A rigorous control of logarithmic corrections in four-dimensional ϕ4 spin systems

Using Gawedzki and Kupiainen's rigorous block spin transformation method, we study critical phenomena in ⁴ spin systems in four dimensions. In Part I of this work we investigate in detail the renormalization group trajectory of the system not exactly at the critical point.     

Equilibrium polymerization in a solvent: Solution on the Bethe lattice

The lattice model for equilibrium polymerization in a solvent proposed by Wheeler and Pfeuty is solved exactly on a Bethe lattice (core of a Caylay tree) with general coordination numberq. Earlier mean-field results are reobtained in the limitq, but the phase diagrams show deviations from them for finiteq. Whenq=2, our results turn into the solution of the one-dimensional problem. Although the model is solved directly, without the use of the correspondence between the equilibrium polymerization model and the diluten0 model, we verified that the latter model may also be solved on the Bethe lattice, its solution being identical to the direct solution in all parameter space. As observed in earlier studies of the puren0 vector model, the free energy is not always convex. We obtain the region of negative susceptibility for our solution and compare this result with mean field and renormalization group (-expansion) calculations.     

Fields as Kolmogzrov flows

It is widely recognized that for highly unstable dynamical systems there exists a fundamental limitation on predictability and determinism. An important class of such highly unstable systems is the class of K-flow, which is further characterized by the existence of time-asymmetric objects in the form of K-partition. Our recent approach to the problem of irreversibility has shown that when the implications of the limitation on determinism arising from strong form of instability and those of the existence of K-partition are consistently taken into account, one is naturally led from the physically unrealizable deterministic evolution of phase points to an entropy-increasing stochastic Markovian evolution. Furthermore, this transition is not the result of extraneously imposed coarse graining and/or approximation schemes, but can be brought about by an invertible transformation whose existence and construction are determined by the nature of the instability of the dynamical system itself. After a brief review of this theory which also contains some relatively new remarks, we prove that classical Klein-Gordon field (both massive and massless) possess the structure of K-flow. This seems to provide the first examples of relativistic systems that are K-flows. Some of the implications of this result are briefly discussed. From a mathematical point of view, this seems to be a first step toward an ergodic theory of partial differential equations. In the process, we also provide an independant group-theoretic proof of the existence of incoming and outgoing subspaces of the scattering theory of Lax and Phillips for the wave equation.     

Infrared asymptotic freedom of a hierarchical φ 3 6 lattice theory

For the weakly coupled lattice ₃ ⁶ theory in a hierarchical model approximation a nonperturbative renormalization group analysis in the spirit of Gawedzki and Kupiainen is performed to study the flow of the effective actions. We deduce a domain of attraction to the tricritical (Gaussian) fixed point. The two relevant coupling constants of the problem are controlled by analytic continuation to complex domains, tracing their images under the renormalization group iterations.     

Characterization of SiO2-P2O5-ZrO2 Sol-Gel/NAFION™ Composite Membranes

Composite membranes were prepared by (a) infiltrating NAFION with SiO₂-P₂O₅-ZrO₂ sol, and (b) recasting a film using NAFION solution containing SiO₂-P₂O₅-ZrO₂ sol. The membranes were characterized by Differential Thermal Analysis and ac-impedance spectroscopy as a function of relative humidity. The influences of the heat treatment (80°C–150°C) and cleaning on the electrical properties were investigated. The incorporation of SiO₂-P₂O₅-ZrO₂ gels into NAFION lead to improvements in its thermal stability and proton conductivity.     

On the initial layer solution of the Boltzmann equation with small Knudsen number

We extend our method of systematic removal of secular terms in a singular perturbation treatment of the Boltzmann equation with small Knudsen numbers to the initial layer. The requirement that the solution through the initial layer should connect smoothly to the normal solution removes an ambiguity noted in our previous paper. We show that removal of secular terms improves Grad's solution for the initial layer and reintroduces soundlike modes associated with higher moments, first found by Wang Chang and Uhlenbeck.     

Electrochemical characteristics of Ce0.8Gd0.2O1.9|La0.6Sr0.4CoO3-δ + Ce0.8Gd0.2O1.9 half-cell

The analysis of the medium temperature half-cell Ce_0.8Gd_0.2O_1.9|70 wt% La_0.6Sr_0.4CoO_3- (LSCO) + 30 wt % Ce_0.8Gd_0.2O_1.9 (CGO) has been made by electrochemical impedance, cyclic voltammetry and chronoamperometry. The shape of complex impedance plots depends on temperature and cathodic polarisation of the electrode. Nyquist (Z, Z-) plots were fitted by equivalent circuit taking into account the electrolyte properties (at very high frequencies), charge transfer process at grain boundaries (at high frequencies), and medium and low frequency O₂ reduction process at the cathode surface and inside the porous cathode material. Two different time constants have been obtained for the cathode process, i.e. for electroreduction of oxygen. It was found that the addition of CGO into the cathode material (LSCO) only somewhat decreases the surface catalytic activity but the noticeably higher low-frequency resistance (i.e. mainly diffusion-like mass transfer resistance R_D) values at lower temperatures have been calculated. It was found that the mainly bulk diffusion-limited process at T773 K deviates toward the kinetically mixed process (diffusion + charge transfer) with increasing temperature.     

Synthesis and Characterization of Tetraosmium Carbonyl Complexes Containing a Bridging CO2 Ligand

Treatment of (thd)H (thd=2,2,6,6-tetramethyl-3,5-heptandionate) with excess Os₃(CO)₁₂ in an autoclave at 180°C gives the formation of a brown metal chain complex [Os₂(CO)₅(thd)₂]₂ (1) and a yellow CO₂ cluster complex [Os₄(-H)(-CO₂)(thd)(CO)₁₃] (2) in low yields. Complex 2 was fully identified by a combination of spectroscopic methods and X-ray diffraction study, showing a unique CO₂ ligand bridging a triosmium metal fragment, Os₃(-H)(CO)₁₀ and a monometallic osmium fragment, Os(CO)₃(thd). Upon treatment of 1 with Me₃NO at an elevated temperature, oxidation of the CO ligand occurred at the position trans to the unique CO₂ ligand on the Os(CO)₃(thd) fragment, giving the formation of a second CO₂ cluster [Os₄(-H)(-CO₂)(thd)(CO)₁₂(NCMe)] (3), which is stabilized by a weakly coordinated acetonitrile molecule.     

Novel type of heterogenized CuCl2 catalytic systems for oxidative carbonylation of methanol

A novel type of heterogenized CuCl₂ catalysts was designed for the oxidative carbonylation of methanol to dimethyl carbonate (DMC) taking account of the plausible reaction mechanism and intermediates. To prevent severe corrosion of the reaction equipment materials due to Cl^– while keeping the catalytic activity of the homogeneous CuCl₂ catalyst, we adopted, as supports (or ligands) of CuCl₂, four polymers, bearing a 2,2-bipyridine (bpy) or pyridine (py) unit, namely, poly(2,2-bipyridine-5,5-diyl) (Pbpy), poly(pyridine-2,5-diyl) (Ppy), poly(N,N-bisphenylene-2,2-bipyridine-4,4-dicarboxylic amide) (Bpya), and poly(4-methyl-4-vinyl-2,2-bipyridine) (Pvbpy), together with one chelate compound, 8-quinolinol. The catalytic activity, stability of heterogenized CuCl₂ and their corrosivities to stainless steels were examined in the liquid-phase reaction of the oxidative carbonylation of methanol. These polymer-supported catalysts showed considerable catalytic activity and stability for the DMC synthesis. In particular, the Pbpy-CuCl₂ and Ppy-CuCl₂ catalysts exhibited high DMC yields and selectivity comparable to those of the homogeneous CuCl₂ catalyst. This high activity appears to be associated with the presence of the -conjugated system in the polymers, which affect the redox reactions of Cu involved in the catalytic reaction. All of the polymer-supported CuCl₂ catalysts could be easily recycled after filtration, and the initial catalytic activity was maintained after three times of use. The corrosive characters of the catalysts were closely related to CuCl₂ leaching from the supports, which reflects the ability of supports to coordinate Cu. These experimental results suggest that both the electronic structure and the coordination ability of the polymer supports are key factors for the development of an effective catalytic system.