Homogenization and concentrated capacity in reticular almost disconnected structuresHomogénéisation et capacité concentrée dans les structures réticulaires presque déconnectées

We compute the homogenized-concentrated limit for a pair of non-linearly coupled diffusion equations in a perforated cylindric domain with coaxial cylindric holes periodically distributed along its axis. This problem arises from visual transduction. To cite this article: D. Andreucci et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 329–332.     

A Wiener-type condition for boundary continuity of quasi-minima of variational integrals

A Wiener-type condition for the continuity at the boundary points of Q-minima, is established, in terms of the divergence of a suitable Wiener integral.     

The bidmensional stefan problem with convection: the time dependent case

This paper considers the time dependent stefan problem with convection in the fluid phase governed by the Stokes equation, and with adherence of the fluid on the lateral boundaries: The existence of a weak solution is obtained via the introduction of a temperature dependent penalty term in the fluid flow equation, together with the application of various compactness arguments.     

On complemented copies of c 0 and ℓ ∞

We furnish examples of pairs of Banach spaces X, Y so that none of c ₀ and l _∞ live inside X ^? and Y, but they embed complementably into the space DP(X,Y) of the Dunford–Pettis operators from X into Y.     

A linear hyperbolic system and an optimal control problem

We prove a theorem of existence, uniqueness, and continuous dependence for a linear hyperbolic system with Darboux-type conditions under assumptions on the coefficients, which are in a sense the most general possible. Moreover, an application of this result to an optimal control problem is given.     

High-capacitance organic nanodielectrics: effective medium models of their response

Molecular and macromolecular high-permittivity organic gate dielectric materials have been the focus of recent experimental research as a consequence of their promising properties for organic and inorganic field effect transistor (FET) applications. Two types of molecular thin films, self-assembled nanodielectrics (SANDs) and cross-linked polymer blends (CPBs), have been shown experimentally to afford high capacitances and low FET operating voltages. In an effort to design optimized nanostructures having even larger capacitances, lower leakage current densities, and further reduced FET operating voltages, we discuss approaches for computing the effective permittivities of each nanodielectric motif and investigate how molecular arrangements impact overall device capacitance. The calculated frequency-dependent capacitances, derived from Maxwell-Wagner theory applied to the Maxwell-Garnett effective medium approximation, agree fairly well with the experimental values for the two types of nanodielectrics. Predictions of larger capacitance SANDs are made with the two-capacitors-in-series equivalent circuit, where the layered, self-assembled structure is viewed as two different capacitors. The Maxwell-Garnett and Polder-Van Santen effective medium approximations are used to predict the dielectric response of higher permittivity polymer cross-linked blends. In calculations showing good agreement between theory and experiment, and with all parameters being equal, it is found that greater capacitances should be achievable with cross-linked composites than with layered composites.     

Crack propagation in amorphous polymers and their composites

The fracture energy of a polymer depends strongly on the viscoelastic responses of the material, and therefore is a function of temperature and crack velocity. The toughness of a composite is determined by the way in which the reinforcing filler modifies the energy dissipating mechanisms of the polymeric matrix.

The fracture toughness of a variety of polymeric glasses and their composites with glass beads, glass fibers, and rubber particles was measured. The velocity of rapidly moving cracks and the crack propagation rates under controlled loading conditions were also measured.

It was found that the crack propagation velocities in unfilled and glass bead filled materials were controlled by the longitudinal stress waves in the matrix and that the only effects of the glass beads were to blunt the crack tip and limit the viscous deformation. The effect on fracture toughness was relatively small and either positive or negative, depending on which of the above two factors dominated.

The presence of rubber particles as a second phase lowered terminal crack propagation velocities and greatly increased the fracture toughness, indicating a crack retarding effect of the rubber particles. This is related to the induction of crazes in the matrix by the rubber phase.

Glass fibers had a tendency to bridge the tip of a propagating crack, thereby greatly increasing the fracture toughness. In this case the work of fracture comes from a combination of the elastic strain energy stored in the fibers, the energy dissipated in debonding the fibers from the matrix, and the fracture energy of the matrix itself.     

Harnack estimates for quasi-linear degenerate parabolic differential equations

We establish the intrinsic Harnack inequality for non-negative solutions of a class of degenerate, quasilinear, parabolic equations, including equations of the p-Laplacian and porous medium type. It is shown that the classical Harnack estimate, while failing for degenerate parabolic equations, it continues to hold in a space-time geometry intrinsic to the degeneracy. The proof uses only measure-theoretical arguments, it reproduces the classical Moser theory, for non-degenerate equations, and it is novel even in that context. Hölder estimates are derived as a consequence of the Harnack inequality. The results solve a long standing problem in the theory of degenerate parabolic equations.