Asymptotic limit law for the close approach of two trajectories in expanding maps of the circle

Summary Given two pointsx, yS ¹ randomly chosen independently by a mixing absolutely continuous invariant measure of a piecewise expanding and smooth mapf of the circle, we consider for each >0 the point process obtained by recording the timesn>0 such that |f ⁿ (x)–f ⁿ (y)|. With the further assumption that the density of is bounded away from zero, we show that when tends to zero the above point process scaled by –1 converges in law to a marked Poisson point process with constant parameter measure. This parameter measure is given explicity by an average on the rate of expansion off.Partially supported by FAPESP grant number 90/3918-5     

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针对准中性Vlasov-Poisson系统中多尺度物理参数共存的问题开展研究,采用渐近保持格式推导出与Vlasov方程相耦合的Poisson方程。数值模拟了一维等离子体在真空中的膨胀,比较了渐近保持PIC算法与传统PIC算法模拟结果的异同。结果表明：两种算法在满足多尺度中小尺度量限制的前提下,其结果保持高度一致;且在克服小尺度量束缚时,渐近保持PIC算法依然可以正确地模拟等离子体的物理行为,大大节省了计算时间。     

Rotational CARS N2 thermometry: validation experiments for the influence of nitrogen spectral line broadening by hydrogen

Rotational coherent anti‐Stokes Raman spectroscopy (CARS) in fuel‐rich hydrocarbon flames, with a large content of hydrogen in the product gases (∼20%), has in previous work shown that evaluated temperatures are raised several tens of Kelvin by taking newly derived N₂ H₂ Raman line widths into account. To validate these results, in this work calibrated temperature measurements at around 300, 500 and 700 K were performed in a cell with binary gas mixtures of nitrogen and hydrogen. The temperature evaluation was made with respect to Raman line widths either from self‐broadened nitrogen only, N₂ N₂ [energy‐corrected‐sudden (ECS)], or by also taking nitrogen broadened by hydrogen, N₂ H₂ [Robert–Bonamy (RB)], Raman line widths into account. With increased amount of hydrogen in the cell at constant temperature, the evaluated CARS temperatures were clearly lowered with the use of Raman line widths from self‐broadened nitrogen only, and the case with inclusion of N₂ H₂ Raman line widths was more successful. The difference in evaluated temperatures between the two different sets increases approximately linearly, reaching 20 K (at T ∼ 300 K), 43 K (at T = 500 K) and 61 K (at T = 700 K) at the highest hydrogen concentration (90%). The results from this work further emphasize the importance of using adequate Raman line widths for accurate rotational CARS thermometry. Copyright © 2010 John Wiley & Sons, Ltd.     

Asymptotic-Preserving Particle-In-Cell method for the Vlasov–Poisson system near quasineutrality

This paper deals with the numerical resolution of the Vlasov–Poisson system in a nearly quasineutral regime by Particle-In-Cell (PIC) methods. In this regime, Classical PIC methods are subject to stability constraints on the time and space steps related to the small Debye length and large plasma frequency. Here, we propose an “Asymptotic-Preserving” PIC scheme which is not subjected to these limitations. Additionally, when the plasma period and Debye length are small compared to the time and space steps, this method provides a consistent PIC discretization of the quasineutral Vlasov equation. We perform several one-dimensional numerical experiments which provide a solid validation of the method and its underlying concepts, and compare the method with Classical PIC and Direct-Implicit methods.     

A least square finite element formulation of the collimated irradiation in frequency domain for optical tomography applications

This paper presents an extension of the least square finite element formulation associated to the discrete ordinates method to solve collimated irradiation problems in frequency domain. The features of the method are shown with a separation of the intensity into its collimated and scattered parts for a better handling of discontinuities due to the boundary conditions of Dirichlet type used in optical tomography applications. Numerical tests are used to gauge the accuracy of the model in both isotropic and anisotropic scattering media, with and without frequency modulation. The results show that the method is accurate compared to some reference solutions.     

Tuning energy relaxation along quantum Hall channels

The chiral edge channels in the quantum Hall regime are considered ideal ballistic quantum channels, and have quantum information processing potentialities. Here, we demonstrate experimentally, at a filling factor of ν(L)=2, the efficient tuning of the energy relaxation that limits quantum coherence and permits the return toward equilibrium. Energy relaxation along an edge channel is controllably enhanced by increasing its transmission toward a floating Ohmic contact, in quantitative agreement with predictions. Moreover, by forming a closed inner edge channel loop, we freeze energy exchanges in the outer channel. This result also elucidates the inelastic mechanisms at work at ν(L)=2, informing us, in particular, that those within the outer edge channel are negligible.     

Real-space observation of spectral degeneracy breaking in a waveguide-coupled disk microresonator

We report on the real-space observation of resonant frequency splitting in a high-Q waveguide-coupled silicon-on-insulator microdisk resonator. Phase sensitive near-field analysis reveals the stationary nature of the two resonant states, and spectral investigations clearly show their orthogonality. These measurements emphasize the role of the coupling waveguide in this splitting phenomenon. The symmetry of the two stationary whispering gallery modes is clearly observed and is found to follow the axial symmetry of the waveguide-coupled microdisk as it has been reported by earlier theoretical predictions.     

Single-mode low-loss optical fibers for long-wave infrared transmission

In this Letter, we report single-mode fibers made of chalcogenide glasses with low loss in the 5-12μm range. Glasses from the Ge-As-Te-Se system were optimized to prevent nucleation and to exhibit low density of charge carriers. Single-mode fibers were obtained through the rod-in-tube method by substituting 2% Te/Se between the core and cladding glasses. The resulting single-mode fibers had a core diameter of 30μm and exhibited losses of ~6 dB/m at 10.6μm, and as low as 3-4dB/m in the 6-10μm range.     

Mechano-chemical oscillations of a gel bead

We present a formalism which describes the spatio-temporal evolution of a gel submitted to an autocatalytic chemical reaction to which it is responsive. This theory is based on an extension of a hydrodynamical multi-diffusional approach of the gel dynamics, which is plunged into a chemically active mixture. Emergent and autonomous volume self-oscillation dynamics of the gel are obtained from the nonlinear coupling of the elastic deformation, the chemical kinetics and the transport phenomena, that take place in the system. We apply this formalism to a spherical bead of gel plunged in a Belouzov-Zhabotinsky oscillatory chemical reaction, for which Yoshida et al. have obtained numerous experimental results. The case of a gel immersed in an autocatalytic bistable chemical reaction is also considered. We show that such formalism describes the autonomous volume self-oscillation dynamics of the gel beads.