Loading aircraft for military operations

In this paper, we describe an aircraft loading problem submitted by the French military agency (DGA) as part of a more general military airlift planning problem. It can be viewed as a kind of bi-dimensional bin-packing problem, with heterogeneous bins and several additional constraints. We introduce two-phase methods for solving this NP-hard problem. The first phase consists in building good initial solutions, thanks to two fast algorithms: a list-based heuristic and a loading pattern generation method. Both algorithms call a constraint-based subroutine, able to determine quickly if the items already loaded can be reshuffled to accommodate a new object. The second phase improves these preliminary solutions using local search techniques. Results obtained on real data sets are presented.     

Amplitude des oscillations d'ondes solitaires généralisées

Various physical systems of dispersive waves admit solutions in the form of generalized solitary waves. Such waves result from the resonance between a long localized wave and short periodic oscillations. Many estimates (rigorous and numerical) have been given for the amplitude of the ripples in the tail of the generalized solitary wave when its central part has a sech² shape. This Note provides estimates (not yet rigorous) for the ripple amplitude when the central part is flat and wide. To cite this article: C. Fochesato, F. Dias, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Biosorption of Chromium(III) by Biomass of Seaweed Sargassum sp. in a Fixed-Bed Column

This work aimed at modeling chromium biosorption using the biomass of seaweed Sargassum sp. in a fixed-bed column. The mathematical model used was obtained from the mass balance of the component in the liquid phase and in the biosorbent material. The effects of both axial dispersion in the column and the resistance to mass transfer in the solid were considered for the solution of the partial differential equations of the model, using the Galerkin method on finite elements. To represent the equilibrium data of the batch system the Langmuir isotherm were used. The chromium ion adsorption capacity of the seaweed Sargassum sp., at a temperature of 30°C and pH 3.5, was 2.61 mmol/g. The model performance was evaluated from experimental data obtained at 30°C for flow rates of 2, 6 and 8 mL/min. The parameters of the model, mass transfer and axial dispersion coefficients, were adjusted from these experimental data. The model proved adequate to describe chromium biosorption dynamics in fixed-bed columns.     

Refraction holodiagrams and Snell's law

The refraction holodiagram RHD is analyzed here with respect to the law of refraction. Particularly, we study the surface that exactly conjugates by refraction a virtual point source with a real image or conversely. By using the total optical path as a parameter we build a diagram that consists in a family of Descartes ovals of the apple type that contains the Pascal's limaçon as a particular extreme case and the spherical surface with the Weierstrass points as another. These representations permit the straightforward application of Fermat's principle in the case of arbitrary refracting surfaces and show the shape of generalized Fresnel's zones in the intersections with any surface. Snell's law is applied to rays incident on the apple type surfaces to find out the conditions for exact conjugation. Sensitivity to optical path variations is also discussed. The RHD curves family can be represented in a Cartesian way where the ovals appear as equally spaced straight lines.     

Lagrangian flows: The dynamics of globally minimizing orbits

The objective of this note is to present some results, to be proved in a forthcoming paper, about certain special solutions of the Euler-Lagrange equations on closed manifolds. Our main results extend to time dependent periodic Lagrangians with minor modifications.We have chosen the autonomous case because this formally simpler framework allows to reach more easily the core of our concepts and results. Moreover the autonomous case exhibits certain special features involving the energy as a first integral that deserve special attention. They are closely related to the link found by Carneiro [C] between the energy and Mather's action function [Ma].Reprinted by permission of Addison Wesley Longman Ltd.     

Diffusing particles with electrostatic repulsion

Summary. We study a diffusion model of an interacting particles system with general drift and diffusion coefficients, and electrostatic inter-particles repulsion. More precisely, the finite particle system is shown to be well defined thanks to recent results on multivalued stochastic differential equations (see [2]), and then we consider the behaviour of this system when the number of particles goes to infinity (through the empirical measure process). In the particular case of affine drift and constant diffusion coefficient, we prove that a limiting measure-valued process exists and is the unique solution of a deterministic PDE. Our treatment of the convergence problem (as ) is partly similar to that of T. Chan [3] and L.C.G. Rogers - Z. Shi [5], except we consider here a more general case allowing collisions between particles, which leads to a second-order limiting PDE. Received: 5 August 1996 / In revised form: 17 October 1996     

Twistor Geometry for Hyperkähler Metrics on Complex Adjoint Orbits

We study the hyperkähler geometry of complex adjoint orbits from the point of view of twistor theory. We introduce, for complex semisimple adjoint orbits, the associated spectral curve and construct the twistor space as a union of certain regular adjoint orbits; we also exhibit the family of twistor lines. Furthermore, we show how our methods may be applied for describing hyperkähler metrics associated to more general spectral curves. In particular, we give an algebraic characterisation of the twistor lines.     

Unreasonable effectiveness of symmetry in physics

We prove that in some reasonable sense, every possible physical law can be reformulated in terms of symmetries. This result explains the well-known success of the group-theoretic approach in physics.     

Preparation and Eh--pH diagrams of Fe(II)--Fe(III) green rust compounds; hyperfine interaction characteristics and stoichiometry of hydroxy-chloride, -sulphate and -carbonate

Fe(II)--Fe(III) hydroxy-chloride, -sulphate and -carbonate were prepared by oxidation of a ferrous hydroxide precipitate in anion-containing aqueous solutions. The compounds are characterized by monitoring the redox potential E_h and the pH of stochiometric suspension vs time with the appropriate concentration ratios. X-ray diffraction allows us to characterize the crystal structure by distinguishing “green rust one” (GR1) from “green rust two” (GR2). Since green rusts (GRs) are of a pyroaurite-sjögrenite-like structure, i.e., consisting of intercalated foreign anions and water molecules in the interlayers between the brucite-like layers of Fe(OH)₂, their chemical formulae can be determined from the Mössbauer spectra. Three quadrupole doublets are observed: D₁ and D₂ correspond to a ferrous state with isomershift IS of about 1.27 mm s^-1 and quadrupole splittings QS of about 2.85 and 2.60 mm s^-1, respectively, whereas D₃ corresponds to a ferric state with IS and QS of about 0.4 mm s^-1. The hyperfine parameters of these doublets are similar from one green rust to another but their intensity ratios vary considerably. Finally, E_h and pH equilibrium diagrams of the Fe species in the presence of chloride, sulphate and carbonate anions contained within the water solution are drawn and the thermodynamic conditions of existence and degrees of oxidation of green rusts are discussed.