Low-cost automated capillary electrophoresis instrument assembled from commercially available parts

A CE instrument that can be assembled from commercially available components with minimal construction effort is described. Except for the electronic control circuitry no specially made parts are required. It is based on a flexible design of microfluidic, electropneumatic, and electronic sections and different configurations can easily be implemented. Automated injection into the capillary is performed hydrodynamically by the application of a pressure for a controlled length of time. The performance of the device was tested with a contactless conductivity detector by separating different metal ions. In addition, nine metal cations related to the quality of honey were separated in 2.3 min and four honey samples were analysed quantitatively to demonstrate the applicability of the method.     

A door to model reduction in high-dimensional parameter space

Model reduction techniques such as Proper Generalized Decomposition (PGD) are decision-making tools that are about to revolutionize many domains. Unfortunately, their computation is still problematic for problems involving many parameters, for which one has to face the “curse of dimensionality”. An answer to this challenge is given in solid mechanics by the so-called “parameter-multiscale PGD”, which is based on Saint-Venant's principle. In this article, a model problem composed of up to a thousand parameters is presented, showing that the method is able to overcome the “curse of dimensionality”.     

On the thermodynamic limit of the B.C.S. state

We consider vector states in the Fock representation of the C.A.R. algebra, representing condensed pair states. We prove that in the thermodynamic limit these states give rise to a direct integral of gauge-dependent B.C.S. states.Partially supported by C.N.R.Equipe de Recherche associée au C.N.R.S. n^o 154.     

Hidden Uq (sl(2)) Uq (sl(2)) Quantum Group Symmetry in Two Dimensional Gravity

In a previous paper, the quantum-group-covariant chiral vertex operators in the spin 1/2 representation were shown to act, by braiding with the other covariant primaries, as generators of the well known U_q(sl(2)) quantum group symmetry (for a single screening charge). Here, this structure is transformed to the Bloch wave/Coulomb gas operator basis, thereby establishing for the first time its quantum group symmetry properties. A U_q(sl(2)) U_q(sl(2)) symmetry of a novel type emerges: The two Cartan-generator eigenvalues are specified by the choice of matrix element (Vermamodules); the two Casimir eigenvalues are equal and specified by the Virasoro weight of the vertex operator considered; the co-product is defined with a matching condition dictated by the Hilbert space structure of the operator product. This hidden symmetry possesses a novel Hopf-like structure compatible with these conditions. At roots of unity it gives the right truncation. Its (non-linear) connection with the U_q(sl(2)) previously discussed is disentangled. Received: 25 April 1996/Accepted: 20 July 1996     

Triangular finite elements of HCT type and classC ρ

Let τ be some triangulation of a planar polygonal domain Ω. Given a smooth functionu, we construct piecewise polynomial functionsv∈C ^ρ(Ω) of degreen=3 ρ for ρ odd, andn=3ρ+1 for ρ even on a subtriangulation τ₃ of τ. The latter is obtained by subdividing eachT∈ρ into three triangles, andv/T is a composite triangular finite element, generalizing the classicalC ¹ cubic Hsieh-Clough-Tocher (HCT) triangular scheme. The functionv interpolates the derivatives ofu up to order ρ at the vertices of τ. Polynomial degrees obtained in this way are minimal in the family of interpolation schemes based on finite elements of this type.