Rotational spectrum of trans-trans diethyl ether in the ground and three excited vibrational states

We report the results of a comprehensive reinvestigation of the rotational spectrum of diethyl ether based on broadband millimetre-wave spectra recently recorded at The Ohio State University and in Warsaw, covering the frequency region 108-366 GHz. The data set for the ground vibrational state of trans-trans diethyl ether has been extended to over 2000 lines and improved spectroscopic constants have been determined. Rotational spectra in the first excited vibrational states of the three lowest vibrational modes of trans-trans-diethyl ether, ν₂₀, ν₃₉, and ν₁₂ have been assigned. The v₂₀ = 1 and v₃₉ = 1 states are near 100 cm⁻¹ in vibrational term value and are coupled by a strong c-axis Coriolis interaction, which gives rise to many spectacular manifestations in the rotational spectrum. All of these effects have been successfully fitted for a dataset comprising over 3000 transitions, leading to precise determination of the energy difference between these states, (ΔE/hc)=10.400222(5) cm⁻¹. A newly developed software package for assignment and analysis of broadband spectra is described and made available.     

On the transition moment of the CO2 40°1II-00°0 band near 7740 cm-1

Using intensity measurements on the CO₂ 40°1_II-00°0 band obtained by Valero and Boese, we have expanded the F(m)-factor for the parallel band by using the Herman-Wallis formula. We have calculated the transition moment and determined the coefficients in the expansion of F(m).     

An equivalent circuit characterization of power MOSFET accounting for high field and high frequency effects

An equivalent circuit model for analyzing the AC characteristics of power VDMOS transistors is presented. The model accounts for high field and saturation effects. This is achieved by incorporating dependent voltage and current sources in the device model. Results are given for the AC characteristics of a POLYFET F2001 Power VDMOSFET rated with a drain current of 1.4A, power out of 2.5W at 1GHz. The linear, quasi-saturation and saturation regions of the IV characteristics are accounted for in the analysis. The small signal device parasitics are extracted through s-parameter methods. The s-parameter results were used to extract the frequency dependent parasitics including parasitic capacitances, inductances and transconductances.     

Dirac index classes and the noncommutative spectral flow

We present a detailed proof of the existence-theorem for noncommutative spectral sections (see the noncommutative spectral flow, unpublished preprint, 1997). We apply this result to various index-theoretic situations, extending to the noncommutative context results of Booss–Wojciechowski, Melrose–Piazza and Dai–Zhang. In particular, we prove a variational formula, in K_*(C_r^*(Γ)), for the index classes associated to 1-parameter family of Dirac operators on a Γ-covering with boundary; this formula involves a noncommutative spectral flow for the boundary family. Next, we establish an additivity result, in K_*(C_r^*(Γ)), for the index class defined by a Dirac-type operator associated to a closed manifold M and a map r:M→BΓ when we assume that M is the union along a hypersurface F of two manifolds with boundary M=M_{+ F} M₋. Finally, we prove a defect formula for the signature-index classes of two cut-and-paste equivalent pairs (M₁,r₁:M₁→BΓ) and (M₂,r₂:M₂→BΓ), where

M₁=M_{+ (F,φ1)} M₋, M₂=M_{+ (F,φ2)} M₋

and φ_jDiff(F). The formula involves the noncommutative spectral flow of a suitable 1-parameter family of twisted signature operators on F. We give applications to the problem of cut-and-paste invariance of Novikov's higher signatures on closed oriented manifolds.     

Coupling of a multilevel fast multipole method and a microlocal discretization for the 3-D integral equations of electromagnetism

The aim of this work is to propose an accurate and efficient numerical approximation for high frequency diffraction of electromagnetic waves. In the context of the boundary integral equations presented in F. Collino and B. Després, to be published in J. Comput. Appl. Math., the strategy we propose combines the microlocal discretization (T. Abboud et al., in: Third International Conference on Mathematical Aspects of Wave Propagation Phenomena, SIAM, 1995, pp. 178–187) and the multilevel fast multipole method (J.M. Song, W.C. Chew, Microw. Opt. Tech. Lett. 10 (1) (1995) 14–19). This leads to a numerical method with a reduced complexity, of order O(N^4/3ln(N)+N_iterN^2/3), instead of the complexity O(N_iterN²) for a classical numerical iterative solution of integral equations. Computations on an academic geometry show that the new method improves the efficiency, for a solution with a good level of accuracy. To cite this article: A. Bachelot et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Dispersion relations in string theory

We analyze the analytic continuation of the formally divergent one-loop amplitude for scattering of the gravitonmultiplet in the Type II superstring. In particular we obtain explicit double and single dispersion relations, formulas for all the successive branch cuts extending out to +, as well as for the decay rate of a massive string state of arbitrary mass2N into two string states of lower mass. We compare our results with the box diagram in a superposition of ³-like field theories. The stringy effects are traced to a convergence problem in this superposition.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98. No. 3, pp. 442–455, March, 1994.     

The maximum degree in a random tree and related problems

Meir and Moon studied the distribution of the maximum degree for simply generated families of trees. We have sharper results for the special case of labelled trees. © 1994 John Wiley & Sons, Inc.     

Matchings in superpositions of (n,n)-bipartite trees

Pick two trees from among all “bipartite trees” with a fixed (n, n) two-coloring. We estimate the probability that the superposition of these two trees contains a perfect matching. As n →∞, this probability approaches 1. © 1994 John Wiley & Sons, Inc.     

On wave propagation in elastic tubes conducting rotational flows

The propagation of perturbations in liquid filled elastic tubes depends on the stream velocity of the basic flow. This phenomenon is currently analyzed with the method of the characteristics which relies upon a basic flow with a rectangular velocity profile. It seems that this one-dimensional flow approximation has not been convincingly validated, which justifies to consider other, more general velocity profiles.In the present analytical study the velocity profile is a quadratic function of the radial coordinate. Small amplitude perturbations are superposed on this inviscid, basic state in which the mean velocity is arbitrarily large. A normal mode analysis shows that the velocity profile and therefore the vorticity of the basic flow influence the more the phenomenon the larger is. For example, a parabolic profile allows countercurrent wave propagation regardless of.This questions the one-dimensional wave propagation theory in compliant tubes and, consequently, the interpretation of several physiological and medical problems mainly in the respiratory and cardio-vascular systems.

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Resumé La propagation de perturbations dans un tube élastique conduisant un écoulement fluide dépend de la vitesse de l'écoulement de base. Ce phénomène est habituellement étudié avec la méthode des caractéristiques, où l'on suppose que le profil de vitesse de l'écoulement est rectangulaire. Comme cette simplification ne semble pas avoir été bien validée, il paraît indiqué d'étudier l'impact d'autres profils.Dans la présente étude analytique, ce profil de vitesse est une fonction quadratique de la coordonée radiale. A cet écoulement non visqueux, dont la vitesse moyenne est arbitraire, l'on superpose des perturbations de faible amplitude. Une analyse linéarisée montre que le profil de vitesse et donc le rotationel de l'écoulement de base influencent d'autant plus ce phénomène d'ondes que est élévée.Ceci met en question la théorie uni-dimensionelle de la propagation d'ondes dans des tubes compliants et, par là-même, l'interpretation de divers problèmes physiologiques et médicaux, avant tout des systèmes respiratoires et cardio-vasculaires.

     

Multicore, tapered optical fiber for nonlinear pulse reshaping and saturable absorption

We present a new method to create a coupled waveguide array via tapering a seven-core telecommunications fiber. The fiber based waveguide array is demonstrated to exhibit the novel physics associated with coupled waveguide arrays, such as discrete diffraction and discrete self-focusing. The saturable absorber characteristics of the device are characterized and an autocorrelation measurement reveals significant single-pass pulse reshaping.