Finite-size scaling and the renormalization group

Renormalization group calculations ind = 4 andd = 4 – are performed for a system of finite size. A form of mean-field theory is used which yields a rounded transition for a finite system, and this allows a sensible expansion in fluctuations. A combination of Ewald and Poisson sum techniques is used to produce explicit numerical results for the specific heat ind = 4 which, with the setting of two nonuniversal metrical factors and the fourth-order coupling constant may be compared with simulations. The numerical visibility of logarithmic corrections is investigated. The universal scaling function for the specific heat to relativeO() is also evaluated numerically.     

Scaling properties of ℤ k- 1 actions on the circle

We derive universal scaling properties for ^k–1 actions on the circle whose generators have rotation numbers algebraic of degreek. As fork=2 these properties can be explained for arbitraryk in terms of a renormalization group transformation. It has at least one trivial fixed point corresponding to an action whose generators are pure rotations. The spectrum of the linearized transformation in this fixed point is analyzed completely. The fixed point is hyperbolic with a (k–1)-dimensional unstable manifold. In the casek=2 the known results are therefore recovered.     

Adsorption of -histidine on copper surface as evidenced by surface-enhanced Raman scattering spectroscopy

The adsorption of -histidine on a copper electrode from H₂O- and D₂O-based solutions is studied by means of surface-enhanced Raman scattering (SERS) spectroscopy. Different adsorption states of histidine are observed depending upon pH, potential, and the presence of the SO²⁻₄ and Cl⁻ ions. In acidic solutions of pH 1.2 the imidazole ring of the adsorbed histidine remains protonated and is not involved in the chemical coordination with the surface. The SO²⁻₄ and Cl⁻ ions compete with histidine for the adsorption sites. In solutions of pH 3.1 three different adsorption states of histidine are observed depending on the potential. Histidine adsorbs with the protonated imidazole ring oriented mainly perpendicularly to the surface at potentials more positive than −0.2 V. Transformation of that adsorption state occurs at more negative potentials. As this takes place, histidine adsorbs through the α-NH₂ group and the neutral imidazole ring. The Cl⁻ ions cause the protonation and detachment of the α-NH₂ group from the surface and the formation of the ion pair NH⁺₃ … Cl⁻ can be observed. In the neutral solution of pH 7.0 histidine adsorbs through the deprotonated nitrogen atom of the imidazole ring and the α-COO⁻ group at E ≥ −0.2 V. However, this adsorption state is transformed into the adsorption state in which the α-NH₂ group and/or neutral imidazole ring participate in the anchoring of histidine to the surface, once the potential becomes more negative. In alkaline solutions of pH 11.9 histidine is adsorbed on the copper surface through the neutral imidazole ring.     

将A-L理论推广到无限维李代数

为使由Alhassid与Levine所提出的动力学李代数方法（简称A－L理论）能适用于更多的散射体系，在h(∞)中引入了有效集合C（有限维）的概念．按照微扰理论的意义，C中的代数元所对应的群参量是较低次微扰的结果，而不属于C的代数元所对应的群参量则相当于较高次做扰所产生的修正结果．因此可以近似地利用C来代替h(∞)．这样，不仅简化了计算程序并且对于很多具有现实意义的散射过程的计算成为可能．     

Chemical applications of group theory and topology

The following procedure is described for investigating the qualitative dynamics of simple chemical systems: 1) A so-called influence diagram is generated representing the relationships between the reference reactants (phase-determining intermediates); 2) This influence diagram is used to generate a truth table indicating possible transitions between state vectors representing the signs of the time derivatives of of the reference reactant concentrations; 3) The truth table is used to determine a state transition diagram representing the flow topology around unstable equilibrium points; 4) The characteristic equation of the adjacency matrix of the influence diagram is solved in order to determine the presence of such unstable equilibrium points. The two types of qualitative dynamics possible for chemical systems containing two reference reactants and one feedback circuit are bifurcation between two attracting regions (bistability) and limit cycle oscillation. However, in two reference reactant systems oscillation requires an additional self-activating loop to generate the unstable equilibrium point required for its realization. Bistability and limit cycle oscillation are also two of the possible types of qualitative dynamics for chemical systems containing three reference reactants. However, chemical systems with three reference reactants and two or more feedback circuits can also contain interlocking limit cycles, which can lead to toroidal oscillations or chaos. The influence diagrams are given for the systems exhibiting these various types of dynamic behavior along with a summary of the important properties of all 729 possible influences for simple chemical systems containing three reference reactants.     

Gas Phase Catalysis by Metal Nanoparticles in Nanoporous Alumina Membranes

Nanoporous alumina membranes, loaded with palladium and ruthenium nanoparticles of various size, were used for gas phase hydrogenation of 1, 3‐butadiene and for oxidation of carbon monoxide, respectively. Those membranes contain 10⁹ ‐ 10¹¹ pores per cm², all running perpendicular to the surface. Membrane discs of 20 mm in diameter and only 60 μm thick, incorporated in a reactor in which the reactants can be pumped in a closed circuit through the pores, turned out to very actively catalyze hydrogenation of butadiene (Pd) and oxidation of CO (Ru). The activity of the Pd catalysts depends characteristically on the particles size, the gas flow, and of the educts ratio. As could be expected, larger particles are less active than smaller ones, whereas increasing gas flows in case of hydrogenation accelerates the reactions. Excessive hydrogen reduces selectivity with respect to the various butenes, but favours formation of butane.     

烯烃氢甲酰化催化剂活性物种的原位1H NMR研究

The rhodium-phosphine complex catalyst Rh(CO)(acac)(PPh3)(Ⅰ) for 1-hexene hydroformylation was studied under the following reaction conditions: CO/H2=1(mole rate), pressure 1.0 MPa, temperature 25-120℃, by using the pressurized in-situ 1H NMR technique. Experimental results indicated that the formation of a rhodium hydride complex from (Ⅰ) began at room temperature and its amount increased with increasing of reaction temperature. This intermediate complex began to decompose at 100℃ and disapeared completely at 120℃. The intensity change of the proton signal was parallel to catalytical activity in hydroformylation of olefins. Under pure CO pressure the proton signal of Ph-H bond was not observed. There was a 0.2 ppm difference in proton chemical shifts of Rh-H bond under pure H2 pressure and under H2+CO pressure. The results showed that the rhodium-hydride carbonyl complex is the active intermediate in the industrial hydroformylation process.     

相分离聚合法:(Ⅰ)羧酸型共聚功能微球的合成

粒径在微米级、粒度分布窄的高分子微球具有十分广泛的应用。但是由于这样规格的微球正是在一般的悬浮聚合和乳液聚合的合成范围之外,而采用二步聚合法和种子聚合法则不是需要使用特殊的反应装置,就是合成步聚十分繁复,因此至今对于这样规格高分子微球的报道不多。     

Surface recombination in breakdown time delay experiments: Effect of different cathode materials

The late afterglow in nitrogen with iron electrode is studied by the breakdown time delay method, i.e., by measuring the breakdown time delay t_d as a function of the afterglow time . It is proposed that the cause of the secondary electrons initiating the breakdown is the energy of the surface recombination of nitrogen atoms on the iron electrode. The gas-phase and macrokinetic diffusive models are used to describe the experimental breakdown time delay data. By fitting the theoretical curve to the experimental data: (1) it has been confirmed that the recombination on the molybdenum glass is of the second order and the value of the surface recombination coefficient is determined at 4 mbar; (2) it has been shown that the surface recombination on the iron electrode is of the second order, and the effective recombination coefficients are determined; (3) the analytical form of the recombination coefficient as a function of the adsorption characteristics of surfaces and the pressure of the parent gas has been derived. In addition, the orders of surface recombination on the molybdenum-, aluminum-, and gold-plated electrode were determined by the same method.