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.     

Validated Infeasible Interior-Point Predictor–Corrector Methods for Linear Programming

Many problems arising in practical applications lead to linear programming problems. Hence, they are fundamentally tractable. Recent interior-point methods can exploit problem structure to solve such problems very efficiently. Infeasible interior-point predictor–corrector methods using floating-point arithmetic sometimes compute an approximate solution with duality gap less than a given tolerance even when the problem may not have a solution. We present an efficient verification method for solving linear programming problems which computes a guaranteed enclosure of the optimal solution and which verifies the existence of the solution within the computed interval.     

Program explanations and causal relevance

Frank Jackson and Philip Pettit have defended a non-reductive account of causal relevance known as the ‘program explanation account’. Allegedly, irreducible mental properties can be causally relevant in virtue of figuring in non-redundant program explanations which convey information not conveyed by explanations in terms of the physical properties that actually do the ‘causal work’. I argue that none of the possible ways to spell out the intuitively plausible idea of a program explanation serves its purpose, viz., defends non-reductive physicalism against Jaegwon Kim’s Causal Exclusion Argument according to which non-reductive physicalism is committed to epiphenomenalism because irreducible mental properties are ‘screened off’ from causal relevance by their physical realizers. Jackson and Pettit’s most promising explication of a program explanation appeals to the idea of invariance of effect under variation of realization, but I show that invariance of effect under variation of realization is neither necessary nor sufficient for causal relevance.     

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.     

Nonvanishing derivatives and normal families

We consider the differential operators Ψ _k , defined by Ψ₁(y) =y and Ψ _k+1(y)=yΨ _k y+d/dz(Ψ _k (y)) fork ∈ ℕ fork∈ ℕ. We show that ifF is meromorphic in ℂ and Ψ _k F has no zeros for somek≥3, and if the residues at the simple poles ofF are not positive integers, thenF has the formF(z)=((k-1)z+a)/(z ²+β z+γ) orF(z)=1/(az+β) where α, β, γ ∈ ℂ. If the residues at the simple poles ofF are bounded away from zero, then this also holds fork=2. We further show that, under suitable additional conditions, a family of meromorphic functionsF is normal if each Ψ _k (F) has no zeros. These conditions are satisfied, in particular, if there exists δ>0 such that Re (Res(F, a)) <−δ for all polea of eachF in the family. Using the fact that Ψ _k (f ^′/f) =f ^(k)/f, we deduce in particular that iff andf ^(k) have no zeros for allf in some familyF of meromorphic functions, wherek≥2, then {f ^′/f :f ∈F} is normal. The first author is supported by the German-Israeli Foundation for Scientific Research and Development G.I.F., G-643-117.6/1999, and INTAS-99-00089. The second author thanks the DAAD for supporting a visit to Kiel in June–July 2002. Both authors thank Günter Frank for helpful discussions.     

A model for the calculation of noise transmission inside dwellings: application to aircraft noise

A numerical model of sound transmission inside dwellings has been developed. It is based on a decoupled method mixing integral, modal and geometric approaches. Kropp's formulation has been adapted to take balconies into account. Architectural effects such as projected roofs or nearby buildings have been analysed. Sound transmission is strongly affected by the angle of incidence of incoming waves. The proposed approach makes use of velocity fields on windows either computed or measured with a laser vibrometer. Comparisons between computations and measurements are reported.     

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