Weak versus strong harmonic-expansion analyses of self-pulsing lasers: I—the Laser Lorenz model

We apply a simple harmonic expansion method to the single-mode laser equations to analyze their dynamic properties. First, we extend the well-known small signal analysis to predict the transient pulsations of the relaxation oscillations. Such transients are characteristic of the laser signal relaxing towards its long-term solution, at any level of excitation, both beyond and below the instability threshold. Secondly, we extend the method to a strong harmonic expansion to analyze the properties of the long-term solutions. These properties are derived for typical examples, extending well beyond the boundary region of the instability domain, for which the laser field amplitude undergoes regular pulsations around zero-mean values.     

Relating quantiles and expectiles under weighted-symmetry

Recently, quantiles and expectiles of a regression function have been investigated by several authors. In this work, we give a sufficient condition under which a quantile and an expectile coincide. We extend some classical results known for mean, median and symmetry to expectiles, quantiles and weighted-symmetry. We also study split-models and sample estimators of expectiles.Work supported by the Natural Science and Engineering Council of Canada and by the Université du Québec à Trois-Rivières.     

Decay property of regularity-loss type of solutions in elastic solids with voids

In this article, we consider two porous systems of nonclassical thermoelasticity in the whole real line. We discuss the long-time behaviour of the solutions in the presence of a strong damping acting, together with the heat effect, on the elastic equation and establish several decay results. Those decay results are shown to be very slow and of regularity-loss type. Some improvements of the decay rates have also been given, provided that the initial data belong to some weighted spaces.     

Electrochemical Impedance Spectroscopic Measurements of Sexithiophene—Effect of the Electrode Nature and the Dopant (CuCl2) Content

Electrochemical impedance spectroscopic (EIS) measurements of sexithiophene (6T) were carried out according to the Pt/6T/M sandwich structure configuration, for various electrode materials (M＝GC, ITO, Ag, Cu, Al) and for different doping levels of copper chloride (CuCl2). The results demonstrate that two types of charge transport are involved in the redox process at the electrode/6T interface and inside the bulk oligomer. The complex-plane impedance plots obtained for various doping levels of CuCl2 exhibit arc shapes. The charge-transfer resistance measured from the diagrams decreases systematically with the addition of the salt, leading to an increase of the oligothiophene conductivity.     

Metal-insulator transitions in an expanding metallic fluid: particle formation kinetics

Core-level photoemission spectroscopy provides a local probe of expansion dynamics and associated transient chemical properties as a highly pressurized, metallic fluid expands into vacuum following impulsive heating of a semiconductor by an intense, ultrashort laser pulse. Transient photoemission peak shifts reveal that metal-insulator transitions occur rapidly following laser heating. These experiments probe constituents species and solidification kinetics occurring in the early moments of material ejection and provide insight into how particles arise in the current laser ablation regime.     

Weak versus strong harmonic-expansion analyses of self-pulsing lasers: II—the inhomogeneously broadened system

A simple harmonic expansion method is applied to investigate some aspects of the dynamic properties of the integro-differential ‘Maxwell-Bloch’ equations that describe the self-pulsing regime of a single-mode inhomogeneously broadened laser. First, we show that the usual small perturbative methods only describe the transient relaxation oscillations, characteristic of the signal relaxing towards its permanent state, either stable or unstable. Second, we show that an adapted strong harmonic expansion analysis applied to the permanent pulsing solutions yields an accurate evaluation of the pulsing frequencies.     

On the wave equation with semilinear porous acoustic boundary conditions

The goal of this work is to study a model of the wave equation with semilinear porous acoustic boundary conditions with nonlinear boundary/interior sources and a nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. The main difficulty in proving the local existence result is that the Neumann boundary conditions experience loss of regularity due to boundary sources. Using an approximation method involving truncated sources and adapting the ideas in Lasiecka and Tataru (1993) [28], we show that the existence of solutions can still be obtained. Second, we prove that under some restrictions on the source terms, then the local solution can be extended to be global in time. In addition, it has been shown that the decay rates of the solution are given implicitly as solutions to a first order ODE and depends on the behavior of the damping terms. In several situations, the obtained ODE can be easily solved and the decay rates can be given explicitly. Third, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution ceases to exists and blows up in finite time. Moreover, in either the absence of the interior source or the boundary source, then we prove that the solution is unbounded and grows as an exponential function.     

Ultrafast internal conversion in ethylene. II. Mechanisms and pathways for quenching and hydrogen elimination

Through a combined experimental and theoretical approach, we study the nonadiabatic dynamics of the prototypical ethylene (C(2)H(4)) molecule upon π → π(?) excitation with 161 nm light. Using a novel experimental apparatus, we combine femtosecond pulses of vacuum ultraviolet and extreme ultraviolet (XUV) radiation with variable delay to perform time resolved photo-ion fragment spectroscopy. In this second part of a two part series, the XUV (17 eV < hν < 23 eV) probe pulses are sufficiently energetic to break the C-C bond in photoionization, or to photoionize the dissociation products of the vibrationally hot ground state. The experimental data is directly compared to excited state ab initio molecular dynamics simulations explicitly accounting for the probe step. Enhancements of the CH(2)(+) and CH(3)(+) photo-ion fragment yields, corresponding to molecules photoionized in ethylene (CH(2)CH(2)) and ethylidene (CH(3)CH) like geometries are observed within 100 fs after π → π(?) excitation. Quantitative agreement between theory and experiment on the relative CH(2)(+) and CH(3)(+) yields provides experimental confirmation of the theoretical prediction of two distinct conical intersections and their branching ratio [H. Tao, B. G. Levine, and T. J. Martinez, J. Phys. Chem. A. 113, 13656 (2009)]. Evidence for fast, non-statistical, elimination of H(2) molecules and H atoms is observed in the time resolved H(2)(+) and H(+) signals.     

Effect of metal diffusion into polycrystalline 6H–SiC prior to its anodization on luminescence response

p-Type porous SiC layers were fabricated by anodization of resistive p-type 6H–SiC samples using HF/ethylene glycol solution. Thin films of lithium (Li) and aluminum (Al) as donor and acceptor elements were vacuum deposited and diffused onto SiC substrates prior to anodization. The aim of this work is to investigate the properties of the nanoporous SiC layer formed by this method and to deduce the effect of diffused lithium as donor and Al as acceptor atoms on their photoluminescence response (PL). The profile distribution of lithium and aluminum diffused atoms was carried out using secondary ion mass spectrometry (SIMS). The photoluminescence spectra of the anodized Al-diffused samples exhibit a broad emission band centered at about 475 nm, while the Li-diffused samples exhibit luminescence with one broad peak located at 655 nm, attributed to Li-related defect centers. In addition, the PL intensity of lithium diffused samples varies with varying the etching time. Finally, the results are expected to have important applications in modern optoelectronic devices and electrode materials of lithium batteries.