Convergence of the Marcus–Lushnikov Process

The Smoluchowski coagulation equation describes the concentration c(t,x) of particles of mass x [ 0,] at the instant t 0, in an infinite system of coalescing particles. It is well-known that in some cases, gelation occurs: a particle with infinite mass appears. But this infinite particle is inert, in the sense that it does not interact with finite particles. We consider the so-called Marcus–Lushnikov process, which is a stochastic finite system of coalescing particles. This process is expected to converge, as the number of particles tends to infinity, to a solution of the Smoluchowski coagulation equation. We show that it actually converges, for t [0,], to a modified Smoluchowski equation, which takes into account a possible interaction between finite and infinite particles.     

Produits dans la cohomologie des variétés de Shimura : quelques calculs

We show how our recent results (arXiv: math.NT/0403407 v1 24 Mar 2004) together with a criterion of Venkataramana can be used to get explicit conditions for the virtual non-vanishing of the product of two cohomology classes of certain Shimura varieties. To cite this article: N. Bergeron, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

A beam tracing method for interactive architectural acoustics

A difficult challenge in geometrical acoustic modeling is computing propagation paths from sound sources to receivers fast enough for interactive applications. This paper describes a beam tracing method that enables interactive updates of propagation paths from a stationary source to a moving receiver in large building interiors. During a precomputation phase, convex polyhedral beams traced from the location of each sound source are stored in a "beam tree" representing the regions of space reachable by potential sequences of transmissions, diffractions, and specular reflections at surfaces of a 3D polygonal model. Then, during an interactive phase, the precomputed beam tree(s) are used to generate propagation paths from the source(s) to any receiver location at interactive rates. The key features of this beam tracing method are (1) it scales to support large building environments, (2) it models propagation due to edge diffraction, (3) it finds all propagation paths up to a given termination criterion without exhaustive search or risk of under-sampling, and (4) it updates propagation paths at interactive rates. The method has been demonstrated to work effectively in interactive acoustic design and virtual walkthrough applications.     

How to measure squeezing and entanglement of Gaussian states without homodyning

We propose a scheme for measuring the squeezing, purity, and entanglement of Gaussian states of light that does not require homodyne detection. The suggested setup needs only beam splitters and single-photon detectors. Two-mode entanglement can be detected from coincidences between photodetectors placed on the two beams.     

Time-resolved tracking of a sound scatterer in a complex flow: nonstationary signal analysis and applications

It is known that ultrasound techniques yield nonintrusive measurements of hydrodynamic flows. For example, the study of the echoes produced by a large number of particles insonified by pulsed wavetrains has led to a now-standard velocimetry device. In this paper, a new technique for the measurement of the velocity of individual solid particles moving in fluid flows is proposed. It relies on the ability to resolve in time the Doppler shift of the sound scattered by the continuously insonified particle. For this signal-processing problem two classes of approaches can be used: time-frequency analysis and parametric high-resolution methods. In the first class the spectrogram and reassigned spectrogram is considered, and applied to detect the motion of a small bead settling in a fluid at rest. In nonstationary flows, methods in the second class are more robust. An approximated maximum likelihood (AML) technique has been adapted, coupled with a generalized Kalman filter. This method allows for the estimation of rapidly varying frequencies; the parametric nature of the algorithm also provides an estimate of the variance of the identified frequency parameters.     

Spectral integration in bands of modulated or unmodulated noise

Spectral integration was measured for pure-tone signals masked by unmodulated or modulated noise bands centered at the signal frequencies. The bands were typically 100 Hz wide, and when modulated, they were sinusoidally amplitude modulated at a rate of 8 Hz and a depth of 100%. In experiment 1, thresholds were first measured for each individual pure tone of a triplet in the presence of its respective masker band, and then for those three tones added together at their respective threshold levels, masked by their respective masker bands. Four sets of triplets were used: 250, 1000, 4000 Hz; 354, 1000, 2828 Hz; 500, 1000, 2000 Hz; and 800, 1000, 1200 Hz. When the masker bands were unmodulated, the amount of spectral integration was about 2.4 dB for all triplets, consistent with the integration expected based on the multiband energy detector model. When the bands were modulated, the amount of integration depended upon the spacing between masker bands; for the two widest spacings, the integration was between about 0 and 3 dB, whereas for the two closest spacings, the integration was approximately 5 dB. Experiments 2 and 3 addressed the cause of this greater spectral integration in the presence of the modulated masker bands with closer spacing. The second experiment demonstrated that sensitivity (d') was proportional to signal power regardless of whether the background noise was modulated or not, and thus the greater integration in dB in the presence of the modulated noise bands could not be accounted for by shallower psychometric functions in those conditions. Instead, the third experiment showed that the greater integration was likely due to the fact that the masker bands were comodulated. In other words, it was probably due to cues related to comodulation masking release when all three bands (and signals) were present.     

Measurement of the positive muon anomalous magnetic moment to 0.7 ppm

A higher precision measurement of the anomalous g value, a(mu)=(g-2)/2, for the positive muon has been made at the Brookhaven Alternating Gradient Synchrotron, based on data collected in the year 2000. The result a(mu(+))=11 659 204(7)(5)x10(-10) (0.7 ppm) is in good agreement with previous measurements and has an error about one-half that of the combined previous data. The present world average experimental value is a(mu)(expt)=11 659 203(8)x10(-10) (0.7 ppm).     

A metamaterial for directive emission

In this paper we present the first results on emission in metamaterial. We show how the specific properties of metallic composite material can modify the emission of an embedded source. We show that under proper conditions the energy radiated by a source embedded in a slab of metamaterial will be concentrated in a narrow cone in the surrounding media. An experimental demonstration of this effect is given in the microwave domain, and the constructed antenna has a directivity equivalent to the best reported results with photonic-crystal-based antennas but using a completely different physical principle [B. Temelkuaran, J. Appl. Phys. 87, 603 (2000)]].     

Convective and absolute Eckhaus instability leading to modulated waves in a finite box

We report an experimental study of the secondary modulational instability of a one-dimensional nonlinear traveling wave in a long bounded channel. Two qualitatively different instability regimes involving fronts of spatiotemporal defects are linked to the convective and absolute nature of the instability. Both transitions appear to be subcritical. The spatiotemporal defects control the global mode structure.     

Synthesis of 2-silyl substituted phospharuthenocenes and an elaboration into the first phospharuthenocene-phosphine

A [1,5] shift protocol transiently hindering the 2-position of phospholide anions provides an access to sterically unencumbered phospharuthenocenes and the first phospharuthenocene-phosphine.