Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames

This paper is devoted to the justification of an asymptotic model for quasisteady three-dimensional spherical flames proposed by G. Joulin [17]. The paper [17] derives, by means of a three-scale matched asymptotics, starting from the classical thermo-diffusive model with high activation energies, an integro-differential equation for the flame radius. In the derivation, it is essential for the Lewis Number – i.e. the ratio between thermal and molecular diffusion – to be strictly less than unity. If is the inverse of the – reduced – activation energy, the idea underlying the construction of [17] is that (i) the time scale of the radius motion is ^-2, and that (ii) at each time step, the solution is -close to a steady solution.In this paper, we give a rigorous proof of the validity of this model under the restriction that the Lewis number is close to 1 – independently of the order of magnitude of the activation energy. The method used comprises three steps: (i) a linear stability analysis near a steady – or quasi-steady – solution, which justifies the fact that the relevant time scale is ^-2; (ii) the rigorous construction of an approximate solution; (iii) a nonlinear stability argument. Mathematics Subject Classification (2000) Primary 80A25, Secondary 35K57, 47G20     

Synthesis and characterization of carboxymethylcelluloses (CMC) from non-wood fibers I.Accessibility of cellulose fibers and CMC synthesis

This paper explores the production of carboxymethylcellulose (CMC) fromseveral bleached cellulose pulps obtained from non-wood species. The chemicalcomposition (-cellulose, hemicellulose and lignin content), the degreeofswelling, viscosity, solubility in concentrated NaOH and crystallinity ofsoda/AQ cellulose pulps from abaca, jute, sisal, linen and Miscanthussinensis were determined. The pulps were carboxymethylated by one andtwo successive reaction steps in aqueous medium under identical conditions. Thedegree of substitution (DS) of CMC was found to be dependent upon the source ofthe cellulose pulp, but generally it was close to 1 with one etherificationtreatment and around 2 after the second. The molar mass of CMC was found to bedependent on the initial intrinsic viscosity of the cellulose pulp. The weightaverage molar mass of our CMCs ranged from 1.5×10⁵ to2.8×10⁵. Increasing the DS up to 2 improved the CMC solubility, butviscosity slightly decreased due to a slight degradation of the polymer.     

Nonlinear optical properties of diazabutadienes and -hexatrienes; experimental and computational aspects

Donor-acceptor substituted diazabutadienes and -hexatrienes were prepared by straightforward procedures and their linear optical (UV-vis) and nonlinear optical second harmonic generation (SGH) properties investigated in a combined theoretical and experimental study. Theoretical and experimental results were in reasonable agreement. For the compounds in this study, which contained a p-nitrophenyl group as electron acceptor, the p-dimethylaminophenyl group was the most powerful electron-donating group, leading to the highest maximum absorption wavelengths, as well as to the maximum SHG efficiency.     

FILO (Field Interaction Ligand Optimization): A simplex strategy for searching the optimal ligand interaction field in drug design

A method (FILO, Field Interaction Ligand Optimization) for obtaining the optimal molecular interaction field was developed on the basis of the Simplex optimization procedure applied to a matrix of interaction energies obtained by performing a GRID computation on a suitable data set. The FILO procedure was tested on a set of nine HIV-1 protease inhibitors with known crystal structures. The results of FILO consist of the optimal molecular interaction field of a putative new ligand with optimal binding affinity. The final FILO model yields R ² and R ² _CV values of 0.993 and 0.936, respectively, and finds eight negative and four positive interaction nodes for the OH probe taken as an example. The eight H bonding interactions pointed out by FILO identified well the binding site AA-residues Gly A27, Asp A29, water 501, Gly B48 and Asp A25 of HIV-1 protease.