Some aspects of diffusion: fluctuations in reaction diffusion,and geometric influences in nonuniform media

Summary We deal with two diffusion problems: Space-integrated conserved entities characterizing very fast - diffusion - controlled reactions, such as time lags, etc. are universal. They are given by relationships which do not reflect the failure of the mean field hydrodynamic equations. We present another application which does not reflect this failure, for determining the surface flux via a diffusion controlled reaction producing a colored product. Another anomalous diffusion process we considered is transport through cellular materials whose cell sizes are highly nonuniform. We have analyzed the effects of extreme nonuniformity by considering fractal-like models of cellular solids. The diffusion current through these models can exhibit anomalous time-dependencies which are not predicted by the diffusion equation. In particular, it is shown that the initial diffusion current can be characterized by a power-law dependence on the time. Furthermore, the exponent of the power law is given in terms of the distribution of cell sizes in the fractal-like cellular solid.     

Thermal cyclization of (2-Ethynylphenyl)triazenes: facile synthesis of substituted cinnolines and isoindazoles

High-temperature intramolecular cyclization of N, N-dialkyl-N'-(4-substituted-2-ethynylphenyl)triazenes provides under neutral conditions both 6-substituted cinnolines and 5-substituted isoindazoles in moderate to excellent yields.     

Improved limits on the mass of the tau neutrino

Several methods to determine (or set an upper bound on) the mass of the tau neutrino are described. The decay spectrum of \(\tau \to e\bar \nu _e \nu _\tau \) near the high center-of-mass electron-energy end is particularly sensitive to the tau-neutrino mass. It is shown that an upper bound of 20 MeV or lower may be feasible. In addition, improved limits on the mass and mixing angle of a heavy component of the tau-neutrino may be readily obtained. We also discuss the purely leptonic decays of theD andF mesons, and show how measurements of the ratiosB(D→τν_τ/B(D→μν_μ,B(F→τν_τ/B(D→μν_μ can be sensitive to tau-neutrino masses of 30 MeV or greater.     

Dimethyldihydropyrene-dehydrobenzoannulene hybrids: studies in aromaticity and photoisomerization

The synthesis and study of dehydrobenzoannulene (DBA)-dimethyldihydropyrene (DDP) hybrids as models for the investigation of aromaticity in weakly diatropic systems is reported. Three new monofused DBA-DDP hybrids have been synthesized, and their NMR spectra are discussed with regard to quantifying the aromaticity remaining in multibenzene-fused DBAs. Nucleus-independent chemical shifts, determined at a series of locations for each compound, bond lengths, and (1)H and (13)C NMR chemical shifts were calculated and used to probe the aromaticity of these hybrids. Systems where more than one annulene/DBA is fused to the DDP core have also been obtained, and their potential use in photoinduced isomerization applications is discussed.     

Two unusual, competitive mechanisms for (2-ethynylphenyl)triazene cyclization: pseudocoarctate versus pericyclic reactivity

The cyclization of (2-ethynylphenyl)triazenes in ODCB at 200 degrees C gives exclusively cinnolines, whereas addition of CuCl to 1,2-dichloroethane solutions of the triazenes at 50 degrees C results in the sole formation of isoindazoles. DFT calculations and deuterium labeling studies suggest the intermediacy of a 3-dehydrocinnolinium ion, produced through a pericyclic transition state. Calculations and trapping studies strongly implicate a carbene intermediate in isoindazole formation, which proceeds through a pseudocoarctate transition state.