On the nilpotent * - Fourier transform

LetG be a nilpotent Lie group. The adapted nilpotent Fourier transform was introduced by D. Arnal and J. C. Cortet,:L(G) C (V,L(^2d )), whereL(G) is the Schwartz space ofG andV × ^2k is aG-invariant Zariski open set ing ^* the dual of the Lie algebra ofG. We prove the surjectivity of this transformation, which allows us to extend it to distribution spaces.     

Study of Spectral Emission Behaviour in the Glow and Microwave Discharges of Oxygen

Because of the very important role of oxygen plasmas in various applications, both direct current and microwave discharges have been analysed from the point of view of emission spectra properties. In both cases silica discharge tubes with practically the same diameters were used. The following transitions of the oxygen discharges were studied: the atomic lines at 777.4 nm (⁵P ‐ ⁵S)and 747.7 nm (³D ‐ ³P⁰), and the head at 759.4 nm of the atmospheric system (b ¹Σ⁺_g, v = 0 ‐ X ³Σ^—_g, v = 0).     

Facetting and (n × 1) reconstructions of SrTiO3(1 1 0) surfaces

(n × 1) reconstructions and facetting of the (1 1 0) polar surface of SrTiO₃ are studied by means of a combination of shell model and density functional calculations. The polarity compensation can be achieved through the formation of {1 0 0} nano-facets, which play a crucial role in the reconstruction process. The behaviors of various possible terminations (Sr, Ti, and O) are analyzed, as well as their atomic structure and energetics. Their stability in different chemical environments is discussed, with respect to previous formulations and experimental results. The Sr-terminated surface tends to expose large facets, while the TiO and O terminations are marginally stabilized or even destabilized by (n × 1) reconstructions, respectively. Trend to facetting results from a subtle competition between the thermodynamic stability of the ideal non stoichiometric (n × 1) surfaces, and huge atomic relaxations that contribute to the lowering of the surface energy differently for each termination.     

Laser heating and ablation at high repetition rate in thermal confinement regime

Laser heating and ablation of materials with low absorption and thermal conductivity (paint and cement) were under experimental and theoretical investigations. The experiments were made with a high repetition rate Q-switched Nd:YAG laser (10 kHz, 90 ns pulse duration and λ = 532 nm). High repetition rate laser heating resulted in pulse per pulse heat accumulation. A theoretical model of laser heating was developed and demonstrated a good agreement between the experimental temperatures measured with the infrared pyrometer and the calculated ones. With the fixed wavelength and laser pulse duration, the ablation threshold fluence of paint was found to depend on the repetition rate and the number of applied pulses. With a high repetition rate, the threshold fluence decreased significantly when the number of applied pulses was increasing. The experimentally obtained thresholds were well described by the developed theoretical model. Some specific features of paint heating and ablation with high repetition rate lasers are discussed.     

Uniqueness of Mass-Conserving Self-similar Solutions to Smoluchowski’s Coagulation Equation with Inverse Power Law Kernels

Uniqueness of mass-conserving self-similar solutions to Smoluchowski’s coagulation equation is shown when the coagulation kernel K is given by \(K(x,x_*)=2(x x_*)^{-\alpha }\), \((x,x_*)\in (0,\infty )^2\), for some \(\alpha >0\).     

An Improved Method to Determine Particle Dispersion Width for Efficient Modeling of Turbulent Two‐Phase Flows

An improved approach is presented for the hybrid Eulerian‐Lagrangian modeling of turbulent two‐phase flows. The hybrid model consists of a nonlinear k–ε model for the fluid flow and an efficient Lagrangian trajectory model for the particulate flow. The improved approach avoids an empirical correlation required to determine the dispersion width for the existing Stochastic‐Probabilistic Efficiency Enhanced Dispersion (SPEED) model. The improved SPEED model is validated using experimental data for a poly‐dispersed water spray interacting with a turbulent annular air jet behind a bluff‐body. Numerical results for the number‐mean and Sauter‐mean droplet diameters, as well as mean and fluctuating droplet velocities are compared with the experimental data and with the predictions of other dispersion models. It is demonstrated that higher computational efficiency and smoother profiles of Sauter‐mean diameter can be obtained with the improved stochastic‐probabilistic model than with the eddy‐interaction model.     

Optimization of direct modulation rate for circular microlasers by adjusting mode Q factor

Semiconductor microcircular lasers have been investigated as potential light sources for photonic integrated circuits and optical interconnections for more than two decades. However, the direct modulation bandwidths of the circular microlasers remain a challenge, especially when being compared with other microlasers, such as photonic crystal lasers. In this paper, microcircular lasers connected to an output waveguide are investigated for high‐speed direct modulation with optimized mode Q factors. Small signal modulation with a resonance frequency of f_R = 12.5 GHz is realized for a AlGaInAs/InP circular microlaser with a radius of 10 µm at 290 K. Furthermore, clear eye diagrams are observed at 12.5 Gbit/s for a 15‐µm radius circular microlaser with f_R = 6.9 GHz.