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

We describe the nonlinear dispersive dissipative evolution of strain waves in a solid in the limiting condition B∼O(R/L), where B is the characteristic amplitude of the wave, L its wavelength and R the radius of a solid rod. We also provide conditions on dissipation and dispersion for the propagation of either shocks or solitary waves of permanent form.

The interfacial area balance equation in a two-phase mixture looks quite different depending whether the area per unit volume is defined as: i) the sum of all the areas contained in the unit volume or ii) the sum of the areas of all the particles with their centers in this unit volume. We prove here the complete compatibility between the two balance equations and show their respective merits.

Second gradient models are usually non local. Recently local second gradient models have been developed. They can be seen as a particular case of microstructured media which obey a kinematic constraint. It is then easy to build up a large strain finite element method useful for 1D as well as for 2D or 3D problems. A one-dimensional example is finally given.

A simplified model of plane Couette flow is derived by means of a cross-stream (y) Galerkin expansion in terms of trigonometric functions appropriate for idealized stress-free boundary conditions at the plates. A set of partial differential equations is obtained, governing the in-plane (x–z) space-dependence of a velocity field taken in the form: u=U₀(x,z,t)+[1+U₁(x,z,t)]sin(πy/2), v=V₁(x,z,t)cos(πy/2), w=W₀(x,z,t)+W₁(x,z,t)sin(πy/2). Beyond Lorenz-like Waleffe's modeling (Waleffe 1997), this Swift–Hohenberg type of approach is expected to give an access to the microscopic mechanism of spatiotemporal intermittency typical of the transition to turbulence in plane Couette flow (Pomeau 1986, Bergé et al. 1998).

Cavitation is a general phenomenon of the fluid flows with obstacles. It appears in the cooling conduits of the fast nuclear engines. A model of this phenomenon using the theory of Laplace and a common non-convex energy for the liquid and vapour bulks is proposed. This model makes it possible to determine a higher limit of the density of bubbles (a number of bubbles per unit of volume in the flow). The maximum intensity of cavitation is associated with the mechanical and thermal characteristics of the fluid flow.

A model of exact solution is proposed about flows with domains bounded by two planes moving in any manner but remaining parallel. Gravity, stratification and dilatations owing to small differences of temperature are taken into account. The miscellaneous forms of streamlines occuring in the flow are characterised and classified thorougthly.

A new model is proposed for low Rm MHD flows which remain turbulent even in the presence of a magnetic field. These flows minimize the Joule dissipation because of their tendency to become two-dimensional and, therefore to suppress all induction effects. However, some small three-dimensional effects, due to inertia and to the electric coupling between the core flow and the Hartmann layers, are present even within the core flow. This new model, which may be seen as an improvement of the Sommeria–Moreau 2D model, introduces this three-dimensionality as a small perturbation. It yields an equation for the average velocity over the magnetic field lines, whose solution agrees well with available measurements performed on isolated vortices.

A three-dimensional structural acoustic model is considered. This model consists of a wave equation defined on a 3-dimensional bounded domain $\text{Ω}$ coupled with a thermoelastic plate equation defined on Γ₀ – a flat surface of the boundary $\text{∂Ω}$. The main issue studied here is that of uniform stabilizability of the overall interactive model. Since the original (uncontrolled) model is only strongly stable, but not uniformly stable, the question becomes: what is the `minimal amount' of dissipation necessary to obtain uniform decay rates for the energy of the overall system? Our main result states that boundary nonlinear dissipation placed only on a suitable portion of the part of the boundary which is complementary to Γ₀, suffices for the stabilization of the entire structure.

The maximal wall shear stress (MWSS) in the convergent part of a stenosis is computed as a function of characteristic geometrical parameters (stenosis degree and length), of the entry velocity profile and of flow Reynolds number, by means of the Interactive Boundary-Layer (IBL) theory, in the simplified case where the flow is axisymmetric and stationary. The independence of the MWSS on the entry velocity profile is showed. A heuristic analysis, followed by regression analysis of the numerical results, allows drawing out the simple dependence of the MWSS on the other parameters, all measurable in clinical practice. The so obtained relationship extends the results found in the literature, achieved by resolution of Navier-Stokes equations for particular geometrical characteristics.

To describe the relationship between shape and rigidity of cultured cells, we attempt to figure out the similarities and discrepancies in geometrical and mechanical behaviors between a continuous cellular solid and a tensegrity structure. The rigidity of the structure is characterized by elementary bending in cellular solid and a spatial rearrangement of the elements in tensegrity model. This spatial reorganization tends to decrease the scale factor influence in tensegrity model. This factor has a major effect in cellular solid model in spite of the lack of internal tension.