A microscopic theory of a quasi-crystalline transition layer on the surface of semi-infinite liquid dielectrics upon brewster light reflection and the near-field effect

An adequate theoretical interpretation of experiments on Brewster light reflection from the surfaces of liquids is given on the basis of the near-field effect in the transition layer. The analysis is carried out in terms of the model of a discrete-continuous dielectric, which takes into account the fields of atomic (molecular) dipoles discretely distributed inside the Lorentz sphere surrounding the point of observation. The liquids under consideration that have anisotropic molecules are characterized by a diagonal polarizability tensor within the transition layer and by scalar polarizability in the bulk of the liquid. It is shown that agreement between theoretical and experimental values of the ellipticity of reflected light is obtained due to a random change within a finite interval of the angle of orientation of molecules in the lattice sites in the transition layer. This makes it possible to conclude that the transition layer in the liquids under consideration is quasi-crystalline.     

Martingales of Random Subsets of a Metric Space of Negative Curvature

We prove extension of classical convergence theorem of P. Lévy for martingales of random subsets of a metric space of negative curvature.     

Arbres de Markov Triplet et fusion de Dempster–Shafer

The hidden Markov chains (HMC) (X,Y) have been recently generalized to triplet Markov chains (TMC), which enjoy the same capabilities of restoring a hidden process X from the observed process Y. The posterior distribution of X can be viewed, in an HMC, as a particular case of the so called “Dempster–Shafer fusion” (DS fusion) of the prior Markov with a probability q defined from the observation Y=y. As such, when we place ourselves in the Dempster–Shafer theory of evidence by replacing the probability distribution of X by a mass function M having an analogous Markov form (which gives again the classical Markov probability distribution in a particular case), the result of DS fusion of M with q generalizes the conventional posterior distribution of X. Although this result is not necessarily a Markov distribution, it has been recently shown that it is a TMC, which renders traditional restoration methods applicable. The aim of this Note is to present some generalizations of the latter result: (i) more general HMCs can be considered; (ii) q, which can possibly be a mass function Q, is itself a result of the DS fusion; and (iii) all these results are finally specified in the hidden Markov trees (HMT) context, which generalizes the HMC one. To cite this article: W. Pieczynski, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Homomo rphisms of the g roup $$L^1_s$$ into the g roup $$L^1_ r$$ fo r r ≤ 3

We determine all homomorphisms of the differential group L¹_sL^1_s with arbitrary s ≥ 2 into the group L¹_rL^1_r for r ≤  3.     

Dynamics of a quantum phase transition in a ferromagnetic Bose-Einstein condensate

We discuss dynamics of a slow quantum phase transition in a spin-1 Bose-Einstein condensate. We analytically determine the scaling properties of the system magnetization and verify them with numerical simulations in a one dimensional model.     

Terahertz emission from collapsing field domains during switching of a gallium arsenide bipolar transistor

Broadband pulsed THz emission with peak power in the sub-mW range has been observed experimentally during avalanche switching in a gallium arsenide bipolar junction transistor at room temperature, while significantly higher total generated power is predicted in simulations. The emission is attributed to very fast oscillations in the conductivity current across the switching channels, which appear as a result of temporal evolution of the field domains generated in highly dense electron-hole plasma. This plasma is formed in turn by powerful impact ionization in multiple field domains of ultrahigh amplitude.     

Microwave frequency modulation in CW EPR at W-band using a loop-gap resonator

Loop-gap resonator (LGR) technology has been extended to W-band (94GHz). One output of a multiarm Q-band (35GHz) EPR bridge was translated to W-band for sample irradiation by mixing with 59 GHz; similarly, the EPR signal was translated back to Q-band for detection. A cavity resonant in the cylindrical TE011 mode suitable for use with 100 kHz field modulation has also been developed. Results using microwave frequency modulation (FM) at 50 kHz as an alternative to magnetic field modulation are described. FM was accomplished by modulating a varactor coupled to the 59 GHz oscillator. A spin-label study of sensitivity was performed under conditions of overmodulation and gamma2H1(2)T1T2<1. EPR spectra were obtained, both absorption and dispersion, by lock-in detection at the fundamental modulation frequency (50 kHz), and also at the second and third harmonics (100 and 150 kHz). Source noise was deleterious in first harmonic spectra, but was very low in second and third harmonic spectra. First harmonic microwave FM was transferred to microwave modulation at second and third harmonics by the spins, thus satisfying the "transfer of modulation" principle. The loaded Q-value of the LGR with sample was 90 (i.e., a bandwidth between 3 dB points of about 1 GHz), the resonator efficiency parameter was calculated to be 9.3 G at one W incident power, and the frequency deviation was 11.3 MHz p-p, which is equivalent to a field modulation amplitude of 4 G. W-band EPR using an LGR is a favorable configuration for microwave FM experiments.