Stability of Semi-Discrete Shock Profiles by Means of an Evans Function in Infinite Dimensions

Semi-discrete shock profiles are traveling wave solutions of hyperbolic systems of conservation laws under discretization in space. The existence of semi-discrete shocks has been investigated in earlier papers. Here the spectral stability of those nonlinear waves is addressed, and formulated in terms of a variational delay differential operator. Constructing a generalized Evans function, in infinite dimensions, it is shown how to derive stability criteria. Some examples are given when the criterion is fully explicit, e.g., for extreme Lax shocks. Additionally, connection is made with the alternative approach proposed by Chow, Mallet-Paret, and Shen (Journal of Differential Equations 1998), regarding the stability of traveling waves in general Lattice Dynamical Systems.     

Linear viscoelastic properties of emulsions and suspensions with thermodynamic and hydrodynamic interactions

We present a new approach to describe the rheological properties of dispersions with non-hydrodynamic interactions (steric, electrostatic and Van der Waals interactions) in the linear viscoelastic domain. Our model is based on the calculation of additional stresses resulting from interaction potentials between spheres and Brownian motion. We start from the statistical mechanical approaches which have been developed by Batchelor and Green and later Lionberger and Russel, to model the viscoelastic properties of emulsions and suspensions. We have extended their calculations to the more general case of viscoelastic deformable inclusions in a viscoelastic matrix. Our contribution lies in the computation of the hydrodynamic functions involved in the term describing interaction stresses. This computation is based on Palierne's results on the deformation field around a viscoelastic inclusion embedded in a viscoelastic matrix. We have also rewritten the conservation equation in the case of interest, over the whole frequency domain. We finally express the complex shear modulus of the dispersion as the sum of two terms : Palierne's complex shear modulus gives the purely hydrodynamic contribution; the interaction contribution depends on both the hydrodynamic properties and the interaction potential.     

Mixed Stieltjes–Hilbert and Fourier Sine and Cosine Convolutions

We introduce generalized convolutions of Stieltjes, Hilbert, and Fourier sine and cosine transforms and consider their applications to integral equations.     

Finite volume schemes for nonhomogeneous scalar conservation laws: error estimate

Summary. In this paper, we study finite volume schemes for the nonhomogeneous scalar conservation law with initial condition . The source term may be either stiff or nonstiff. In both cases, we prove error estimates between the approximate solution given by a finite volume scheme (the scheme is totally explicit in the nonstiff case, semi-implicit in the stiff case) and the entropy solution. The order of these estimates is in space-time -norm (h denotes the size of the mesh). Furthermore, the error estimate does not depend on the stiffness of the source term in the stiff case. Received October 21, 1999 / Published online February 5, 2001     

Bio-dissolution of colloidal-size clay minerals entrapped in microporous silica gels

Four colloidal-size fractions of strongly anisotropic particles of nontronite (NAu-2) having different ratios of basal to edge surfaces were incubated in the presence of heterotrophic soil bacteria to evaluate how changes in mineral surface reactivity influence microbial dissolution rate of minerals. To avoid any particle aggregation, which could change the reactive surface area available for dissolution, NAu-2 particles were immobilized in a biocompatible TEOS-derived silica matrix. The resulting hybrid silica gels support bacterial growth with NAu-2 as the sole source of Fe and Mg. Upon incubation of the hybrid material with bacteria, between 0.3% and 7.5% of the total Fe included in the mineral lattice was released with a concomitant pH decrease. For a given pH value, the amount of released Fe varied between strains and was two to twelve-fold higher than under abiotic conditions. This indicates that complexing agents produced by bacteria play an important role in the dissolution process. However, in contrast with proton-promoted NAu-2 dissolution (abiotic incubations) that was negatively correlated with particle size, bacterial-enhanced dissolution was constant for all size fractions used. We conclude that bio-dissolution of nontronite particles under acidic conditions seems to be controlled by bacterial metabolism rather than by the surface reactivity of mineral.     

Physical-chemistry of silica/alkaline silicate interactions during consolidation. Part 1: Effect of cation size

The purpose of this work is to identify the effect of the cation nature on mechanisms of the sand consolidation with alkaline silicate solution at low temperature (70 °C). Three diluted lithium, sodium and potassium silicate solutions with [Si] = 2.8 mol/l were used to agglomerate sand composed of grains which mean diameter is 340 μm. According to the cation, different behaviors were observed in terms of the drying time and the material cohesion. Essentially, the drying time increases with decreasing cation size. In contrast, the compressive strength raises when the cation size increases inducing intra-granular rupture highlighted by SEM observations. This could find an explanation in the cation hydration sphere of cations. The strength of the cation–water electrostatic interaction becomes less important as the size of the cations increase leading to more ionic bonds. Despite their strong consolidation, potassium-based materials have a high solubility in water. This result is consistent with the ionic nature of bonds.     

Molecular electrotatic potential of a triple stranded helix: Poly(dT)·poly(dA)·poly(dT)

The molecular electrostatic potential of the triple helix poly(dT)·tpoly(dA)·poly(dT) is calculated, and the results are examined in relation to those obtained for its component double and single helical parts. For the double helix presenting the standard Watson–Crick hydrogen bonds, the deepest potentials are formed on the side of the major groove, a situation similar to that observed in the A-DNA duplex. For the double helix presenting Hoogsteen-type hydrogen bonds the deepest potentials lie in the major groove, on the side of the pyrimidine strand. In the triple helix the deepest potentials are located in the major groove in a narrow zone over the thymine bases of the Watson–Crick pair.