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.     

The stereoselective synthesis of aziridine analogues of diaminopimelic acid (DAP) and their interaction with dap epimerase

Aziridine analogues of diaminopimelic acid (DAP) have been prepared stereoselectively for the first time and evaluated as inhibitors of DAP epimerase. (2R,3S,3'S)-3-(3'-Aminopropane)aziridine-2,3'-dicarboxylate was synthesised and shown to be a reversible inhibitor of DAP epimerase with an IC(50) value of 2.88 mM. (2S,4S)- and (2S,4R)-2-(4-Amino-4-carboxybutyl)aziridine-2-carboxylic acid (ll-azi-DAP and dl-azi-DAP ) were made as pure diastereomers, and both were shown to be irreversible inhibitors of DAP epimerase. ll-Azi-DAP selectively binds to Cys-73 of the enzyme active site whereas dl-azi-DAP binds to Cys-217 via attack of sulfhydryl on the methylene of the inhibitor aziridine ring. These observations are consistent with the two base mechanism proposed for the epimerization of ll-DAP and meso-DAP by DAP epimerase.     

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.     

Selective crystallization of calcium salts by poly(acrylate)-grafted chitosan

The biopolymer chitosan was chemically modified by grafting polyacrylamide or polyacrylic acid in a homogeneous aqueous phase using potassium persulfate (KPS) as redox initiator system in the presence of N,N-methylene-bis-acrylamide as a crosslinking agent. The influence of the grafted chitosan on calcium salts crystallization in vitro was studied using the sitting-drop method. By using polyacrylamide grafted chitosan as substrate, rosette-like CaSO4 crystals were observed. This was originated by the presence of sulfate coming from the initiator KPS. By comparing crystallization on pure chitosan and on grafted chitosan, a dramatic influence of the grafted polymer on the crystalline habit of both salts was observed. Substrates prepared by combining sulfate with chitosan or sulfate with polyacrylamide did not produce similar CaSO4 morphologies. Moreover, small spheres or donut-shaped CaCO3 crystals on polyacrylic acid grafted chitosan were generated. The particular morphology of CaCO3 crystals depends also on other synthetic parameters such as the molecular weight of the chitosan sample and the KPS concentration.     

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.