Showing papers by "École Polytechnique published in 1988"

On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain

Abstract: Soit Ω un ensemble ouvert borne regulier et connexe de R N , N≥3. On considere u:Ω→R telle que −Δu=u (N+2)/(N−2) dans Ω, u>0 dans Ω, u=0 sur ∂Ω. On note par Hd(Ω; Z 2 ) l'homologie de diemnsion d de Ω a coefficients Z 2 . S'il existe un entier positif d tel que Hd(Ω, Z 2 )¬=0, alors l'equation a une solution

The optical kerr effect in small metal particles and metal colloids: The case of gold

Abstract: We first consider theoretically the various mechanisms contributing to the Kerr nonlinearity in small gold particles. The major ones are the conduction electron intraband contribution, the saturation of direct interband transitions and the change in dielectric constant due to hot photoexcited electrons. We present experimental results obtained using optical phase conjugation in gold-doped glasses. By varying several parameters, we were able to ascertain the origin of the nonlinear response: the main contributions are the hotelectron and the interband contributions. All experimental results, including saturation behaviour, are fully understood.

Rates of primary electron transfer in photosynthetic reaction centres and their mechanistic implications

Abstract: The conversion of light energy to chemical energy during photosyn-thesis involves the transfer of electrons between pigments embedded in a membrane protein. This process occurs with high quantum efficiency, the result of extremely fast electron transfer over a long distance preventing back transfer and energy loss. Recently the three-dimensional structures of the photosynthetic reaction centres of the bacteria Rhodopseudomonas viridis1 and Rhodobacter sphaeroides2 have been determined, allowing a molecular descrip-tion of the primary charge separation process. There are two symmetrically related branches of pigments in the structure (L and M), extending from the special pair of bacteriochlorophyll molecules (P) to the two bacteriopheophytins (HL and HM) via two bacteriochlorophylls (BLand BM). Many features of the electron transfer process are poorly understood, such as the nature of the excited states involved, the identity of the primary charge separation step and the roles of the protein and of B3–13. We have determined the rates of electron transfer in isolated reaction centre complexes of Rps. viridis and Rb. sphaeroides as a function of temperature. The rates increase as temperature is decreased, which may be due to either changes in electronic coupling of the pigments or changes in the population of coupled vibrational modes, or a combination of the two. We see no evidence of a B−L intermediate, which sets a lower limit on the rate of electron transfer from BL to HL. This is so high as to rule out transfer by two non-adiabatic steps.

Finite-dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra

Abstract: Let\(G\) be a complex simple Lie algebra. We show that whent is not a root of 1 all finite dimensional representations of the quantum analogU t \(G\) are completely reducible, and we classify the irreducible ones in terms of highest weights. In particular, they can be seen as deformations of the representations of the (classical)U\(G\).

Photophysics and reactivity of heme proteins: a femtosecond absorption study of hemoglobin, myoglobin, and protoheme

Abstract: On the basis of our time-resolved absorption measurements of hemoglobin (Hb), myoglobin (Mb), and protoheme (PTH), either unligated or ligated with CO, O2, or NO, we propose a description of the photophysics of heme proteins that encompasses their photodissociation, the origin and fate of the observed short-lived transients, and the appearance of the ground-state, unligated heme proteins. Two distinct species are formed upon ligand photodissociation, which occurs in less than 50 fs. We assign these species to excited states of the unligated heme and label them (for the case of hemoglobin) as Hb*I and Hb*II. We suggest that Hb*I is already at least partially domed and has a spin state of at least S = 1. Hb*I decays in 300 fs to the ground-state unligated heme species, which we consider to be S = 2 and at least partially domed. The population of Hb*II varies with the ligand. It is more significant when the ligand is O2 or NO than when the ligand is CO. The similarities of the picosecond and femtosecond bleaching and absorption kinetics of HbCO with those of PTHCO (and of HbNO with those of PTHNO) indicate that in this time domain the importance of steric features of the protein are less important than the nature of the ligand itself in the geminate recombination process as well as in the relative amounts of the two heme excited states created. It is suggested that the quantum yield of ligand photodissociation is unity whether the ligand is O2, NO, or CO. The low yield of photodissociated heme-O2 or heme-NO compounds as measured on the microsecond time scale is thus attributed to a fast (2.5 ps) recombination of O2 or NO with Hb*II. We discuss geminate recombination measurements of cyanomet hybrid hemoglobins with NO and consider these results in terms of alpha and beta subunit heterogeneity. The first picosecond transient absorption spectra of cyanomet-CO hybrid hemoglobins are presented and are compared with the spectra of other heme compounds. The superimposability of the transient spectra on the equilibrium spectra of heme compounds that exhibit minimal or no cooperativity is noted and is compared with the case of cooperative systems where the transient spectra are distorted with respect to the equilibrium spectra. This distortion is interpreted in terms of an interaction of a domed heme with the F helix.

Chiral perturbation theory and final-state theorem.

Abstract: Timelike scalar and vector form factors are recalculated by use of chiral perturbation theory and dispersion theory. It is shown that chiral perturbation theory at the one-loop level violates the final-state theorem (i.e., unitarity). In order to satisfy this theorem, chiral perturbation theory should be applied to the inverse of the form factor whose result is shown to be equivalent to the Pade-approximant method.

Morse index of some min‐max critical points. I. Application to multiplicity results

Abstract: On donne un resultat general sur des bornes inferieures pour des indices de Morse de points critiques obtenus par des principes de min-max. En combinant cette information avec une inegalite semiclassique on obtient des estimations pointues sur la croissance de certaines valeurs critiques, a partir desquelles on deduit de nouveaux resultats de multiplicite pour des solutions d'equations elliptiques semi-lineaires d'ordre 2

Selective low-power plasma decomposition of silane-methane mixtures for the preparation of methylated amorphous silicon.

Abstract: We report on a systematic study of the deposition and the physical properties of amorphous-silicon\char21{}carbon alloys produced by glow discharge from silane-methane mixtures. We define a ``low-power'' regime of preparation in which the chemistry of deposition is separated from the chemistry of the plasma. In this regime there is no primary decay of the methane, which then acts as a buffer gas. The carbon is incorporated in the solid only by reaction of the methane gas with the active species produced by the plasma decomposition of the silane. In this mode of preparation, we find the following. (1) The physical properties (in particular, the optical properties) are insensitive to the preparation conditions, depending mostly on the methane-to-silane ratio. (2) There is a smooth ``chemical'' incorporation of carbon in the amorphous silicon network, giving an alloy with good semiconducting properties. (3) The amount of carbon that can be incorporated is limited to less than 40 at. %, whereas in the high-power regime alloys can be produced with arbitrary [C]/[Si] proportions. (4) In the low-power regime the carbon is incorporated mostly in the form of methyl groups ${\mathrm{CH}}_{3}$, so that the material produced in this condition should be labeled as ``methylated amorphous silicon.''

Evidence from base-pair kinetics for two types of adenine tract structures in solution: their relation to DNA curvature.

Abstract: We have measured the base-pair lifetimes in oligodeoxynucleotides containing tracts of A.T base pairs using imino proton magnetic resonance. When the tract contains more than four consecutive A.T base pairs, possibly including a 5'-AT step but not a 5'-TA step, anomalously long lifetimes are observed. For example, the lifetimes of the central A.T base pairs of the dodecamer 5'-d-CGCAAAAAAGCG are 122 and 91 ms at 15 degrees C whereas, in the same conditions, the lifetime of the central A.T pair of the decamer 5'-d-CGCGATCGCG is only 4 ms, a value similar to those measured in several other B-DNA oligoduplexes [Leroy et al. (1988) J. Mol. Biol. 200, 223-238]. This strongly suggests that, in tracts of four A.T pairs or more, a conformation distinct from standard B-DNA is formed cooperatively. All sequences known to generate curved DNA exhibit anomalously long base-pair lifetimes. This is the first local and physical property shown to correlate with DNA curvature. Our observations suggest that the structure responsible for the long lifetimes is involved in the curvature of DNA.

Wide‐angle one‐way wave equations

Abstract: A one‐way wave equation, also known as a paraxial or parabolic wave equation, is a differential equation that permits wave propagation in certain directions only. Such equations are used regularly in underwater acoustics, in geophysics, and as energy‐absorbing numerical boundary conditions. The design of a one‐way wave equation is connected with the approximation of (1−s2)1/2 on [−1,1] by a rational function, which has usually been carried out by Pade approximation. This article presents coefficients for L2, L∞, and other alternative classes of approximants that have better wide‐angle behavior. For theoretical results establishing the well posedness of these wide‐angle equations, see the work of Trefethen and Halpern [‘‘Well‐posedness of one‐way wave equations and absorbing boundary conditions,’’ Math. Comput. 47, 421–435 (1986)].

Direct-energy-gap dependence on Al concentration in Al x Ga 1 − x As

Abstract: The direct exciton energy at 2 K in ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As epitaxial layers (0.10lxl0.75) has been determined by optical transmission measurements. Microprobe analysis has been employed for the evaluation of the aluminum concentration. From these data, the direct-energy-gap dependence on x has been obtained; its comparison with the literature clearly shows that the relation ${E}_{\mathrm{gap}{}^{\ensuremath{\Gamma}}(\mathrm{x}}$) commonly used in the optical determination of the alloy concentration must be revised. Contrary to older evaluations, our determination of the nonlinear contribution to ${E}_{\mathrm{gap}{}^{\ensuremath{\Gamma}}(\mathrm{x}}$) agrees with the theoretically predicted values.

Band structure of carbonated amorphous silicon studied by optical, photoelectron, and x-ray spectroscopy

Abstract: Hydrogenated silicon-carbon films prepared by glow discharge from silane-methane mixtures at low power density are used as a model system for the analysis of optical properties and band structure of amorphous tetrahedral semiconductors. Between 0 and 20 at. % of carbon in the solid, the optical gap and the static refractive index can be varied over a wide range without changing the chemical structure of the solid and its good semiconducting properties. The optical constants are well described by a simple two-band model of optical transitions, and the information on the band structure in the solid is condensed into one parameter, the average gap ${E}_{M}$, which corresponds to the energy difference between the centers of gravity of the valence and conduction bands. This value is very close to the energy spacing of the maxima in the distributions of the conduction and valence band deduced from soft-x-ray spectra, and exhibits a similar increase with carbon content. Beyond a carbon concentration of about 20 at. %, we observe a change in the nature of the material. The average gap ${E}_{M}$ increases much more rapidly than the optical gap; x-ray photoelectron spectroscopy indicates an incorporation of carbon in the form of Si-C-Si units in a tetrahedral network, whereas for concentrations smaller than 20 at. % the carbon is mainly incorporated as methyl groups ${\mathrm{CH}}_{3}$.

Entropy weak solutions to nonlinear hyperbolic systems under nonconservative form

Abstract: For nonlinear hyperbolic systems in nonconservation form, we consider weak solutions in the class of bounded functions of bounded variation A generalized global entropy inequality is proposed and studied In this mathematical framework, we solve the Riemann problem and prove, for the Cauchy problem, the consistancy of the random choice method for systems in nonconservation form Our theory of entropy weak solutions is applied to nonconservative systems of elastodynamics and gasdynamics In particular, we give here a nonconservation form of the system of conservation laws of gasdynamics, which is equivalent for weak solutions in BV

Angular distributions of muon pairs produced by negative pions on deuterium and tungsten

Abstract: We present the angular distributions of high-mass muon pairs produced in a high-statistics experiment by 140 and 194 GeV/c π− beams impinging on a tungsten target, and by 286 GeV/c π− beam on deuterium and tungsten targets We find no evidence for a center-of-mass energy dependence or a nuclear dependence of the angular distribution parameters The two parameters λ and μ are found to be essentially independent of any kinematical variable In contrast, the parameterv increase with the dimuon transverse momentumPT, at variance with recent perturbative QCD predictions Our statistics at largex1 are insufficient to substantiate the highertwist prediction

Identification of the d+p-->3He

Abstract: From the interactions of a deuteron beam in a liquid-hydrogen target at energies near the $d+p\ensuremath{\rightarrow}^{3}\mathrm{He}+\ensuremath{\eta}$ threshold, $\ensuremath{\eta}$ events were selected on the basis of the momentum-analyzed $^{3}\mathrm{He}$ with a background of less than 2%. This opens the way to a $^{3}\mathrm{He}$-tagged $\ensuremath{\eta}$ beam at Saturne, with a possible flux of ${10}^{4}$-${10}^{5}$ $\ensuremath{\eta}'\mathrm{s}$ per pulse. The present data allow an evaluation of the cross section down to less than 0.5 MeV above threshold. The deuteron tensor analyzing power ${t}_{20}$ has also been measured: The small negative value found at threshold (-0.15 \ifmmode\pm\else\textpm\fi{} 0.05) seems incompatible with models based on one-pion exchange.

Coherent effects in pump-probe spectroscopy of excitons.

Abstract: Femtosecond measurements of coherent effects arising from exciton bleaching in bulk GaAs are reported. This phenomenon, which is characterized by spectral oscillatory structures, is general and appears whenever the temporal resolution is shorter than the material coherence time. This is shown to be a manifestation of the uncertainty relation in time-resolved spectroscopy.

Localization of gravity waves on a channel with a random bottom

Abstract: We present a theoretical study of the localisation phenomenon of gravity waves by a rough bottom in a one-dimensional channel. After recalling localisation theory and applying it to the shallow-water case, we give the first study of the localisation problem in the framework of the full potential theory; in particular we develop a renormalised-transfer-matrix approach to this problem. Our results also yield numerical estimates of the localisation length, which we compare with the viscous dissipation length. This allows the prediction of which cases localisation should be observable in and in which cases it could be hidden by dissipative mechanisms.

Keto-enol tautomers and distonic ions: The chemistry of [CnH2nO] radical cations. Part I

Abstract: Cette revue porte l'accent sur les aspects energetiques des reactions d'isomerisation et de dissociation des ions radicalaires du titre

Electrical response of fractal and porous interfaces

Abstract: The electrical response of porous electrodes is calculated in several particular cases, which permit one to approach the response of a realistic model for a porous interface. The case of nonblocking surfaces and the case of the diffusion impedance of a fractal electrode are also considered. The use of Bode diagrams is shown to provide a very simple means for calculating phase angles and algebraic values for the impedance. It is demonstrated that for a blocking deterministic Sierpi\ifmmode \acute{n}\else \'{n}\fi{}ski electrode the impedance presents oscillations around a constant phase angle (CPA). Various electrochemical regimes (blocking, nonblocking, and diffusive) are considered, giving rise to a variety of exponents. For blocking electrodes it is shown that at a given frequency, the power is dissipated in certain parts of the electrodes having a characteristic size which is a direct function of frequency. The fact that the response of the system is linear permits one to relate in general the dc response to the phase angle in the blocking regime and to study certain diffusive cases. It also permits one to deal with cases very common practically where the response of a flat surface would itself exhibit a CPA. In the case of a pure diffusion impedance the response is shown to be related directly to the Minkowski-Bouligand exterior dimension of the interface through the exponent (D-1)/2. This approach can be generalized to any type of irregular electrode independently of its fractal character. If both diffusion and Faradaic (electrochemical) impedance play a role, a CPA response exists for a porous electrode with an exponent equal to D-2. We discuss various regimes in which diffusion plays a role together with Faradaic, resistive, and capacitive effects. It is shown that there is in general no relation between fractal dimension and constant phase angle except in the case of diffusion. The response of irregular electrodes is shown to be related to the fractal dimension when the electrochemical regime is local.

Explicit formula for scalar non-linear conservation laws with boundary condition

Abstract: We prove an uniqueness and existence theorem for the entropy weak solution of non-linear hyperbolic conservation laws of the form , with initial data and boundary condition. The scalar function u = u(x, t), x > 0, t > 0, is the unknown; the function f = f(u) is assumed to be strictly convex. We also study the weighted Burgers' equation: α ϵ ℝ . We give an explicit formula, which generalizes a result of Lax. In particular, a free boundary problem for the flux f(u(.,.)) at the boundary is solved by introducing a variational inequality. The uniqueness result is obtained by extending a semigroup property due to Keyfitz.

Fluctuating proton size and oscillating color transparency

Abstract: The unexpected energy dependence of high-energy fixed-angle pp elastic scattering in a nuclear target can be intrepreted in terms of interference between two perturbative QCD subprocesses. By proposing the attenuation of Landshoff-type contributions in nuclei, we obtain a parameter-free relation that matches the energy dependence of the data of Carroll et al. The approximations improve with larger A and higher energy, leading to a prediction of oscillatory energy dependence for the transparency ratio at higher energy.