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.     

Overpartitions

We discuss a generalization of partitions, called overpartitions, which have proven useful in several combinatorial studies of basic hypergeometric series. After showing how a number of finite products occurring in -series have natural interpretations in terms of overpartitions, we present an introduction to their rich structure as revealed by -series identities.

     

Spin-polarized surface states on Fe-deposited Au(111) surface: A theoretical study

We have studied electronic structure of Fe-deposited Au(111) by performing ab initio density functional theory calculations. We find that the magnetic moment on the deposited Fe layer is enhanced as compared to that in bulk iron. We observe a large number of new states on the Fe-deposited surface — one of which is in the majority spin channel having similar dispersion to that on the clean surface, and others in the minority spin channel. The effective mass of electrons in surface states near the Fermi level increases on Fe deposition. The electronic properties are found to be insensitive to the stacking of near-surface layers. We need to use very thick slabs in our calculations to avoid splitting of surface states due to spurious interactions between the two surfaces of the slab. Using the local density of states profiles for different surface states, we conclude that in scanning tunneling microscope experiments one can detect two of the surface states — one in the majority channel below the Fermi level, and another in the minority channel appearing just above the Fermi energy. We compare our results to those from scanning tunneling spectroscopy experiments.     

Electrochemical Behavior of Ce(IV)/Ce(III) Couple in N,N-Di(2-ethylhexyl)-n-butanamide (DEHBA), N,N-Di(2-ethylhexyl)-iso-butanamide (DEHiBA), and N,N-Di(2-ethylhexyl)-3,3-dimethyl Butanamide (DEHDMBA)

In this work we report on the electrochemical behavior of Ce(IV)/Ce(III) redox couple in pure N,N-dialkyl amides (N,N-DA), namely N,N-di(2-ethylhexyl)-n-butanamide (DEHBA), N,N-di(2-ethylhexyl)-iso-butanamide (DEHiBA), and N,N-di(2-ethylhexyl)-3,3-dimethyl butanamide (DEHDMBA) equilibrated with nitric aqueous solutions as an entry to the direct electrochemical characterization of plutonium in these extractants. Ce(IV)/Ce(III) redox process was used as a model. Its potential (E_1/2≅1.02 V/SCE) is not affected by the temperature and the nature of the N,N-DA and this clearly indicates that the functionalities of these extractants produce the same relative effect on both +IV and +III oxidation states of the cerium cation. Linear variations of the current intensity of the reduction peak of Ce(IV) with the concentration of Ce(IV)/N,N-DAs/HNO₃(5 M) solutions were obtained from cyclic voltammograms recorded at 25 °C and 40 °C. Due to the poor definition of the voltammograms in DEHiBA and DEHDMBA, such characterization allows only the evaluation of the performances of the chemical extraction of Ce(IV) from aqueous nitric acid solution by the undiluted DEHBA. To our knowledge, the electrochemical behavior of Ce(IV)/Ce(III) in N,N-DAs was not previously studied and our findings will for sure open the door for further investigations in this field.