Decomposability problem on branched coverings

Given a branched covering of degree d between closed surfaces, it determines a collection of partitions of d, the branch data. In this work we show that any branch data are realized by an indecomposable primitive branched covering on a connected closed surface N with chi(N) <= 0. This shows that decomposable and indecomposable realizations may coexist. Moreover, we characterize the branch data of a decomposable primitive branched covering. Bibliography: 20 titles.

Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

In this paper we present a finite difference method for solving two-dimensional viscoelastic unsteady free surface flows governed by the single equation version of the eXtended Pom-Pom (XPP) model. The momentum equations are solved by a projection method which uncouples the velocity and pressure fields. We are interested in low Reynolds number flows and, to enhance the stability of the numerical method, an implicit technique for computing the pressure condition on the free surface is employed. This strategy is invoked to solve the governing equations within a Marker-and-Cell type approach while simultaneously calculating the correct normal stress condition on the free surface. The numerical code is validated by performing mesh refinement on a two-dimensional channel flow. Numerical results include an investigation of the influence of the parameters of the XPP equation on the extrudate swelling ratio and the simulation of the Barus effect for XPP fluids. (C) 2010 Elsevier B.V. All rights reserved.

Calculating Flash Point Numbers from Molecular Structure: An Improved Method for Predicting the Flash Points of Acyclic Alkanes

We report a novel method for calculating flash points of acyclic alkanes from flash point numbers, N(FP), which can be calculated from experimental or calculated boiling point numbers (Y(BP)) with the equation N(FP) = 1.020Y(BP) - 1.083 Flash points (FP) are then determined from the relationship FP(K) = 23.369N(FP)(2/3) + 20.010N(FP)(1/3) + 31.901 For it data set of 102 linear and branched alkanes, the correlation of literature and predicted flash points has R(2) = 0.985 and an average absolute deviation of 3.38 K. N(FP) values can also be estimated directly from molecular structure to produce an even closer correspondence of literature and predicted FP values. Furthermore, N(FP) values provide a new method to evaluate the reliability of literature flash point data.

Cellulose swelling by protic solvents: which properties of the biopolymer and the solvent matter?

The question posed in the title has been addressed by studying the swelling of celluloses at 20 C by twenty protic solvents, including water; linear- and branched-chain aliphatic alcohols; unsaturated aliphatic alcohols, and alkoxyalcohols. The biopolymers investigated included microcrystalline cellulose, MC, native and never-dried mercerized cotton cellulose, cotton and M-cotton, and native and never-dried mercerized eucalyptus cellulose, eucalyptus and M-eucalyptus, respectively. In most cases, better correlations with the physico-chemical properties of the solvents were obtained when the swelling was expressed as number of moles of solvent/anhydroglucose unit, nSw, rather than as % increase in sample weight. The descriptors employed in these correlations included, where available, Hildebrand`s solubility parameters, Gutmann`s acceptor and donor numbers, solvent molar volume, V(S), as well as solvatochromic parameters. The latter, employed for the first time for correlating the swelling of biopolymers, included empirical solvent polarity, E(T)(30), solvent ""acidity"", alpha(S), ""basicity"", beta(S), and dipolarity/polarizability, pi(S)*, respectively. Small regression coefficients and large sums of the squares of the residues were obtained when values of nSw were correlated with two solvent parameters. Much better correlations were obtained with three solvent parameters. The most statistically significant descriptor in the correlation equation depends on the cellulose, being pi(S)* for MC, cotton, and eucalyptus, and V(S) for M-cotton and M-eucalyptus. The best correlations were obtained with the same set of four parameters for all celluloses, namely, solvent pKa (or alpha(S)) beta(S), pi(S)*, and V(S), respectively. These results indicate that the supra-molecular structure of the biopolymer, in particular the average sizes of crystallites and micro-pores, and the presence of its chains in parallel (cellulose I) or anti-parallel (cellulose II) arrangements control its swelling. At least for the present biopolymer/solvent systems, use of solvatochromic parameters is a superior alternative to Hildebrand`s solubility parameters and/or Gutmann`s acceptor and donor numbers. The relevance of these results to the accessibility of the hydroxyl groups of cellulose, hence to its reactivity, is briefly discussed.