AN APPROXIMATE PROJECTION SCHEME FOR INCOMPRESSIBLE FLOW USING SPECTRAL ELEMENTS

An approximate projection scheme based on the pressure correction method is proposed to solve the Navier–Stokes equations for incompressible flow. The algorithm is applied to the continuous equations; however, there are no problems concerning the choice of boundary conditions of the pressure step. The resulting velocity and pressure are consistent with the original system. For the spatial discretization a high-order spectral element method is chosen. The high-order accuracy allows the use of a diagonal mass matrix, resulting in a very efficient algorithm. The properties of the scheme are extensively tested by means of an analytical test example. The scheme is further validated by simulating the laminar flow over a backward-facing step.     

Preparation and characterization of poly(butylene terephthalate)/poly(ethylene terephthalate) copolymers via solid‐state and melt polymerization

To increase the T_g in combination with a retained crystallization rate, bis(2‐hydroxyethyl)terephthalate (BHET) was incorporated into poly(butylene terephthalate) (PBT) via solid‐state copolymerization (SSP). The incorporated BHET fraction depends on the miscibility of BHET in the amorphous phase of PBT prior to SSP. DSC measurements showed that BHET is only partially miscible. During SSP, the miscible BHET fraction reacts via transesterification reactions with the mobile amorphous PBT segments. The immiscible BHET fraction reacts by self‐condensation, resulting in the formation of poly(ethylene terephthalate) (PET) homopolymer. ¹H‐NMR sequence distribution analysis showed that self‐condensation of BHET proceeded faster than the transesterification with PBT. SAXS measurements showed an increase in the long period with increasing fraction BHET present in the mixtures used for SSP followed by a decrease due to the formation of small PET crystals. DSC confirmed the presence of separate PET crystals. Furthermore, the incorporation of BHET via SSP resulted in PBT‐PET copolymers with an increased T_g compared to PBT. However, these copolymers showed a poorer crystallization behavior. The modified copolymer chain segments are apparently fully miscible with the unmodified PBT chains in the molten state. Consequently, the crystal growth process is retarded resulting in a decreased crystallization rate and crystallinity. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 882–899, 2007.     

Modelling the velocity of air through beds of cereal grains

The quality of cereal grains in storage will deteriorate toan unacceptable level if they are not kept dry and cool. Tomodel the drying and cooling process, an accurate knowledgeof the airflow distribution is required. In this paper, theequations used to model the air velocity are analysed. To study the flow of air through a typical drying system forstored grain, a two-dimensional rectangular bin is considered,with a single source of air on the bin floor. Two paths ofstudyare undertaken: the first is a linear analysis for low velocities,and following on from this is a nonlinear approach for largervelocities. The linear analysis is used to study a bin witha semi-infinite height, and the drying pattern is studied inthis bin using the air traverse time. Then bins with a finiteheight are analysed: it is shown that, for tall enough bins,the semi-infinite solution is accurate enough. A perturbationanalysis is used to study the semi-infinite bin when the airvelocity is too large for the linear analysis to be accu rate.It is shown that the effect of the nonlinearity is to move theair away from the high-velocity regions towards the areas oflower velocity.     

On a Moving Boundary Problem Aristing in Fluidized Bed Combustion

We consider a model describing the combustion of a coal particlein a fluidized bed, in which attrition plays a dominant role.The model consists of (1) a quasi-linear elliptic equation forthe oxygen concentration, supplemented by boundary conditionson the moving surface representing the burning particle interface,(2) an evolution equation for the carbon consumption, and (3)an equation governing the motion of the interface in terms ofa specified function of the carbon consumption at the interface.We prove a global existence and uniqueness result, togetherwith a priori bounds for the solution; the existence of travellingwaves will also be established.     

A supersonic beam of cold lithium hydride molecules

We have developed a source of cold LiH molecules for Stark deceleration and trapping experiments. Lithium metal is ablated from a solid target into a supersonically expanding carrier gas. The translational, rotational, and vibrational temperatures are 0.9+/-0.1, 5.9+/-0.5, and 468+/-17 K, respectively. Although they have not reached thermal equilibrium with the carrier gas, we estimate that 90% of the LiH molecules are in the ground state, X (1)Sigma(+)(v=0,J=0). With a single 7 ns ablation pulse, the number of molecules in the ground state is 4.5+/-1.8 x 10(7) molecules/sr. A second, delayed, ablation pulse produces another LiH beam in a different part of the same gas pulse, thereby almost doubling the signal. A long pulse, lasting 150 micros, can make the beam up to 15 times more intense.     

Kinetic and mechanistic studies of the electrocatalytic reduction of O2 TO H2O with mononuclear Cu complexes of substituted 1,10-phenanthrolines

Mononuclear Cu complexes with a 1,10-phenanthroline-based ligand adsorbed onto an edge-plane graphite electrode act as electrocatalysts for the 4-electron reduction of O2 to H2O. A mechanism is proposed for the electrocatalytic O2 reduction that accounts for the observed redox and kinetic dependences on coordinating anions and proton donors in the buffer. Systematic increases of ligand electron-withdrawing properties and/or the steric demands near the Cu center increase the E0 of the Cu catalysts but decrease the rate of O2 reduction. The kinetic rate of O2 reduction at E0, reported as kinetic current divided by catalyst redox charge, decreases as E0 increases: from 16 s(-1) measured at E0 in air-saturated solutions for adsorbed Cu(phen) to 0.4 s(-1) for Cu(2,9-Et2-phen). The maximum value of E for which catalytic activity can be attained is estimated to be +350 mV vs NHE. Near E0, the kinetic current deviates from that expected if O2 binding were the sole rate-limiting step. This indicates that one or more of the electrochemical reduction steps are rate limiting at potentials near E0.     

Commutators with idempotent values on multilinear polynomials in prime rings

Let R be a prime ring of characteristic different from 2, C its extended centroid, d a nonzero derivation of R, f(x ₁, . . . , x _n ) a multilinear polynomial over C, ρ a nonzero right ideal of R and m > 1 a fixed integer such that

$$\qquad \left ([d(f(r_{1},\ldots ,r_{n})),f(r_{1},\ldots ,r_{n})]\right )^{m}=[d(f(r_{1},\ldots ,r_{n})),f(r_{1},\ldots ,r_{n})] $$

for all r ₁, . . . , r _n ∈ρ. Then either [f(x ₁,…,x _n ),x _n+1]x _n+2 is an identity for ρ or d(ρ)ρ = 0.

     

金属卟啉催化条件下有机化合物与二氧化碳的电羧化反应Ⅰ. 金属卟啉对苄基氯电羧化催化活性的研究

本文研究了系列金属卟啉对苯基氯(phCH~2Cl)和CO~2电羧化反应的催化活性.用熔点,MS,IR,UV鉴别产物为苯乙酸卟脂,利用高效液相色谱(HPLC)定量分析了羧化产物,选出最佳电羧化电解电位为-1.6v(相对于饱和甘汞电极,vs.SCE,下同). 并对催化活性较高的钴卟啉系列配合物进行了深入研究. 探讨了金属卟啉具有催化活性的原因,认为能形成M(Ⅰ)中间体的金属卟啉配合物.具有较高的催化活性.