Cellular automata approach to site percolation on ℤ2. A numerical study

We present a cellular automata model as a new approach to Bernoulli site percolation on the square lattice. A new macroscopic quantity is defined and numerically computed at each level step of the automata dynamics. Its limit manifests a critical behavior at a value of the site occupancy probability quite close to those obtained for site percolation on ² with the best-known numerical methods.     

Design and synthesis of push-pull chromophores for second-order nonlinear optics derived from rigidified thiophene-based pi-conjugating spacers.

Two series of push-pull chromophores built around thiophene-based pi-conjugating spacers rigidified either by covalent bonds or by noncovalent intramolecular interactions have been synthesized and characterized by UV-vis spectroscopy, electric field induced second harmonic generation (EFISH) and differential scanning calorimetry. Comparison of the linear and second-order nonlinear optical properties of chromophores based on a covalently bridged dithienylethylene (DTE) spacer with those of their analogues based on open chain DTE shows that the rigidification of the spacer produces a considerable bathochromic shift of the absorption maximum together with a dramatic enhancement of the molecular quadratic hyperpolarizability (mu beta) which reaches values among the highest reported so far. A second series of NLO-phores has been derived from a 2,2'-bi(3,4-ethylenedioxythiophene) (BEDOT) pi-conjugating spacer. As indicated by X-ray and UV-vis data, rigidification of the spacer originates in that case, from noncovalent intramolecular interactions between sulfur and oxygen atoms. Again, comparison with the parent compounds based on an unsubstituted bithiophene spacer reveals a marked red shift of the absorption maximum and a large enhancement of mu beta. In an attempt to distinguish the contribution of the electronic and geometrical effects of the ethylenedioxy group, a third series of NLO-phores based on 3,4-ethylenedioxythiophene (EDOT) and 3,4-dihexyloxythiophene spacers has been synthesized. Comparison with compounds based on unsubstituted thiophene shows that, despite a red shift of lambda(max), introduction of alkoxy groups leads to a decrease of mu beta. Theoretical calculations indicate that this effect results from a decrease of the dipole moment (mu) caused by the auxiliary electron-donor alkoxy groups on the thiophene ring. In contrast, replacement of BT by BEDOT produces an increase of mu, which associated with the noncovalent rigidification of the BT system accounts for the observed enhancement of mu beta.     

Probing electrochemical properties of pi-conjugated thienylenevinylenes/fullerene C(60) adducts by ESI/MS: evidence for dimerized cation-radicals

Oligothienylenevinylenes/C(60) dyads n-C and triads n-C(2) are studied by electrospray mass spectrometry. A clear correlation is observed between the nature of the charged species detected by mass spectrometry, i.e. protonated molecule [M + H], (+) cation radical M(+.) and dication M(++), and the oxidation potentials of the molecules. Moreover, under defined solubility conditions, mass spectrometry provides conclusive evidences for the reversible dimerization of cation-radicals of n-C(2) compounds.     

Cationic copolymerization of tetrahydrofuran with propylene oxide. IV. Use of antimony pentachloride as catalyst

Propylene oxide and tetrahydrofuran were polymerized cationically by an in situ catalytic system composed of antimony pentachloride and 1,2-propanediol. The rates of polymerization were measured by vapor-phase chromatography in the temperature range from ?20°C to +20°C. The Arrhenius parameters pertaining to the reaction of each of the comonomers were evaluated and compared with data published earlier for other catalytic systems. The present catalyst system was incapable of initiating a homo-polymerization of tetrahydrofuran in the absence of propylene oxide, while the latter was readily homopolymerized. In a copolymerization system, the rates of consumption of both monomers were first-order in respect to the catalyst, but the reaction ceased when all of the propylene oxide had been consumed. The relative reactivity of the two monomers as characterized by the copolymerization parameters r₁ (PO) = 1.15 and r₂ (THF) = 0.70 suggests that in the copolymerization system, tetrahydrofuran is capable of a reaction with its own active center. This is discussed in terms of a possible mechanism involving the effects of penultimate units and extensive chain transfer. The latter is well evident from the molecular weights of resulting copolyethers, which do not exceed one thousand.     

Total synthesis of zincophorin methyl ester

[reaction: see text]. A convergent total synthesis of the methyl ester of zincophorin, an ionophore antibiotic, has been realized relying on a diastereoselective titanium-mediated aldol coupling between the C1-C12 and C13-C25 subunits. The latter fragment was prepared by using a Carroll-Claisen rearrangement.     

Correlation of mercury concentrations in tree core and lichen samples in southeastern Louisiana

To determine if a correlation exists between mercury concentrations in lichens and wood from tree cores, tree core and lichen samples were taken from sites under mercury advisories and analyzed for mercury using a Bacharach 50B Mercury Analyzer System employing the Manual Cold Vapor Atomic Absorption EPA method 7471A. Wood from tree cores was dated using tree ring data. Wood samples from the cores were analyzed for various depths in the tree core (periods of time) to determine if variations occur throughout the cores. Preliminary data indicate that a strong correlation exists between mercury concentrations in tree core and lichen samples. Samples were analyzed for the 6-month period of summer 2003–winter 2004. A correlation coefficient of 0.882 was found between the tree core and lichen data sets. The derived correlations were used to estimate concentrations of mercury in tree rings for sites in lichen samples which were previously analyzed. These predicted values compared favorably to recently determined concentrations of Hg in tree cores. The strong correlation between lichen and tree core Hg concentrations suggests similar uptake mechanism for the two types of biota.     

A well-tested procedure for instrumental neutron activation analysis of silicate rocks and minerals

Procedures for instrumental neutron activation analysis (INAA) have been developed and used on more than a thousand small samples of terrestrial and lunar silicate rocks and minerals for determination of Co, Cr, Fe, Hf, Na, Ni, Sc, Ta, Th, and the rare earths La, Ce, Sm, Eu, Tb, Yb, and Lu. Precision has been determined by repeated analysis of Knippa basalt and DTS-1 to be better than ±5 percent for all elements except Ni, Yb, Lu, and Hf. Mean values and estimates of accuracy are given for Knippa basalt and USGS standards AGV-1, G-2, GSP-1, and W-1. Important features of the method are its precision and ease of data reduction.     

Feynman path integrals and the trace formula for the Schrödinger operators

We study Schrödinger operators of the form on ^d , whereA ² is a strictly positive symmetricd×d matrix andV(x) is a continuous real function which is the Fourier transform of a bounded measure. If _n are the eigenvalues ofH we show that the theta function is explicitly expressible in terms of infinite dimensional oscillatory integrals (Feynman path integrals) over the Hilbert space of closed trajectories. We use these explicit expressions to give the asymptotic behaviour of (t) for smallh in terms of classical periodic orbits, thus obtaining a trace formula for the Schrödinger operators. This then yields an asymptotic expansion of the spectrum ofH in terms of the periodic orbits of the corresponding classical mechanical system. These results extend to the physical case the recent work on Poisson and trace formulae for compact manifolds.Partially supported by the USP-Mathematisierung, University of Bielefeld (Forschungsprojekt Unendlich dimensionale Analysis)     

Temperature dependence of X- and Q-band EPR spectra of the dinuclear manganese(II) complex [(NO2Bpmp)Mn2(mu-OAc)2]+: determination of the exchange constant and of the spin parameters for the S=1, 2, and 3 spin states

A new dinuclear manganese(II) complex was synthesised with the biscompartimental ligand 2,6-bis[bis(2-pyridylmethyl)aminomethyl]-4-nitrophenol (NO(2)BpmpH) and characterised by X-ray crystallography. Magnetic susceptibility measurements revealed that the two high-spin Mn(II) ions are antiferromagnetically coupled with a singlet-to-triplet separation of 7.2 cm(-1). The powder EPR spectra were recorded for both X- and Q-bands between 1.8 K and 35 K. A detailed analysis of these spectra led to the determination of three out of five individual spin-state zero-field splitting parameters. From the proposed simulations, the exchange coupling constant J and the intermetallic distance have been computed.     

Measurement of the dispersity of supported ruthenium catalysts by oxygen chemisorption

A highly dispersed (Ø (Ru)<10 Å, from electron microscopy) Al₂O₃-supported catalyst and not so well dispersed silica supported Pt, Ru, Pt, Ru-alloy catalysts were investigated. Oxygen coverage of Ru is found to be close to 2 at 20 °C over the monometallic Ru catalysts as well as over the Pt, Ru-alloy catalysts.

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(Ø (Ru)<10 Å ) Al₂O₃ Pt Ru Pt Ru . Ru 2 20°C Ru, Pt Ru.