Excess enthalpy of ternary mixture for diamine+heptane+cyclohexan

The excess molar enthalpy of ternary mixture for 3-diethylaminopropylamine+heptane+cyclohexane were measured using a Calvet microcalorimeter at 303.15 K. Empirical equations, Redlich-Kister, Tsao-Smith, and Kohler and group contribution models, UNIFAC (modified version) and DISQUAC have been applied. A reasonable representation of ternary data is obtained. This revised version was published online in August 2006 with corrections to the Cover Date.     

Phosphorylated cellulose for water purification: a promising material with outstanding adsorption capacity towards methylene blue

Cellulose - Enhancing the sorption properties of cellulose is a prerequisite for its efficient use in water purification as an alternative to costly activated carbon. Here, solvent-free...     

A fast algorithm for Gaussian type quadrature formulae with mixed boundary conditions and some lumped mass spectral approximations

After studying Gaussian type quadrature formulae with mixed boundary conditions, we suggest a fast algorithm for computing their nodes and weights. It is shown that the latter are computed in the same manner as in the theory of the classical Gauss quadrature formulae. In fact, all nodes and weights are again computed as eigenvalues and eigenvectors of a real symmetric tridiagonal matrix. Hence, we can adapt existing procedures for generating such quadrature formulae. Comparative results with various methods now in use are given. In the second part of this paper, new algorithms for spectral approximations for second-order elliptic problems are derived. The key to the efficiency of our algorithms is to find an appropriate spectral approximation by using the most accurate quadrature formula, which takes the boundary conditions into account in such a way that the resulting discrete system has a diagonal mass matrix. Hence, our algorithms can be used to introduce explicit resolutions for the time-dependent problems. This is the so-called lumped mass method. The performance of the approach is illustrated with several numerical examples in one and two space dimensions.

     

Effects of the polydispersity on the viscoelasticity of low molecular weight polymers

The viscoelastic behavior of low molecular weight polymers exhibiting a fairly broad distribution has been deduced from the behavior of narrow samples by way of a linear law as a function of the density of the molecular weight distribution. Rheology of polydisperse linear polymers where the entire distribution of molecular weights is lower than 2 M _ehas been investigated using both binary mixtures and a broad sample of polystyrene. A decrease of the friction coefficient and of the viscosity compared to that of a narrow sample with the same M _w is observed. Therefore, the low components of broad samples play the role of plasticizers or lubricants which has been investigated in relation with the molecular weight distribution.     

Identities of arithmetic type between values of the theta function associated to a lattice in ℝ d and its derivatives

In this paper, we introduce a notion of similarly self dual lattice in a d-dimensional Euclidean space and a classical Jacobi theta function is associated to such a lattice. We establish identities of arithmetic type between values of this theta function and its successive derivatives. This work can be related to the spectral theory of the Landau operators.      

Series and integral representations of the Taylor coefficients of the Weierstrass sigma-function

We provide two kinds of representations for the Taylor coefficients of the Weierstrass σ-function σ(?;Γ) associated to an arbitrary lattice Γ in the complex plane \(\mathbb{C}=\mathbb{R}^{2}\) , the first one in terms of the so-called Hermite–Gauss series over Γ and the second one in terms of Hermite–Gauss integrals over \(\mathbb{C}\) .     

Negative Definite Cubature Formulae, Extremality and Delaunay Triangulation

Let Ω⊂ℝ ^d be a compact convex polytope of positive measure. We study cubature formulae on Ω which approximate the integral of every convex function f∈C(Ω) from above. They are called negative definite formulae or nd-formulae for short. In particular, we characterize nd-formulae by certain partitions of unity or, alternatively, by a class of positive linear operators. For aiming at ‘good’ nd-formulae, we introduce three extremal properties named as minimal, best and optimal. We show that the Delaunay triangulation and one of its generalizations give access to efficient algorithms for computing nd-formulae with one of these properties.     

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.