Roe‐type Riemann solver for gas–liquid flows using drift‐flux model with an approximate form of the Jacobian matrix

This work presents an approximate Riemann solver to the transient isothermal drift ‐ flux model. The set of equations constitutes a non‐linear hyperbolic system of conservation laws in one space dimension. The elements of the Jacobian matrix A are expressed through exact analytical expressions. It is also proposed a simplified form of A considering the square of the gas to liquid sound velocity ratio much lower than one. This approximation aims to express the eigenvalues through simpler algebraic expressions. A numerical method based on the Gudunov's fluxes is proposed employing an upwind and a high order scheme. The Roe linearization is applied to the simplified form of A . The proposed solver is validated against three benchmark solutions and two experimental pipe flow data. Copyright © 2015 John Wiley & Sons, Ltd.     

Image Analysis Technique as a Tool to Identify Morphological Changes in Trametes versicolor Pellets According to Exopolysaccharide or Laccase Production

Image analysis technique was applied to identify morphological changes of pellets from white-rot fungus Trametes versicolor on agitated submerged cultures during the production of exopolysaccharide (EPS) or ligninolytic enzymes. Batch tests with four different experimental conditions were carried out. Two different culture media were used, namely yeast medium or Trametes defined medium and the addition of lignolytic inducers as xylidine or pulp and paper industrial effluent were evaluated. Laccase activity, EPS production, and final biomass contents were determined for batch assays and the pellets morphology was assessed by image analysis techniques. The obtained data allowed establishing the choice of the metabolic pathways according to the experimental conditions, either for laccase enzymatic production in the Trametes defined medium, or for EPS production in the rich Yeast Medium experiments. Furthermore, the image processing and analysis methodology allowed for a better comprehension of the physiological phenomena with respect to the corresponding pellets morphological stages.     

The quantum strip: Liouville theory for open strings

The quantum group structure of 2D gravity recently put forward by one of us (J.-L. G.) is used to study quantum gravity on the strip. The boundary conditions, previously studied by A. Neveu and this author become easy to implement when one introduces the universal family of chiral operators associated withU _q (sl(2)). A general formula for inverse powers of the metric-tensor operator is thereby derived. It contains a new universal matrixA, acting in representation-space, which obeys identities involving theR matrix, the Clebsch-Gordon coefficients, and the co-products ofU _q (sl(2)). The physical meaning of these identities is to ensure that these powers of the metric are local and closed by fusion.     

Fondements d'une théorie générale de la courbure linéaire

Sans résumé     

Ueber Spectralapparate und Spectralanalyse

Ohne Zusammenfassung