Approximating <Emphasis Type="Italic">J</Emphasis>-holomorphic curves by holomorphic ones

Given an almost complex structure J in a cylinder of (p > 1) together with a compatible symplectic form and given an arbitrary J-holomorphic curve without boundary in that cylinder, we construct an holomorphic perturbation of , for the canonical complex structure J ₀ of , such that the distance between these two curves in W ^1,2 and norms, in a sub-cylinder, are controled by quantities depending on J, and by the area of only. These estimates depend neither on the topology nor on the conformal class of . They are key tools in the recent proof of the regularity of 1-1 integral currents in [RT].Received: 2 October 2003, Accepted: 18 November 2003, Published online: 25 February 2004     

Thermoelectric efficiency and compatibility

The intensive reduced efficiency eta(r) is derived for thermoelectric power generation (in one dimension) from intensive fields and currents, giving eta(r)=(E x J) divided by (- inverted Delta)T x J(S). The overall efficiency is derivable from a thermodynamic state function, Phi=1 divided by u + alphaT, where we introduce u=J divided by kappa (inverted Delta)T as the relative current density. The method simplifies the computation and clarifies the physics behind thermoelectric devices by revealing a new materials property s=(sqrt[1+zT]-1) divided by (alphaT), which we call the compatibility factor. Materials with dissimilar compatibility factors cannot be combined by segmentation into an efficient thermoelectric generator because of constraints imposed on u. Thus, control of the compatibility factor s is, in addition to z, essential for efficient operation of a thermoelectric device, and thus will facilitate rational materials selection, device design, and the engineering of functionally graded materials.     

Magnetization and specific heat of DyFe3(BO3)4 single crystal

We present thermodynamic and magnetic studies of single crystalline DyFe₃(BO₃)₄. The data indicate an easy axis antiferromagnetic order below T_N~ 38 K which we attribute to the Fe subsystem. The Dy subsystem remains paramagnetic down to the lowest investigated temperatures of 2 K, but it is polarized by the Fe spins due to a f-d interaction. External magnetic field leads to a spin-flop transition in the iron subsystem as well as to superposed magnetization in the Dy subsystem. The repopulation of two low-lying Kramers doublets in Dy³⁺ ions results in well defined Schottky anomalies in specific heat and magnetization.     

Calabi-Yau manifolds as complete intersections in products of complex projective spaces

We consider constructions of manifolds withSU(3) holonomy as embedded in products of complex projective spaces by imposing certain homogeneous holomorphic constraints. We prove that every such construction leads to one deformation class of manifolds withSU(3) holonomy. For a subset of these manifolds we prove simple connectedness, address the problem of calculating the second Betti number and explicitly calculate it for a class of constructions. This establishes a very wide class of manifolds withSU(3) holonomy, that can give rise to yet many more constructions via dividing out the action of suitably chosen discrete groups. Some of the examples studied may yield phenomenologically acceptable models.     

Metal-acetylide addition to tetracyanoethylene

Two push-pull chromophores that have shown utility in the field of molecular electronics and non-linear optics are DDMEBT (1, 2-(4-dimethylamino)phenyl)-3-((4-(dimethylamino)phenyl)ethynyl)buta-1,3-diene-1,1,4,4-tetracarbonitrile) and TDMEE (2, 4-(4-dimethylamino)phenyl)but-1-en-3-yne-1,1,2-tricarbonitrile). Unfortunately, the methods reported for their synthesis give variable yields, use toxic solvents, and only provide small amounts of material. We report improved synthetic protocols, providing access to larger quantities of material. By investigating multiple metal-acetylides of 4-ethynyl-N,N-dimethylaniline and their subsequent addition to TCNE, we obtained various products depending on the identity of the metal ion. This led to the simple synthesis of push-pull chromophoric compounds.     

Deformable two-dimensional photonic crystal slab for cavity optomechanics

We have designed photonic crystal suspended membranes with optimized optical and mechanical properties for cavity optomechanics. Such resonators sustain vibration modes in the megahertz range with quality factors of a few thousand. Thanks to a two-dimensional square lattice of holes, their reflectivity at normal incidence at 1064?nm reaches values as high as 95%. These two features, combined with the very low mass of the membrane, open the way to the use of such periodic structures as deformable end mirrors in Fabry-Perot cavities for the investigation of cavity optomechanical effects.     

Nanopatterns of molecular spoked wheels as giant homologues of benzene tricarboxylic acids

Molecular spoked wheels with D_3h and C_s symmetry are synthesized by Vollhardt trimerization of C_2v-symmetric dumbbell structures with central acetylene units and subsequent intramolecular ring closure. Scanning tunneling microscopy of the D_3h-symmetric species at the solid/liquid interface on graphite reveals triporous chiral honeycomb nanopatterns in which the alkoxy side chains dominate the packing over the carboxylic acid groups, which remain unpaired. In contrast, C_s-symmetric isomers partially allow for pairing of the carboxylic acids, which therefore act as a probe for the reduced alkoxy chain nanopattern stabilization. This observation also reflects the adsorbate substrate symmetry mismatch, which leads to an increase of nanopattern complexity and unexpected templating of alkoxy side chains along the graphite armchair directions. State-of-the-art GFN-FF calculations confirm the overall structure of this packing and attribute the unusual side-chain orientation to a steric constraint in a confined environment. These calculations go far beyond conventional simple space-filling models and are therefore particularly suitable for this special case of molecular packing.

Scanning tunneling microscopy investigations of phenylene-based molecular spoked wheels with D_3h and C_s symmetries on graphite show the competitive or complementary effects of carboxylic acid groups and alkoxy chains on the nanopattern formation.     

Synthesis of unsymmetrical biaryl ureas from N-carbamoylimidazoles: kinetics and application

N-Carbamoylimidazoles dissociate in solution to yield imidazole and an isocyanate that may be reacted with another aryl amine to form an unsymmetrical biaryl urea. This paper investigates the reaction kinetics and the influence of electron withdrawing/donating substituents on the reaction of N-carbamoylimidazoles with aniline. The overall reaction mechanism involves two zwitterionic intermediates, formed during dissociation and upon reaction of the liberated isocyanate with aniline. The rate limiting step for the reaction is a base catalysed proton transfer from the second zwitterionic intermediate. Although electron withdrawing substituents on the aryl group hinder dissociation, they significantly increase reaction rates compared to compounds bearing electron donating substituents. The imidazole liberated upon dissociation catalyses the rate determining step so that reactions of dissociated N-carbamoylimidazoles proceed more rapidly than those involving only isocyanates. In addition, the imidazole eliminates the need for anhydrous reaction conditions. The N-carbamoylimidazole methodology was demonstrated by preparing sorafenib, a biaryl urea kinase inhibitor, in good yield and excellent purity.