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.     

Thiolated poly(ε-caprolactone) macroligand with vacant coordination sites on gold substrate: Synthesis and surface characterization

Surface-confined telechelic poly(ε-caprolactone) macroligand with two distinct functional groups per polymeric chain has been synthesized and characterized. The molecular microstructure of the macroligand with regard to the properties of the end-capped functionalities and with those on surface substrate has been studied by solution and surface analytical methods (i.e., X-ray photoelectron spectroscopy (XPS), grazing angle reflectance-Fourier transform IR spectroscopy (GA-FTIR), water contact angle measurements, and atomic force microscopy (AFM)) to elucidate the structure and properties of such multifunctional polymer on gold (1 1 1) substrate.     

Rigidity percolation in particle-laden foams

We study the viscoelastic behavior of aqueous foam mixed with solid noncolloidal particles. We show that adding a tiny amount of grains can enhance the elastic and loss shear moduli by more than 1 order of magnitude. The scaling of these moduli with solid volume fraction is in qualitative agreement with that predicted by an effective-medium rigidity percolation model. We present a simple model, based on capillary attraction, to explain the particle-size dependence of the threshold.     

Elliptic operators in the functional quantisation for gauge field theories

Given a gauge theory with gauge groupG acting on a path spaceX,G andX being both infinite dimensional manifolds modelled on spaces of sections of vector bundles on a compact riemannian manifold without boundary, it is shown that when the action ofG onX is smooth, free and proper, the same ellipticity condition on an operator naturally given by the geometry of the problem yields both the existence of a principal fibre bundle structure induced by the canonical projection :XX/G and the existence of the Faddeev-Popov determinant arising in the functional quantisation of the gauge theory. This holds for certain gauge theories with anomalies like bosonic closed string theory in non-critical dimension and also holds for a class of gauge theories which includes Yang-Mills theory.     

Inelastic scattering of 108.5 MeV 3He particles at very small momentum transfer to the giant monopole resonance of 90Zr and 208Pb

Inelastic scattering spectra from the (³He, ³He′) reaction at 108.5 MeV have been measured down to 1.85° scattering angle on ⁹⁰Zr and ²⁰⁸Pb, allowing a giant monopole resonance study in these nuclei. DWBA analysis is reported.     

Studies of silicophosphate derivatives by 31P-->29Si CP MAS NMR

We show that it is possible to efficiently transfer magnetization from ³¹P to ²⁹Si, using variable amplitude CP MAS experiment. This experiment is demonstrated by using Si₅O(PO₄)₆, the synthesis protocol of which is described. From the obtained results, we show that the experiment allows the spectral edition of ²⁹Si spectra from ³¹P→²⁹Si CP, enabling the studies of derivatives involving Si–O–P linkages, such as phosphosilicate glasses, microporous silicoaluminophosphates (SAPO) and bioactive phosphosilicates.