Closure laws for a two-fluid two-pressure modelLois de fermeture pour un modèle à deux pressions d'écoulement diphasique

Closure laws for interfacial pressure and interfacial velocity are proposed within the frame work of two-pressure two-phase flow models. These enable us to ensure positivity of void fractions, mass fractions and internal energies when investigating field by field waves in the Riemann problem. To cite this article: F. Coquel et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 927–932.     

Analysing the information flow between financial time series

Following the recently introduced concept of transfer entropy, we attempt to measure the information flow between two financial time series, the Dow Jones and DAX stock index. Being based on Shannon entropies, this model-free approach in principle allows us to detect statistical dependencies of all types, i.e. linear and nonlinear temporal correlations. However, when available data is limited and the expected effect is rather small, a straightforward implementation suffers badly from misestimation due to finite sample effects, making it basically impossible to assess the significance of the obtained values. We therefore introduce a modified estimator, called effective transfer entropy, which leads to improved results in such conditions. In the application, we then manage to confirm an information transfer on a time scale of one minute between the two financial time series. The different economic impact of the two indices is also recovered from the data. Numerical results are then interpreted on one hand as capability of one index to explain future observations of the other, and on the other hand within terms of coupling strengths in the framework of a bivariate autoregressive stochastic model. Evidence is given for a nonlinear character of the coupling between Dow Jones and DAX.     

Universal Overconvergence of Polynomial Expansions of Harmonic Functions

For each compact subset K of ^N let (K) denote the space of functions that are harmonic on some neighbourhood of K. The space (K) is equipped with the topology of uniform convergence on K. Let Ω be an open subset of ^N such that 0Ω and ^N\Ω is connected. It is shown that there exists a series ∑H_n, where H_n is a homogeneous harmonic polynomial of degree n on ^N, such that (i) ∑H_n converges on some ball of centre 0 to a function that is continuous on Ω and harmonic on Ω, (ii) the partial sums of ∑H_n are dense in (K) for every compact subset K of ^N\Ω with connected complement. Some refinements are given and our results are compared with an analogous theorem concerning overconvergence of power series.     

Climbing Mount Scalable: Physical Resource Requirements for a Scalable Quantum Computer

The primary resource for quantum computation is Hilbert-space dimension. Whereas Hilbert space itself is an abstract construction, the number of dimensions available to a system is a physical quantity that requires physical resources. Avoiding a demand for an exponential amount of these resources places a fundamental constraint on the systems that are suitable for scalable quantum computation. To be scalable, the effective number of degrees of freedom in the computer must grow nearly linearly with the number of qubits in an equivalent qubit-based quantum computer.     

The limits of hamiltonian structures in three-dimensional elasticity,shells, and rods

Summary This paper uses Hamiltonian structures to study the problem of the limit of three-dimensional (3D) elastic models to shell and rod models. In the case of shells, we show that the Hamiltonian structure for a three-dimensional elastic body converges, in a sense made precise, to that for a shell model described by a one-director Cosserat surface as the thickness goes to zero. We study limiting procedures that give rise to unconstrained as well as constrained Cosserat director models. The case of a rod is also considered and similar convergence results are established, with the limiting model being a geometrically exact director rod model (in the framework developed by Antman, Simo, and coworkers). The resulting model may or may not have constraints, depending on the nature of the constitutive relations and their behavior under the limiting procedure. The closeness of Hamiltonian structures is measured by the closeness of Poisson brackets on certain classes of functions, as well as the Hamiltonians. This provides one way of justifying the dynamic one-director model for shells. Another way of stating the convergence result is that there is an almost-Poisson embedding from the phase space of the shell to the phase space of the 3D elastic body, which implies that, in the sense of Hamiltonian structures, the dynamics of the elastic body is close to that of the shell. The constitutive equations of the 3D model and their behavior as the thickness tends to zero dictates whether the limiting 2D model is a constrained or an unconstrained director model. We apply our theory in the specific case of a 3D Saint Venant-Kirchhoff material andderive the corresponding limiting shell and rod theories. The limiting shell model is an interesting Kirchhoff-like shell model in which the stored energy function is explicitly derived in terms of the shell curvature. For rods, one gets (with an additional inextensibility constraint) a one-director Kirchhoff elastic rod model, which reduces to the well-known Euler elastica if one adds an additional single constraint that the director lines up with the Frenet frame. This paper is dedicated to the memory of Juan C. Simo This paper was solicited by the editors to be part of a volume dedicated to the memory of Juan Simo.     

A simple yet accurate boundary element method for continuum dielectric calculations

A simple yet accurate method for calculating electrostatic potentials using the boundary element continuum dielectric method is presented. It is shown that the limiting factor in accuracy is not the evaluation of integrals involving the interaction between boundary elements but rather a proper estimation of the self-polarization of a patch upon itself. We derive a sum rule that allows us to calculate this important self-polarization term in a self-consistent and simple way. Intricate integration schemes used in previous treatments are consequently rendered unnecessary while concurrently achieving at least comparable accuracy over earlier methods. In some model systems for which analytic solutions are available, the computed surface polarization charge and reaction field energy are correct to better than six significant figures. An application of the method to the calculation of hydration free energies is presented. Good agreement with experimental values is obtained.     

On estimating pressure build-up in severely accelerated,shocked flow

A new approach to the calculation of the high pressures characterizing the flow field in front of a piston undergoing severe acceleration over the short term is presented. In contrast with previous approaches where the computational domain is altered but which stop short of transforming velocities, here the problem is solved in an accelerating non-Euclidean co-ordinate system where the piston is stationary. The method is applied to a study of the problem of premature sabot separation. Through use of Harten's second-order-accurate TVD scheme, flow simulations are performed for both 1D and 3D axisymmetric geometries. The simple 1D model gives pressure profiles surprisingly close to those of the more physical 3D model.     

Thermal stability of poly(mono-n-alkylitaconates) and mono-n-alkylitaconate-co-vinylpyrrolidone copolymers I

Poly(monoitaconates) containing octyl, decyl and dodecyl groups and random monoalkylitaconate-co-vinylpyrrolidone copolymers were studied by thermogravimetric analysis. Copolymers of mono-n-octylitaconate (MOI), mono-n-decylitaconate (MDI), and mono-n-dodecylitaconate (MDoI), respectively, with N-vinyl-2-pyrrolidone (VP) of different compositions were studied by dynamic thermogravimetric analysis. The thermal stability of the copolymers depends on the structure of the monoitaconate comonomer and on the composition of the copolymer The kinetic analysis of the degradation data shows that the thermal decomposition of these copolymers can be described by several kinetic orders depending on the copolymer and on the composition. The relative thermal stability of the copolymers increases as the VP content increases and as the length of the side chain of the itaconate increases, following the same trend as the flexibility of the copolymers in solution.     

The ternary system CsCl−NaCl−LaCl3

The ternary system CsCl?NaCl?LaCl₃ was investigated by means of differential thermal analysis and X-ray powder diffraction analysis. There exists one congruently melting compound, Cs₂NaLaCl₆, crystallizing with the cubic elpasolite structure. No quasi-binary section exists for the whole system, however three binaries range from the ternary compound Cs₂NaLaCl₆ to NaCl, CsLa₂Cl₇ and Cs₃LaCl₆ resp., dividing the system in three areas of composition: one triangle, Cs₃LaCl₆?Cs₂NaLaCl₆?CsLa₂Cl₇, containing additionally a compound Cs₂LaCl₅ below 510°C, and the two areas CsCl?NaCl?Cs₂NaLaCl₆?Cs₃LaCl₆ and Cs₂NaLaCl₆?NaCl?LaCl₃?CsLa₂Cl₇, containing a mixed crystal range between LaCl₃ and Na₃La₅Cl₁₈. These areas could be further divided in five triangles, so that the whole system contains six Alkemade triangles.