Analysis of a Poisson system with boundary conditions

We consider a class of problems originating from a Raman laser amplification model, for which the equations can be written as a Poisson system with boundary conditions. Once reformulated, this system becomes an integro-differential equation that we study here in some detail. In particular, we show the existence of a smooth solution under general assumptions, and prove its uniqueness for boundary values that are not too far apart. Eventually, we completely solve the question of uniqueness for systems of dimensions one and two. To cite this article: F. Castella et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Une note sur les lemmes div–curl

Let $\text{Ω}$ be a strongly Lipschitz domain of $\text{R}{}^{\mathrm{n}}$ (n?2). We give endpoint versions of div–curl lemmata on $\text{Ω}$, for a given function f on $\text{Ω}$ whose gradient belongs to a Hardy space on $\text{Ω}$. To cite this article: P. Auscher et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Thermal emission stimulated by excitation of metastable states

Waves interference inside thin films creates fine structures in the thermal emission spectrum of film when the magnitude of film thickness is of the same order than the coherence length of light. Here, we present an alternative to the theory of partially coherent light to explain these ripples pattern and easily predict the radiative properties of films in intermediate regime. The starting point of this theory is based on the observation that unlike vacuum, matter supports the presence of unstable electromagnetic waves with a finite lifetime. For thin absorbing films, we demonstrate that many of these metastable states are quantified and can be excited by an external radiation field. A direct connection is then established between the peaks of emission and these modes. These results open new prospects for the theoretical study and modelling of radiative exchanges inside and between microscale media.     

Fundamental processes in long air gap discharges

The development of atmospheric lightning is initiated and sustained by the formation in virgin air of ‘streamer corona’ and ‘leader’ discharges, very similar to those observed in laboratory long sparks. Therefore, the experimental and theoretical investigations of these laboratory discharges have become of large interest to improve the physical knowledge of the lightning process and to develop self-consistent models that could be applied to new protection concepts.In the present paper the fundamental processes of the subsequent phases of long air gap discharges are analyzed, from the first corona inception and development to the leader channel formation and propagation. For all these processes simulations models are discussed that have been essentially derived and simplified by the authors, in order to develop sequential time-dependent simulation of the laboratory breakdown, with both positive and negative voltages. The possibility of extending these models to the case of natural lightning is discussed in the companion paper, presented in this same volume. To cite this article: I. Gallimberti et al., C. R. Physique 3 (2002) 1335–1359.     

Radiative transfer in static and spherically symmetric distording media: from the effective geometry to a kinetic theory

In numerous new media (superfluids, Bose-Einstein condensates, nonlinear dielectrics,…) and multiple settings (accretion flows onto compact objects, optics EIT, stellar collapses, supernovae expanding envelopes, relativistic vortex flow, early Universe…) matter appears to light as an effective curved spacetime. These media that we call ‘distording media’ induce spatial modifications on the phases functions of the electromagnetic fields so that light paths become curved lines. This nonlinear optical behavior gives birth to singular effects (confinement of light, black hole effect…) which confer in the same time a local and a non-local dimension to the radiative transfer. We develop a general phenomenological theory of radiative transfer inside any static and spherically symmetric distorting media. We especially prove that the curvature of the effective spacetime plays a fundamental role in the specific intensity balance.     

Numerical study of the heat transfer and electro-thermo-convective flow patterns in dielectric liquid layer subjected to unipolar injection

In this article we study the electro-thermal convection in a dielectric liquid layer placed between two electrodes and subjected to the simultaneous action of an electric field and a thermal gradient. The full set of equations describing the electro-thermo-convective phenomena is directly solved using a finite volume method. We first heat the liquid from below at time t = 0, wait for the thermal steady state and then inject the electric charges by applying the electric potential. The development of the electro-convective motion is analysed in detail in two cases: 1) strong injection from the lower electrode, 2) strong injection from the upper one. We also study the heat transfer enhancement due to electro-convection. The evolution in time of the Nusselt number Nu for different combinations of the two usual non-dimensional parameters associated to the electro-thermo-convection phenomena (Rayleigh number Ra and the electrical parameter T) is also given and analysed.     

Structure of precipitates and orientation relationships in Al,Ge, Mo-doped higher manganese silicide crystals

Abstract

The structure of Al, Ge, Mo-doped Higher Manganese Silicide (HMS) crystals with the general formulas Mn(Si_0.99Ge_0.01)_1.75, Mn(Si_0.995Ge_0.005)_1.75 and (Mn_0.98Mo_0.02)[(Si_0.98Ge_0.02)_1.75]_0.99Al_0.01 was investigated by scanning and transmission electron microscopy, electron diffraction and X-ray energy dispersive spectrometry in a wide scale range from a few mm to several Å. Several secondary phases were identified in the Mn₄Si₇ matrix: Ge_1?xSi_x (0.1 < x < 0.9) solid solution precipitates with Ge concentration ranging from 5 at. % up to 93 at.%, MoSi₂ platelets, MnSi and Mn₅Si₃ precipitates. Their morphology, structure and crystallographic relationships with the HMS matrix were determined. Mostly local strains in the matrix and precipitates due to lattice misfits at interfaces derived from crystallographic relationships were found two orders of magnitude higher than deformation induced by thermal expansion mismatch. Only a few exceptions of specific relationships were found when the lattice misfit and thermal mismatch have close values. The largest misfit of about 22% was observed between MnSi and Mn₄Si₇ what led to big and numerous cracks in crystals. Therefore, doping can improve the material performance (1) by preventing the formation of MnSi precipitates with metallic properties and (2) by reduction of cracking and crack propagation because of larger MnSi /Mn₄Si₇ lattice misfit compared to Ge_1?xSi_x /Mn₄Si₇ or MoSi₂/Mn₄Si₇ misfits.     

The dimension of leaf closures of K-contact flows

For K-contact flows on (2n+1)-dimensional compact manifolds, we show that the dimension of any leaf closure is at most the smaller of (n+1) and 2n+1) minus the rank of the vector space of harmonic vector fields.     

On the transition moment of the CO2 40°1II-00°0 band near 7740 cm-1

Using intensity measurements on the CO₂ 40°1_II-00°0 band obtained by Valero and Boese, we have expanded the F(m)-factor for the parallel band by using the Herman-Wallis formula. We have calculated the transition moment and determined the coefficients in the expansion of F(m).     

Soluble models for dynamics driven by a super-diffusive noise

We explicitly discuss scalar Langevin type of equations where the deterministic part is linear, but where the integrated noise source is a non-linear diffusion process exhibiting superdiffusive behavior. We calculate transient and stationary probabilities and study the possibility of noise induced transitions from a unimodal to a bimodal probability shape. Illustrations from finance and dynamical systems are given.