Femtosecond optical vortices in air

We examine the robustness of ultrashort optical vortices propagating freely in the atmosphere. We first approximate the stability regions of femtosecond spinning pulses as a function of their topological charge. Next, we numerically demonstrate that atmospheric optical vortices are capable of conveying high power levels in air over hundreds of meters before they break up into filaments.     

Stability of rocksalt (111) polar surfaces: beyond the octopole

Stable polar oxide surfaces must be simultaneously electrostatically compensated and in thermodynamic equilibrium with the environment. As a paradigm, the MgO(111)-p(2x2) reconstructed surface is shown to involve combinations of Mg-covered terminations with peculiar insulating electronic structure, favored in O-poor conditions, and the O-terminated octopole, stabler in more O-rich environments. Such a picture, which could not have been foreseen by either experiments or simulations separately, goes beyond the Wolf model and reconciles the theory with the experimental data taken in variable thermodynamic conditions.     

Singular Limit and Homogenization for Flame Propagation in Periodic Excitable Media

This paper is concerned with a class of singular equations modelling the combustion of premixed gases in periodic media. The model involves two parameters: the period of the medium |L| and a singular parameter related to the activation energy. The existence of pulsating travelling fronts for fixed and |L| was proved by Berestycki & Hamel in [BH]. In the present paper, we investigate the behaviour of such solutions when More precisely, we establish that pulsating travelling fronts behave like travelling waves, when the period |L| is small and . We also study the convergence of the solution, as goes to zero (and |L| is fixed), toward a solution of a free boundary problem.     

Rate Optimality of Wavelet Series Approximations of Fractional Brownian Motion

Consider the fractional Brownian motion process $B_H(t), t\in [0,T]$, with parameter $H\in (0,1)$. Meyer, Sellan and Taqqu have developed several random wavelet representations for $B_H(t)$, of the form $\sum_{k=0}^\infty U_k(t)\epsilon_k$ where $\epsilon_k$ are Gaussian random variables and where the functions $U_k$ are not random. Based on the results of Kühn and Linde, we say that the approximation $\sum_{k=0}^n U_k(t)\epsilon_k$ of $B_H(t)$ is optimal if $$ \displaystyle \left( E \sup_{t\in [0,T]} \left| \sum_{k=n}^\infty U_k(t) \epsilon_k\right|^2 \right)^{1/2} =O \left( n^{-H} (1+\log n)^{1/2} \right), $$ as $n\rightarrow\infty$. We show that the random wavelet representations given in Meyer, Sellan and Taqqu are optimal.     

The filtering approach to solvent peak suppression in MRS: a critical review

Suppressing the solvent peak is important in many applications of biomedical NMR spectroscopy in order to quantify the metabolites with a great accuracy. Among the postprocessing methods proposed in the literature, many deal with the concept of filtering. However, several proposals lack a theoretical perspective and some have not been explicitly applied to quantification problems. The present article is intended to bridge this gap: five methods are analyzed from a theoretical perspective. Subsequently the different methods are applied to the same set of data, and then the latter are quantified using the model fitting method AMARES. With our set, the scheme proposed by T. Sundin et al. (J. Magn. Reson. 139(2), 189-204 (1999)) proved to be the most reliable method.     

Laryngostroboscopic Evaluation After Supracricoid Partial Laryngectomy

BACKGROUND: Supracricoid partial laryngectomy (SCPL) results in laryngeal preservation in more than 95% of patients with T2 glottic carcinoma. Postsurgical glottic function is characterized by an absence of vocal cords, and phonation quality is a key post-SCPL quality-of-life factor. OBJECTIVE: This investigation was designed to enhance post-SCPL vocal function, study anatomic function of the post-SCPL larynx, and correlate anatomic findings with perceptual and instrumented measurements of voice. METHOD: Twenty-five patients were included. All had undergone SCPL with cricoepiglottopexy for T2 glottic carcinoma. All patients were evaluated by laryngostroboscopic examination, voice sample recording, and instrumented voice analysis with the aim of gaining further insight into postoperative larynx function. Laryngostroboscopic parameters such as laryngeal occlusion, epiglottic length, arytenoid movement, and vibratory area were assessed. The perceptual evaluation was based on the GRBAS scale. Acoustic and aerodynamic parameters were recorded, including fundamental frequency (F0), intensity, jitter, shimmer, signal-to-noise ratio (SNR), oral airflow (OAF), maximum phonation time (MPT), and estimated subglottic pressure (ESGP). Nonparametric tests were used to compare laryngostroboscopic parameters with instrumented measurements and perceptual evaluations of voice quality. RESULTS: Correlations were established among occlusion, epiglottic length, and general grade of dysphonia. Oral air flow (P = 0.006) was found to be correlated with occlusion. Voice roughness was correlated with the presence of a clearly identifiable vibratory area (P = 0.003), whereas these vibratory areas were correlated with shimmer (P = 0.041), OAF (P = 0.001), and SNR (P = 0.001). The number of preserved arytenoids was not identified as a voice quality factor (P = 0.423). CONCLUSION: This study highlighted correlations between the laryngostroboscopic examination results and the perceptive and instrumented measurements of voice. Glottis occlusion and epiglottis length were found to be key factors for postoperative voice quality. These results should help to advance technical development on surgical techniques to enhance voice results.     

Fractional Diffusion Limit for Collisional Kinetic Equations

This paper is devoted to diffusion limits of linear Boltzmann equations. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate time scale, the small mean free path limit gives rise to a diffusion equation. In this paper, we consider situations in which the equilibrium distribution function is a heavy-tailed distribution with infinite variance. We then show that for an appropriate time scale, the small mean free path limit gives rise to a fractional diffusion equation.