Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Chemistry-Astronomy最新文献

We present a justification of the nonlinear Koiter's shallow-shell model using an asymptotic approach. Our method needs no a priori assumptions. Putting equilibrium equations into a nondimensional form, dimensionless numbers naturally appear. These numbers characterize level forces and shell geometry. In the case of a shallow-shell subjected to moderate level forces, the nonlinear Koiter's shallow-shell model is obtained.

We present the results of a statistical analysis carried out from a data base of six solar chromospheric emission lines recorded simultaneously and with high spectral resolution. An empirical and a clustering method for separating the different solar structure contributions have been used and been found to be in good agreement. Mean profiles corresponding to the different populations have been built. Correlations of different parameters for each profile allowed us to deduce different properties of the solar chromosphere, such as the existence of magnetic canopies and downflows in active regions.

Numerical simulations are used to study the transition to turbulence of a spatially developed compressible mixing layer between rigid walls. The fast and slow flows are supersonic with Mach numbers M₁ = 4.5 and M₂= 1.6 respectively. The full Navier-Stokes equations are solved for a 2D compressible flow with a high order Godunov 's scheme piecewise parabolic method (PPM) with the approximate Riemann solver of Roe. The purpose is to study the transition to turbulence from the linear regime of instability, with comparison to the linear stability analysis of Tam and Hu.

A similarity solution for a steadily moving semi-infinite fluid-driven fracture in an impermeable linear elastic solid is described in this note. The existence of a lag, of a priori unknown length, between the crack tip and the fluid front is explicitly taken into account. The asymptotic behavior of the solution at the tip is consistent with linear elastic fracture mechanics, whereas its asymptotic behaviour at infinity corresponds to a singular solution constructed under the assumption of zero fluid lag. A universal relation between fluid lag and fracture toughness is obtained.

The present study aims at providing insights into the understanding of the formation of bubbles at a submerged orifice under constant flow conditions, in both Newtonian and non-Newtonian fluids. A rigorous theoretical model was developed for describing the non-spherical bubble formation as well as the detachment at the orifice. The results predicted by this model compare satisfactorily with the experimental investigation. However, a deviation was observed in elastic fluids with the increase of gas flow rates when the memory effects become important.

A particular superposition of coaxial cylinders is used to describe the adhesive contact between an axi-symmetric punch and an elastic material. The proposed formalism allows us to simply find the equations of the adhesive contact when the range of the interfacial forces is supposed to be zero (Maugis and Barquins ' generalisation of Johnson et al. 's results) and when the interfacial force law is described using the Dugdale model. In the latter case, explicit expressions are given for an arbitrary axi-symmetric punch profile.

The present work examines the turbulent flow in a rotor-stator system subjected to a radial inflow and heat transfer effects. In the scope of this study, compressibility can be neglected which leads us to dissociate the heat transfer process from the dynamical effects. A method for making simultaneous temperature and velocity measurements is used to provide qualitative and quantitative data. An analysis of the results and comparisons with a theoretical prediction issued from an asymptotical formulation brings typical properties of the flow to light.

We present an analytical study of the structure of the flow of a molten alloy. The alloy is contained in a cylindrical crucible and locally heated on its free surface by an electron beam. Due to the high temperature under the electron beam, local evaporation of alloy components occurs. The difference of volatility of the two components creates a concentration gradient in the melt. The study consists of determining analytically the structure of the flow with the following approximations: the aspect ratio height over diameter of the liquid layer is small and for moderate heat supply. We show that in the first significant order, the flow pattern in the conductive regime is governed by two dimensionless numbers, a Marangoni and a Rayleigh number that measure the relative strengths of the thermal and solutal effects.

In this note we show that the space of configurations of a medium with a microstructure is a principal bundle over the manifold of embeddings of the underlying macromedia. The structure group is just the group of gauge transformations. An appropriate Lagrangian function is chosen defining the dynamics of the system. The Cosserat media are considered as an example.

The bending inertia of a circular cross section is derived within the couple-stress theory where only the gradient of the rate of rotation is taken into account.