Links between microscopic and macroscopic fluid mechanics

The microscopic and macroscopic versions of fluid mechanics differ qualitatively. Microscopic particles obey time-reversible ordinary differential equations. The resulting particle trajectories {q(t)} may be time-averaged or ensemble-averaged so as to generate field quantities corresponding to macroscopic variables. On the other hand, the macroscopic continuum fields described by fluid mechanics follow irreversible partial differential equations. Smooth particle methods bridge the gap separating these two views of fluids by solving the macroscopic field equations with particle dynamics that resemble molecular dynamics. Recently, nonlinear dynamics have provided some useful tools for understanding the relationship between the microscopic and macroscopic points of view. Chaos and fractals play key roles in this new understanding. Non-equilibrium phase-space averages look very different from their equilibrium counterparts. Away from equilibrium the smooth phase-space distributions are replaced by fractional-dimensional singular distributions that exhibit time irreversibility.     

Gaussian Property of the Rings R(X) and R〈X〉

The content of a polynomial f over a commutative ring R is the ideal c(f) of R generated by the coefficients of f. A commutative ring R is said to be Gaussian if c(fg) = c(f)c(g) for every polynomials f and g in R[X]. A number of authors have formulated necessary and sufficient conditions for R(X) (respectively, R?X?) to be semihereditary, have weak global dimension at most one, be arithmetical, or be Prüfer. An open question raised by Glaz is to formulate necessary and sufficient conditions that R(X) (respectively, R?X?) have the Gaussian property. We give a necessary and sufficient condition for the rings R(X) and R?X? in terms of the ring R in case the square of the nilradical of R is zero.     

Solubilization chromatography: Ethers,carboxylic acids,and hydrocarbons

Synthetic mixtures of aliphatic and aromatic ethers, satmated fatty acids, and substituted benzenes and naphthalenes were separated by elution through columns of ion-exchange resins with aqueous solutions of acetic acid as eluent An attempt was made to use a resin of low capacity for the separation of such mixtures, and the results of this attempt are used to help elucidate the theory of solubilization chromatography     

Rapid catalytic oxidation of CO to CO(2) - On the development of a new approach to on-line oxygen isotope analysis of organic matter

A new approach to on-line oxygen isotope analysis has been developed which utilises existing elemental analyser and mass spectrometry technology to produce a sample of carbon dioxide gas for oxygen isotople analysis. The method relies on on-line high temperature pyrolysis of the sample over a carbon source followed by a rapid, non-contributive partial catalytic oxidation over nickel powder at between 550 and 600 degrees C. Initial results demonstrate both good precision (better than 0.2 per thousand) and accuracy for both cellulose and silver nitrate samples. Copyright 1999 John Wiley & Sons, Ltd.     

A direct method for the solution of evolution problemsLa méthode directe

An alternative numerical method to solve structural evolution problems is presented. It belongs to the family of Large Time Increment Methods. The problem is solved on the whole time interval separating a global stage where a SA and KA solution is searched and a local stage where the constitutive law is satisfied. To solve the global stage, consuming the most CPU time, the mechanical fields are decomposed in a wavelet basis and the equilibrium is solved only for the largest coefficients. To cite this article: F. Comte et al., C. R. Mecanique 334 (2006).     

Effects of dehydration on the apolar surface energetics of inorganic paper fillers

The surface energies of various inorganic fillers including kaolin clay, titanium dioxide, and talc were examined using inverse gas chromatography (IGC). In an earlier investigation that examined calcium carbonate fillers, dehydration by heating under a dry nitrogen purge had a substantial influence on the apolar (gammaS(LW)) and polar (gammaS(AB)) components of surface energy as measured using IGC. Using the same approach, the influence of such conditioning on several inorganic fillers used in papermaking were determined using preconditioning IGC from 100 to 300 degrees C, and sequential isothermal analysis at 100 degrees C. Results from IGC analysis of titanium dioxides (rutile and anatase) were similar to precipitated calcium carbonate (PCC) for temperatures up to 200 degrees C. PCC was significantly more energetic after preconditioning at 300 degrees C, which may indicate the onset of significant thermal decomposition that titanium dioxides will not exhibit. Kaolin clay samples had relatively high apolar surface energy similar to that of the chalk samples. Calcination gave lower gammaS(LW) values that could not be accounted for by changes in the microporous structure. More likely the differences resulted from contamination of highly energetic surface sites with adsorbates other than water. Talc samples exhibited relatively high apolar surface energies that increased with preconditioning temperature. The results provided insight into the significance of water on the final adhesion properties of fillers in the sheet structure or coating layer.     

The origin and elimination of spurious peaks in threshold electron photoionization spectra

Autoionization electrons in threshold photoionization spectra are known to occur. The effect of such electrons on the interpretation of threshold electron spectra is discussed and a new method is described which enables one to discriminate between zero kinetic energy electrons and energetic electrons in photoionization experiments with little ambiguity. The method largely overcomes the main problem present in some previously described threshold electron studies; namely, the line-of-sight transmission of energetic electrons which gives rise to non-threshold electron peaks. A rejection ratio of 25 is readily obtained for 0.038 eV electrons compared with threshold (zero kinetic energy) electrons and the (small) transition probability for energetic electrons falls off more rapidly than for analysers previously described. Design parameters based on electron trajectory calculations are given for the analyser used, and photoionization results on argon are presented.