Soluble models for dynamics driven by a super-diffusive noise

We explicitly discuss scalar Langevin type of equations where the deterministic part is linear, but where the integrated noise source is a non-linear diffusion process exhibiting superdiffusive behavior. We calculate transient and stationary probabilities and study the possibility of noise induced transitions from a unimodal to a bimodal probability shape. Illustrations from finance and dynamical systems are given.     

Preparation d'alkyl-4 γ-lactones insaturee optiquement pures. Application a la synthese de la (+) tetrahydrocerulenine.

Optically pure enantiomers of unsaturated 4-alkyl γ-lactones are synthesized from optically active propargylic carbinols obtained by asymmetric reduction of α-acetylenic ketones with the complex [LiAlH₄,N-methylephedrine,3-5 dimethylphenol]. (+) Tetrahydrocerulenin is prepared from the butenolide 6 obtained by this way.     

Anionic polymerization of 1,2-butylene oxide

Anionic polymerizations of 1,2-butylene oxide were carried out in vacuum-sealed dilatometers in the range of 30–60°C. Potassium terbutoxide and dimsyl sodium were used as initiators; dimethyl sulfoxide (DMSO) and mixtures of DMSO with tetrahydrofuran were solvents. The polymer products were analyzed by gel permeation chromatography and infrared spectroscopy. The object of the investigation was to obtain information on the mechanism of the reaction and to elucidate some of its kinetic aspects. It has been shown that the polymerizations occur by two different processes, depending on the choice of experimental conditions. One of the processes involves free ions and ion-pairs, the other, ion-pairs alone. In the first case, where dimethyl sulfoxide is used as solvent, the order of the reaction with respect to the initiator concentration far exceeds unity (～1.8), while in the second case, involving mixed solvents, the order of the reaction, for all practical purposes, is one.     

Crosslinking,filler, or transition constraint of polymer networks. I

The basic theory of modulus/swelling is developed to allow for limited extensibility, filler reinforcement or transition effects, and steric hindrance of aligned segments by extended chains or filler particles. Filler forms an effective hard fraction C_h per cubic centimeter of compound with v_c a new (compound) index of swelling. For 1/M_c + σ fix points having ratio φ to gum values 1/F₀(v_r) and with F(v_c) replacing the Flory function F(v_r): where σ denotes entanglement. Linkage reinforcement φ does not vary with sulfur crosslinking of SBR. Vacuoles invalidate φ from mass-increment F₀(v_r)/F(v_r) for inert fillers. Then, or for Graphon, with negligible φ ≈ 1: The effective C_h includes rubber stretched hard on Graphon by swelling or trapped inside hard aggregates. Only the right-hand equation fits normal blacks. In theory, C_h can always be obtained from swollen moduli G by linear slopes (1 + 1.4C_h) relating F(v_c) and (1 ? C)ρRT/G. For filler fractions C ≥ 0 cm^?3 and low strains α = 1.5?2.0 below prestretch the modulus G is given a new basic definition: Here C₂* ≈ 0.7 corresponds to Mooney-Rivlin C₂ and the effective crosslinking 1/[M_c] = (ρRT)^?1G is equal to (1 ? C)(1/M_c + σ) for unswollen prestretched rubber (v_r = 1). For higher strains a hypothesis of strain hardening is proposed. This is distinct and opposite in character to the initial prestretch softening (Mullins effect). Nonlinear effects of crosslinks are expressed by a fractional stress-upturn Ω (1/M_c + σ), effective mesh wieght (1/M_c + σ)^?1 ? Ω, and hard fraction Ω(1/M_c + σ). For μ_h characterizing strain hardening up to the prestretch (α_h ? 1) their contribution is: The sixth-power refinement has J = j(α_b ? 1)^1/2 with j ≈ 0.4. The hard phase is augmented by filler and grows with increasing strain up to the prestretch.     

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.     

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.     

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.