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.     

Treating bias as variance for experimental design purposes

When an empirical model is fitted to data, bias can arise from terms that have not been incorporated, and this can have an important effect on the choice of an experimental design. Here, the biases are treated as random, and the consequences of this action are explored for the fitting of models of first and second order.     

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.     

ABSOLUTELY UNSTABLE WAVES IN INVISCID HYDROELASTIC SYSTEMS

The effect of inviscid plug flow on the stability of several hydroelastic systems is investigated by determining the absolute or convective nature of the instability from the linear dispersion relation. The fluid-structure systems consist of plates and membranes with bounded and unbounded flow. A method is proposed to derive systematically in parameter space the boundary between convective and absolute instability, based on the particular symmetries of the dispersion relation as originally noted by Crighton and Oswell. This method is then applied to the case of plates with superimposed tension, thick plates with rotary inertia and walls made of plates or membranes bounding channel flow, oscillating in a sinuous or varicose mode of deformation. A relation is drawn with solutions by previous authors for plates, for pipes and for the Kelvin-Helmholtz instability with surface tension. To illustrate these results some temporal evolutions are calculated by using an integration in the wavenumber space. Based on the large set of new cases solved in the paper some general trends are discussed as to the influence of flow velocity, confinement and structural stiffness on the existence of absolutely unstable waves in inviscid hydroelastic systems.     

Measurement of the total and differential cross sections for the reaction π − p → ηn with the Crystal Ball detector

The first results obtained in 1998 by the Crystal Ball collaboration from a measurement of the total and differential cross sections for the reaction π ^? p → ηn are presented. These new experimental results for the total cross sections are compared with the predictions of the K-matrix model for pion-nucleon scattering. The angular distribution at momenta near the reaction threshold (685 MeV/c) is determined by the S-wave contribution. The P-wave contribution begins to manifest itself from a momentum of 720 MeV/c.     

Superdeformation in lead nuclei

For the first time, collective bands have been observed in the doubly-odd nucleus¹²⁴Cs. They are proposed to result in the coupling of an h_11/2 proton to h_11/2 and positive parity neutrons. The relative residual protonneutron interaction in¹²⁴Cs is calculated and compared to that of neighbouring odd-odd nuclei.     

Observation of superdeformed bands in194Hg

Two rotational bands, with energy spacings characteristic of superdeformed shapes, have been observed following bombardment of¹⁵⁰Nd with⁴⁸Ca. The more intensively populated band consists of 18 transitions and is assigned to¹⁹⁴Hg. The depopulation of this band occurs around spin 10. The second band, consisting of at least 16 transitions, was populated less strongly and is tentatively assigned to¹⁹⁴Hg also. The lowest level in this band is assigned spin 8. The energy differences between transitions for both bands decrease from ～40 keV at low rotational frequencies to ～30 keV at the highest observed frequencies. The moments of inertia of the bands are similar to those of the two previously observed superdeformed bands in^191,192Hg. The similarities and differences of the four known bands in the mercury region are discussed.     

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.