An analysis of over-relaxation in a kinetic approximation of systems of conservation laws

The over-relaxation approach is an alternative to the Jin–Xin relaxation method in order to apply the equilibrium source term in a more precise way. This is also a key ingredient of the lattice Boltzmann method for achieving second-order accuracy. In this work, we provide an analysis of the over-relaxation kinetic scheme. We compute its equivalent equation, which is particularly useful for devising stable boundary conditions for the hidden kinetic variables.     

A Switch in the Hydrophobic/Hydrophilic Gas-Adsorption Character of Prussian Blue Analogues: An Affinity Control for Smart Gas Sorption

Porous coordination polymers are molecule-based materials presenting a high degree of tunability, which offer many advantages for targeted applications over conventional inorganic materials. This work demonstrates that the hydrophilic/hydrophobic character of Prussian blue analogues having a lipophilic feature may be tuned to optimize the gas adsorption properties. The role of the coordinatively unsaturated metal sites is emphasized through a combination of theoretical and experimental study of water, ethanol, and n-hexane adsorption.     

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.     

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.     

Up to isometries,a deformation is a continuous function of its metric tensorAux isométries près,une déformation est une fonction continue de son tenseur métrique

If the Riemann–Christoffel tensor associated with a field of class $\text{C}{}^2$ of positive definite symmetric matrices of order three vanishes in a connected and simply connected open subset $\text{Ω?}\text{R}{}^3$, then this field is the metric tensor field associated with a deformation of class $\text{C}{}^3$ of the set $\text{Ω}$, uniquely determined up to isometries of $\text{R}{}^3$. We establish here that the mapping defined in this fashion is continuous, for ad hoc metrizable topologies. To cite this article: P.G. Ciarlet, F. Laurent, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 489–493.     

The mesa problem for Neumann boundary value problem

In this paper, we study the singular limit of the Porous Medium equation u_t=Δu^m+g(x,u), as m→∞, in a bounded domain with Neumann boundary condition.     

Controlled synthesis of amphiphilic biodegradable polylactide‐grafted dextran copolymers

The whole controlled synthesis of novel amphiphilic polylactide (PLA)‐grafted dextran copolymers was achieved. The control of the architecture of such biodegradable and potentially biocompatible copolymers has required a three‐step synthesis based on the “grafting from” concept. The first step consisted of the partial silylation of the dextran hydroxyl groups. This protection step was followed by the ring‐opening polymerization of D ,L ‐lactide initiated from the remaining OH functions of the partially silylated polysaccharide. The third step involved the silylether group deprotection under very mild conditions. Based on previous studies, in which the control of the first step was achieved, this study is focused on the last two steps. Experimental conditions were investigated to ensure a controlled polymerization of D ,L ‐lactide, in terms of grafting efficiency, graft length, and transesterification limitation. After polymerization, the final step was studied in order to avoid degradation of both polysaccharide backbone and polyester grafts. The chemical stability of dextran backbone was checked throughout each step of the synthesis. PLA‐grafted dextrans and PLA‐grafted (silylated dextrans) were proved to adopt a core‐shell conformation in various solvents. Furthermore, preliminary experiments on the potential use of these amphiphilic grafted copolymers as liquid/liquid interface stabilizers were performed. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2577–2588, 2004