A Fujita type global existence-global nonexistence theorem for a weakly coupled system of reaction-diffusion equations

LetDR ^N be a region with smooth boundaryD. Letp·q>1,p, q1. We consider the system:u _t=u+v ^p,v _t=u+u ^q inD×[0, ) withu=v=0 inD×[0, ) andu ₀,v ₀ nonnegative. Let=max(p, q). We show that ifD isR ^N, a cone or the exterior of a bounded domain, then there is a numberpc(D) such that (a) if (+1)/(pq–1)>pc(D) no nontrivial global positive solutions of the system exist while (b) if (+1)/(pq–1)<pc(D) both nontrivial global and nonglobal solutions exist. In caseD is a cone orD=R ^N, (a) holds with equality. An explicit formula forpc(D) is given.This research was supported in part by NSF Grant DMS-8822788 and in part by the Air Force Office of Scientific Research.     

Solution properties of cellulose triacetate. I. Fractional precipitation

Using petroleum ether as a precipitant and chloroform–acetone mixture as solvent, six fractions of cellulose triacetate were obtained by fractional precipitation. The molecular weight of each fraction was obtained from osmotic pressure measurements carried out on chloroform solutions. It was shown that virtual nonfractionability of cellulose triacetate with regard to molecular weight occurred in this system. This behavior was also observed in attempts to fractionate it from tetrachloroethane or acetic acid solutions. These results are explained by the hypothesis that specific polymer–solvent interaction takes place due to hydrogen bonding.     

Incoherent inelastic neutron scattering studies of potassium bicarbonate and caesium hydrogen dinitrate

Inelastic neutron scattering spectra of KHCO₃ and CsH(NO₃)₂ have been obtained in the region 400 → 2400 and 400 → 2800 cm^?1 respectively. The in- and out-of-phase bending vibrations of the hydrogen bonds have been observed and assigned. For CsH(NO₃)₂ the two bending modes are closer in frequency than in KHCO₃ and they are not resolved from the antisymmetric stretch.     

Solution properties of cellulose triacetate. II. Solubility and viscosity studies

The solubility of cellulose triacetate in a range of solvents was measured, and the results for tetrachloroethane, chloroform, and acetic acid were compared with those from initial phase separation in solvent–nonsolvent mixtures and viscosity–concentration studies. The correlation found between solubilities, precipitation values, and values of the Huggins viscosity constant is discussed with reference to the type of polymer–solvent interaction proposed previously to explain fractionation behavior. A qualitative comparison of solubility–swelling behaviour was also made for a very low molecular weight cellulose triacetate sample in a wide range of solvents. Results are compared with those for higher molecular weight samples and discussed with regard to the cohesiveenergy densities of solvent and polymer. Some attempt has been made to predict suitable solvents for cellulose triacetate, based on consideration of their molecular structures.     

Aerodynamic optimization of the flat-plate leading edge for experimental studies of laminar and transitional boundary layers

This work is concerned with the design of a leading edge for a flat-plate model used to study laminar and transitional boundary layers. For this study, the flow over the complete boundary-layer model, including leading edge, flat section, and trailing-edge flap, is modeled. The effect of important geometrical features of the leading edge on the resulting pressure distribution, starting from the well-known symmetric modified super ellipse, is investigated. A minimal pressure gradient on the measurement side of the plate is achieved using an asymmetrical configuration of modified super ellipses, with a thickness ratio of 7/24. An aerodynamic shape optimization is performed to obtain a novel leading edge shape that greatly reduces the length of the non-zero pressure gradient region and the adverse pressure gradient region compared to geometries defined by ellipses. Wind tunnel testing is used to validate the numerical solutions.     

Production of Polymers from the Seed Oil of Crambe Abyssinica. III. Polyurethane Elastomers Based on Tridecanedioic (Brassylic) Acid

A series of predominately hydroxyl-ended polyesters were made from tridecanedioic acid derived from crambe oil. Comparison materials with sebacic and adipic acids were also prepared. Suitable polyesters were converted into polyurethane elastomers by chain extension and cross-linking with a diisocyanate and further diol. Polyesters based on ethandiol were unsuitable for the production of flexible urethanes as a slow crystallization occurred on standing; this did not happen when mixed ethane- and propan-diols were employed in polyesterification. Polyurethanes based on diphenylmethane diisocyanate are stronger than those made with the mixed isomers of toluene diisocyanate. Polyurethane networks based on brassylic acid have a lower     

Why irreversibility is not a sufficient condition for ergodicity

Khinchin's theorem of ergodicity is examined by means of linear response theory. The resulting ergodic condition shows that, contrary to the theorem, irreversibility is not a sufficient condition for ergodicity. By the recurrence relations method, we prove that irreversibility is broader in scope than ergodicity, showing why it can only be a necessary condition for ergodicity.