Showing papers by "École Polytechnique published in 1995"

Dissipative Structures and Weak Turbulence

Abstract: We present a brief overview of the current understanding of temporal and spatio-temporal chaos, both termed weak turbulence according to the context [1]. The process which allows one to reduce the primitive problem to a low-dimensional dynamical system is discussed. It turns out to be appropriate as long as confinement effects are sufficiently strong to freeze the space dependence of unstable modes, hence temporal chaos only. Otherwise modulated patterns arise, yielding genuine space-time chaos. The corresponding theory rests on envelope equations providing a useful framework for weak turbulence in a globally super-critical setting. spatio-temporal intermittency analyzed next is the relevant scenario in the sub-critical case. Finally, the connection with hydrodynamic turbulence and the more general relevance of some of the ideas developed here are examined.

Electron acceleration from the breaking of relativistic plasma waves

Abstract: ELECTRONS in a plasma undergo collective wave-like oscillations near the plasma frequency. These plasma waves can have a range of wavelengths and hence a range of phase velocities1. Of particular note are relativistic plasma waves2,3, for which the phase velocity approaches the speed of light; the longitudinal electric field associated with such waves can be extremely large, and can be used to accelerate electrons (either injected externally or supplied by the plasma) to high energies over very short distances2a¤-4. The maximum electric field, and hence maximum acceleration rate, that can be obtained in this way is determined by the maximum amplitude of oscillation that can be supported by the plasma5a¤-8. When this limit is reached, the plasma wave is said to a¤˜breaka¤™. Here we report observations of relativistic plasma waves driven to breaking point by the Raman forward-scattering instability9,10 induced by short, high-intensity laser pulses. The onset of wave-breaking is indicated by a sudden increase in both the number and maximum energy (up to 44 MeV) of accelerated plasma electrons, as well as by the loss of coherence of laser light scattered from the plasma wave.

Synchrony in excitatory neural networks

Abstract: Synchronization properties of fully connectec. netwoi,s of identical oscillatory neurons are studied, assuming purely excitatory interactions. We analyze their dependence on the time course of the synaptic interaction and on the response of the neurons to small depolarizations. Two types of responses are distinguished. In the first type, neurons always respond to small depolarization by advancing the next spike. In the second type, an excitatory postsynaptic potential (EPSP) received after the refractory period delays the firing of the next spike, while an EPSP received at a later time advances the firing. For these two types of responses we derive general conditions under which excitation destabilizes in-phase synchrony. We show that excitation is generally desynchronizing for neurons with a response of type I but can be synchronizing for responses of type I1 when the synaptic interactions are fast. These results are illustrated on three models of neurons: the Lapicque integrate-and-fire model, the model of Connor et al., and the Hodgkin-Huxley model. The latter exhibits a type I1 response, at variance with the first two models, that have type I responses. We then examine the consequences of these results for large networks, focusing on the states of partial coherence that emerge. Finally, we study the Lapicque model and the model of Connor et al. at large coupling and show that excitation can be desynchronizing even beyond the weak coupling regime.

Thermodynamic observation of first-order vortex-lattice melting transition in Bi2Sr2CaCu2O8

Abstract: The lattice of magnetic flux lines that can permeate a type ii superconductor, such as the high-transition-temperature copper oxide materials, melts from a solid-like stale to a liquid-like state at a temperature below the superconducting transition temperature. Contrary to the predictions of mean-field theory, this phase transition in Bi2Sr2CaCu2O8 is found to be first-order. The vortex liquid discontinuously expands on freezing.

A way to break supersymmetry

Abstract: I study the spontaneous breakdown of supersymmetry when higher-dimensional Yang-Mills or the type-I $SO(32)$ string theory are compactified on magnetized tori. Because of the universal gyromagnetic ratio $g=2$, the splittings of all multiplets are given by the product of charge times internal helicity operators. As a result such compactifications have two remarkable and robust features: {\it (a)} they can reconcile {\it chirality} with {\it extended} low-energy supersymmetry in the limit of large tori, and {\it (b)} they can trigger gauge-symmetry breaking, via Nielsen-Olesen instabilities, at a scale tied classically to $m_{SUSY}$. I exhibit a compactification of the $SO(32)$ superstring, in which magnetic fields break spontaneously $N=4$ supersymmetry, produce the standard-model gauge group with three chiral families of quarks and leptons, and trigger electroweak symmetry breaking. I discuss supertrace relations and the ensuing ultraviolet softness. As with other known mechanisms of supersymmetry breaking, the one proposed here faces two open problems: the threat to perturbative calculability in the decompactification limit, and the problem of gravitational stability and in particular of the cosmological constant. I explain, however, why a good classical description of the vacuum may require small tadpoles for the dilaton, moduli and metric.

TiO2 anatase thin films as gas sensors

Abstract: The anatase modification of TiO2 shows properties quite different from those of the extensively studied and used rutile phase. We have investigated the chemi-resistive behavior of anatase TiO2 thin films exposed to oxidizing and reducing gases (O2, H2 and ethanol) in the temperature range between 300 and 400 °C. The undoped anatase films demonstrate significant and rapid response to ethanol as well as an appreciable response to hydrogen. The high electron mobility and the low density of trapping or compensating centers are considered to have contributed to this good response. Doping the anatase thin films with Sr, Ce, Y and Tb makes then insensitive to hydrogen, but still sensitive to ethanol. The modification of the sensitivity and its dynamics by dopants have been measured and analyzed.

Approximate controllability of the semilinear heat equation

Abstract: This article is concerned with the study of approximate controllability for the semilinear heat equation in a bounded domain Ω when the control acts on any open and nonempty subset of Ω or on a part of the boundary. In the case of both an internal and a boundary control, the approximate controllability in LP(Ω) for 1 ≦ p < + ∞ is proved when the nonlinearity is globally Lipschitz with a control in L∞. In the case of the interior control, we also prove approximate controllability in C0(Ω). The proof combines a variational approach to the controllability problem for linear equations and a fixed point method. We also prove that the control can be taken to be of “quasi bang-bang” form.

On a variational problem with lack of compactness: the topological effect of the critical points at infinity

Abstract: We study the subcritical problemsP ɛ :−Δu=u p−ɛ,u>0 onΩ;u=0 on ∂Ω,ω being a smooth and bounded domain in ℝN,N−3,p+1=2N/N−2 the critical Sobolev exponent and ɛ>0 going to zero — in order to compute the difference of topology that the critical points at infinity induce between the level sets of the functional corresponding to the limit case (P0).

[16] Studies of base pair kinetics by NMR measurement of proton exchange

Abstract: Publisher Summary This chapter discusses the studies of base pair kinetics by nuclear magnetic resonance (NMR) measurement of proton exchange. Base pairing is ubiquitous in nucleic acids; it plays a key role in the structure and function of biological molecules (B-DNA, tRNA, etc.) and of biochemical constructs in PCR, antisense strategy, etc. The systematic disruption of base pairs is a prerequisite for replication and transcription of double-stranded DNA. Local disruption could play a role in mechanical properties of nucleic acids and in the specificity of protein-nucleic acid recognition. It is involved in chemical reactions of nucleic acids. As a probe of structural properties, the kinetics of base pair opening forms a useful complement to structure determination by NMR. The most common approach to base pair opening is the measurement of imino-proton exchange, with water, by proton NMR. With NMR, an exchange event can be directly assigned to an imino (rather than amino or ribose) proton of a specific base pair, in contrast to the earlier procedures based on isotope exchange, monitored by radioactivity or ultraviolet, infrared, or Raman spectroscopy. The measurement methods are of two types: the kinetics of real-time exchange and of magnetization transfer measure exchange times directly, whereas the measurements of longitudinal relaxation and line broadening can only determine the differential effect of added catalyst on the exchange time.

Bayesian interactions and collective dynamics of opinion: Herd behavior and mimetic contagion

Abstract: Much recent work has been devoted to the analysis of herd behavior within sequential decision models. The present article generalizes their results to non-sequential contexts. We will show that, as soon as the hypothesis of sequentiality is dropped, a large variety of situations can be observed. Our model has been designed to study the collective learning process through which a group of interacting agents deals with environmental uncertainty. The crucial question revolves around the relative weight given by each individual to the different sources of information: his private information and his observation of the group opinion.

Representation for the radical of a finitely generated differential ideal

Abstract: We give an algorithm which represents the radical J of a finitely generated differential ideal as an intersection of radical differential ideals. The computed representation provides an algorithm for testing membership in J. This algorithm works over either an ordinary or a partial differential polynomial ring of characteristic zero. It has been programmed. We also give a method to obtain a obtain a characteristic set of J, if the ideal is prime.

Ab initio calculations of the quasiparticle and absorption spectra of clusters: The sodium tetramer.

Abstract: We report the first ab initio quasiparticle calculation in a real cluster ${\mathrm{Na}}_{4}$ within Hedin's $\mathrm{GW}$ approximation for the valence electron self-energy. Our approach avoids the summations over empty states, and also eliminates the problem of residual interactions between the periodic images. Self-energy corrections open the local density approximation gap by more than 2 eV; finite-size effects on screening are shown to play an important role. The absorption spectrum calculated by including excitonic effects using our ab initio screened interaction gives a good account of the experimental photodepletion data.

Exact Gerstenhaber Algebras and Lie Bialgebroids

Abstract: We show that to any Poisson manifold and, more generally, to any triangular Lie bialgebroid in the sense of Mackenzie and Xu, there correspond two differential Gerstenhaber algebras in duality, one of which is canonically equipped with an operator generating the graded Lie algebra bracket, i.e. with the structure of a Batalin-Vilkovisky algebra.

Confined Electrons and Photons

Abstract: The scientific fields of confined electrons and photons have become areas of major efforts worldwide. Their appeal originates in the many facets they offer in fundamental and applied science, in technology and device development, and to high technology, large-scale industries.

A three dimensional analytical solution of the longitudinal wave propagation in an infinite linear viscoelastic cylindrical bar. Application to experimental techniques

Abstract: This paper presents an original three dimensional (3D) analytical general solution of the longitudinal wave propagation in an infinite linear viscoelastic cylindrical bar and its applications to some experimental methods of material behaviour testing to improve their accuracy. One application is to take into account the wave dispersion effects in the split Hopkinson pressure bar (SHPB) setup composed of viscoelastic bars. Another is to eliminate the geometrical effects in an impulse test in which the linear viscoelastic material properties can be deduced from the change in the wave shape due to the propagation between two points of measurement in a specimen bar.

Trees, forests and jungles: a botanical garden for cluster expansions

Abstract: Combinatoric formulas for cluster expansions have been improved many times over the years. Here we develop some new combinatoric proofs and extensions of the tree formulas of Brydges and Kennedy, and test them on a series of pedagogical examples.

Spontaneous Breaking of N=2 Global Supersymmetry

Abstract: We study spontaneous supersymmetry breaking in N=2 globally supersymmetric theories describing a system of abelian vector multiplets. We find that the most general form of the action admits, in addition to the usual Fayet-Iliopoulos term, a magnetic Fayet-Iliopoulos term for the auxiliary components of dual vector multiplets. In a generic case, N=2 supersymmetry is broken down spontaneously to N=1. In some cases however, the scalar potential can drive the theory towards a N=2 supersymmetric ground state where massless dyons condense in the vacuum.