FROG characterisation of SOA-based wavelength conversion using XPM in conjunction with shifted filtering up to line rates of 80 GHz

The work we present here builds on recent work where we obtained 80 Gb/s error free performance using cross phase modulation (XPM) in an SOA in conjunction with a blue shifted bandpass filter. Here we present a detailed characterisation of this wavelength conversion scheme using a Frequency Resolved Optical Gating (FROG) measurement scheme for both red and blue shifted filtering. This type of characterisation has not been provided before to the best of our knowledge and is an important analysis firstly to achieve a full understanding of the gain and phase dynamics exploited by the wavelength conversion scheme presented and secondly to design a filter so that an optimum performance can be obtaine

Spatio-temporal patterns in a mechanical model for mesenchymal morphogenesis

We present an in-depth study of spatio-temporal patterns in a simplified version of a mechanical model for pattern formation in mesenchymal morphogenesis. We briefly motivate the derivation of the model and show how to choose realistic boundary conditions to make the system well-posed. We firstly consider one-dimensional patterns and carry out a nonlinear perturbation analysis for the case where the uniform steady state is linearly unstable to a single mode. In two-dimensions, we show that if the displacement field in the model is represented as a sum of orthogonal parts, then the model can be decomposed into two sub-models, only one of which is capable of generating pattern. We thus focus on this particular sub-model. We present a nonlinear analysis of spatio-temporal patterns exhibited by the sub-model on a square domain and discuss mode interaction. Our analysis shows that when a two-dimensional mode number admits two or more degenerate mode pairs, the solution of the full nonlinear system of partial differential equations is a mixed mode solution in which all the degenerate mode pairs are represented in a frequency locked oscillation

Analysis of bit rate dependence up to 80 Gbit/s of a simple wavelength converter based on XPM in a SOA and a shifted filtering

This paper provides the analysis of wavelength converted pulses obtained with a simple semiconductor optical amplifier (SOA)-based wavelength conversion scheme, which exploits cross phase modulation (XPM) in an SOA in conjunction with shifted filtering. The analysis includes experimental measurements of the back-to-back system performances as well as frequency-resolved optical gating (FROG) characterisations of the wavelength converted pulses. These measurements are implemented at different bit rates up to 80 Gbit/s and for both red and blue-shifted filtering, particularly showing different patterning effect dependencies of red and blue-shifting techniques. This analysis is developed by the addition of a numerical study which corroborates the experimental results. A further understanding of the different performances of red and blue filtering techniques, presented in the literature, can thus be proposed. The placement of the filter to undertake red-shifted filtering (RSF) allows us to achieve very short pulse widths but high bit rate operation is limited by pattern effects. The blue-shifted filtering (BSF) technique shows optimum performance as regards to patterning effects even if the wavelength converted pulses can be larger

AC electrokinetic phenomena over semiconductive surfaces: effective electric boundary conditions and their applications

Electrokinetic boundary conditions are derived for AC electrokinetic (ACEK) phenomena over leaky dielectric (i.e., semiconducting) surfaces. Such boundary conditions correlate the electric potentials across the semiconductor-electrolyte interface (consisting of the electric double layer (EDL) inside the electrolyte solutions and the space charge layer (SCL) inside the semiconductors) under AC electric fields with arbitrary wave forms. The present electrokinetic boundary conditions allow for evaluation of induced zeta potential contributed by both bond charges (due to electric polarization) and free charges (due to electric conduction) from the leaky dielectric materials. Subsequently, we demonstrate the applications of these boundary conditions in analyzing the ACEK phenomena around a semiconducting cylinder. It is concluded that the flow circulations exist around the semiconducting cylinder and are shown to be stronger under an AC field with lower frequency and around a cylinder with higher conductivity.Comment: 29 pages, 4 figure

On the numerical approximation of p-biharmonic and ∞-biharmonic functions

In [KP16] (arXiv:1605.07880) the authors introduced a second-order variational problem in L∞. The associated equation, coined the ∞-Bilaplacian, is a \emph{third order} fully nonlinear PDE given by Δ2∞u:=(Δu)3|D(Δu)|2=0. In this work we build a numerical method aimed at quantifying the nature of solutions to this problem which we call ∞-Biharmonic functions. For fixed p we design a mixed finite element scheme for the pre-limiting equation, the p-Bilaplacian Δ2pu:=Δ(|Δu|p−2Δu)=0. We prove convergence of the numerical solution to the weak solution of Δ2pu=0 and show that we are able to pass to the limit p→∞. We perform various tests aimed at understanding the nature of solutions of Δ2∞u and in 1-d we prove convergence of our discretisation to an appropriate weak solution concept of this problem, that of -solutions

Évolution des cancers de l’œsophage : impact de la stratégie thérapeutique

PURPOSE: To assess the outcome of esophageal cancer according to therapeutic strategy. PATIENTS AND METHODS: One-hundred and twenty patients with esophageal cancer treated by an association of radiotherapy and chemotherapy and possibly surgery, between 2004 and 2010, were retrospectively studied. The first site of relapse was classified as follows: local (tumour), locoregional (tumour and/or nodal: celiac, mediastinal, sus-clavicular) or metastatic. RESULTS: With a 15.7-months (1.4-62) median follow-up, there were 89 deaths and 79 recurrences. Three types of treatments were performed: 50Gy exclusive chemoradiotherapy (47 patients) or 50 to 65Gy exclusive chemoradiotherapy (44 patients) or chemoradiotherapy followed by surgery (27 patients). The local first relapse was as much frequent as distant relapse (50 patients). With a-5cm margin up and down to the tumour, there was only one nodal relapse. Two-year survival was 39.5% (95% confidence interval [IC]: 30.5-40.8) and relapse-free survival was 26.5% (CI: 18.6-35). Multivariate analysis revealed that treatment type and disease stage had a significant impact on survival, relapse-free survival and locoregional control. Compared to exclusive chemoradiotherapy, surgery improved locoregional control (40.2 versus 8.7 months, P=0.0004) but in a younger population. Despite postoperative mortality, the gain was maintained for distance relapse-free survival (40.2 versus 10 months, P=0.0147) and overall survival (29.3 versus 14.2 months, P=0.0088). Compared to 50Gy chemoradiotherapy, local control was improved if high dose chemoradiotherapy was performed (13.8 versus 7.5 months, P=0.05) but not overall survival (14.0 versus 15.4 months, P=0.24). CONCLUSION: More than one-third relapse is local. Locoregional control is better with high dose chemoradiotherapy. In this study, surgery performed in selected patients only, improved locoregional control, relapse-free disease and overall survival

Ginzburg-Landau theory of phase transitions in quasi-one-dimensional systems

A wide range of quasi-one-dimensional materials, consisting of weakly coupled chains, undergo three-dimensional phase transitions that can be described by a complex order parameter. A Ginzburg-Landau theory is derived for such a transition. It is shown that intrachain fluctuations in the order parameter play a crucial role and must be treated exactly. The effect of these fluctuations is determined by a single dimensionless parameter. The three-dimensional transition temperature, the associated specific heat jump, coherence lengths, and width of the critical region, are computed assuming that the single chain Ginzburg-Landau coefficients are independent of temperature. The width of the critical region, estimated from the Ginzburg criterion, is virtually parameter independent, being about 5-8 per cent of the transition temperature. To appear in {\it Physical Review B,} March 1, 1995.Comment: 15 pages, RevTeX, 5 figures in uuencoded compressed tar file

Microscopic theory of the pseudogap and Peierls transition in quasi-one-dimensional materials

The problem of deriving from microscopic theory a Ginzburg-Landau free energy functional to describe the Peierls or charge-density-wave transition in quasi-one-dimensional materials is considered. Particular attention is given to how the thermal lattice motion affects the electronic states. Near the transition temperature the thermal lattice motion produces a pseudogap in the density of states at the Fermi level. Perturbation theory diverges and the traditional quasi-particle or Fermi liquid picture breaks down. The pseudogap causes a significant modification of the coefficients in the Ginzburg-Landau functional from their values in the rigid lattice approximation, which neglects the effect of the thermal lattice motion. To appear in Physical Review B.Comment: 21 pages, RevTeX, 5 figures in uuencoded compressed tar fil

Random division of an interval

The well-known relation between random division of an interval and the Poisson process is interpreted as a Laplace transformation. With the use of this interpretation a number of (in part known) results is derived very easily

Friedel Oscillations and Charge-density Waves Pinning in Quasi-one-dimensional Conductors: An X-ray Access

We present an x-ray diffraction study of the Vanadium-doped blue bronze K0.3(Mo0.972V0.028)O3. At low temperature, we have observed both an intensity asymmetry of the +-2kF satellite reflections relative to the pure compound, and a profile asymmetry of each satellite reflections. We show that the profile asymmetry is due to Friedel oscillation around the V substituant and that the intensity asymmetry is related to the charge density wave (CDW) pinning. These two effects, intensity and profile asymmetries, gives for the first time access to the local properties of CDW in disordered systems, including the pinning and even the phase shift of FOs.Comment: 4 pages REVTEX, 5 figure