy (CP-AFM). The TTF substituent changes the molecular orbital energy levels and decreases the HOMO-LUMO energy gap, resulting in a 9-fold increase in conductance for both TTF cruciform OPEs compared to the unsubstituted analogues. The difference in electrical transport properties of the SAMs was reproduced by the theoretical transport calculations for the single molecules.     

Microwave-assisted McMurry polymerization utilizing low-valent titanium for the synthesis of poly 2,6-[1,5-bis(dodecyloxy)naphthylene vinylene] (PNV)

Poly 2,6-[1,5-bis(dodecyloxy)naphthylene vinylene] is synthesized by microwave-assisted McMurry polymerization utilizing low-valent titanium generated from titanium tetrachloride and zinc. The obtained polymer is fluorescent with an average molecular weight of approximately 65,000 g/mol and a polydispersity of M_w/M_n ≈ 3. Absorption and fluorescence spectroscopy in solution and on spin-cast thin films reveal that the bis-alkoxy substituted PNV has a short effective conjugation length but a quite efficient exciton migration.     

Quantifying the working stroke of tetrathiafulvalene-based electrochemically-driven linear motor-molecules

A highly constrained [2]rotaxane, constructed in such a way that the tetracationic cyclobis(paraquat-p-phenylene) ring is restricted to reside on a monopyrrolotetrathiafulvalene unit, has been synthesised and characterised. This design allows the deslipping free energy barrier for the tetracationic ring in all three redox states of the rotaxane to be determined.     

Locking down the electronic structure of (monopyrrolo)tetrathiafulvalene in [2]rotaxanes

[reaction: see text] The redox potentials of a highly constrained [2]rotaxane have been measured and used to model the energy of the HOMO of tetrathiafulvalene-based bistable [2]rotaxanes in their two co-conformationally isomeric states. Restrained from co-conformational movements, the measured oxidation and reduction potentials provide insights into the orbital energies and electronic structure of a (monopyrrolo)tetrathiafulvalene unit when encircled by a tetracationic cyclobis(paraquat-p-phenylene) ring.