A meshless method for an inverse two-phase one-dimensional nonlinear Stefan problem

We extend a meshless method of fundamental solutions recently proposed by the authors for the one-dimensional two-phase inverse linear Stefan problem, to the nonlinear case. In this latter situation the free surface is also considered unknown which is more realistic from the practical point of view. Building on the earlier work, the solution is approximated in each phase by a linear combination of fundamental solutions to the heat equation. The implementation and analysis are more complicated in the present situation since one needs to deal with a nonlinear minimization problem to identify the free surface. Furthermore, the inverse problem is ill-posed since small errors in the input measured data can cause large deviations in the desired solution. Therefore, regularization needs to be incorporated in the objective function which is minimized in order to obtain a stable solution. Numerical results are presented and discussed. © 2014 IMACS.

Analytical and numerical analysis of 40 Gbit/s regenerated transmissions using simple black box optical regenerator

A simplified (without phase modulator) scheme of a black box optical regenerator is proposed, where an appropriate nonlinear propagation is used to enhance regeneration. Applying semi-theoretical models the authors optimise and demonstrate feasibility of error-free long distance transmission at 40 Gbit/s.

Serum α-tocopherol has a nonlinear inverse association with periodontitis among US adults

Background: Previous experimental models suggest that vitamin E may ameliorate periodontitis. However, epidemiologic studies show inconsistent evidence in supporting this plausible association. Objective: We aimed to investigate the association between serum α-tocopherol (αT) and γ-tocopherol (γT) and periodontitis in a large cross-sectional US population. Methods: This study included 4708 participants in the 1999–2001 NHANES. Serum tocopherols were measured by HPLC and values were adjusted by total cholesterol (TC). Periodontal status was assessed by mean clinical attachment loss (CAL) and probing pocket depth (PPD). Total periodontitis (TPD) was defined as the sum of mild, moderate, and severe periodontitis. All measurements were performed by NHANES. Results: Means ± SDs of serum αT:TC ratio from low to high quartiles were 4.0 ± 0.4, 4.8 ± 0.2, 5.7 ± 0.4, and 9.1 ± 2.7 μmol/mmol. In multivariate regression models, αT:TC quartiles were inversely associated with mean CAL (P-trend = 0.06), mean PPD (P-trend < 0.001), and TPD (P-trend < 0.001) overall. Adjusted mean differences (95% CIs) between the first and fourth quartile of αT:TC were 0.12 mm (0.03, 0.20; P-difference = 0.005) for mean CAL and 0.12 mm (0.06, 0.17; P < 0.001) for mean PPD, whereas corresponding OR for TPD was 1.65 (95% CI: 1.26, 2.16; P-difference = 0.001). In a dose-response analysis, a clear inverse association between αT:TC and mean CAL, mean PPD, and TPD was observed among participants with relatively low αT:TC. No differences were seen in participants with higher αT:TC ratios. Participants with γT:TC ratio in the interquartile range showed a significantly lower mean PPD than those in the highest quartile. Conclusions: A nonlinear inverse association was observed between serum αT and severity of periodontitis, which was restricted to adults with normal but relatively low αT status. These findings warrant further confirmation in longitudinal or intervention settings.

Soliton's eigenvalue based analysis on the generation mechanism of rogue wave phenomenon in optical fibers exhibiting weak third order dispersion

One of the extraordinary aspects of nonlinear wave evolution which has been observed as the spontaneous occurrence of astonishing and statistically extraordinary amplitude wave is called rogue wave. We show that the eigenvalues of the associated equation of nonlinear Schrödinger equation are almost constant in the vicinity of rogue wave and we validate that optical rogue waves are formed by the collision between quasi-solitons in anomalous dispersion fiber exhibiting weak third order dispersion.

Analysis of rogue wave phenomenon in optical fiber based on soliton's eigenvalue

The impact of third-order dispersion (TOD) on optical rogue wave phenomenon is investigated numerically. We validate the TOD coefficient by utilizing the eigenvalue of the associated equation of the nonlinear Schrödinger equation (NLSE). © 2014 OSA.

Generation of optical frequency combs in fibres:an optical pulse analysis

The innovation of optical frequency combs (OFCs) generated in passive mode-locked lasers has provided astronomy with unprecedented accuracy for wavelength calibration in high-resolution spectroscopy in research areas such as the discovery of exoplanets or the measurement of fundamental constants. The unique properties of OCFs, namely a highly dense spectrum of uniformly spaced emission lines of nearly equal intensity over the nominal wavelength range, is not only beneficial for high-resolution spectroscopy. Also in the low- to medium-resolution domain, the OFCs hold the promise to revolutionise the calibration techniques. Here, we present a novel method for generation of OFCs. As opposed to the mode-locked laser-based approach that can be complex, costly, and difficult to stabilise, we propose an all optical fibre-based system that is simple, compact, stable, and low-cost. Our system consists of three optical fibres where the first one is a conventional single-mode fibre, the second one is an erbium-doped fibre and the third one is a highly nonlinear low-dispersion fibre. The system is pumped by two equally intense continuous-wave (CW) lasers. To be able to control the quality and the bandwidth of the OFCs, it is crucial to understand how optical solitons arise out of the initial modulated CW field in the first fibre. Here, we numerically investigate the pulse evolution in the first fibre using the technique of the solitons radiation beat analysis. Having applied this technique, we realised that formation of higherorder solitons is supported in the low-energy region, whereas, in the high-energy region, Kuznetsov-Ma solitons appear.

Long-range and high-resolution correlation optical time-domain reflectometry utilizing an all optical chaotic source

A high resolution optical time domain reflectometry (OTDR) based on an all-fiber chaotic source is demonstrated. We analyze the key factors limiting the operational range of such an OTDR, e.g., integral Rayleigh backscattering and the fiber loss, which degrade the optical signal to noise ratio at the receiver side, and then the guideline for counter-act such signal fading is discussed. The experimentally demonstrated correlation OTDR presents ability of 100km sensing range and 8.2cm spatial resolution (1.2 million resolved points), as a verification of the theoretical analysis. To the best of our knowledge, this is the first time that correlation OTDR measurement is performed over such a long distance with such high precision.

Capacity of dispersion-non-compensated nonlinear fibre channels

We present the analytical description of a specific nonlinear fibre channel with non-compensated dispersion. Information theory analysis shows that capacity of such nonlinear fibre channel does not decay with growing signal-to-noise ratio. © 2012 IEEE.

Analysis of Wiener-Hammerstein equalizer for downlink LTE system

We propose a Wiener-Hammerstein (W-H) channel estimation algorithm for Long-Term Evolution (LTE) systems. The LTE standard provides known data as pilot symbols and exploits them through coherent detection to improve system performance. These drivers are placed in a hybrid way to cover up both time and frequency domain. Our aim is to adapt the W-H equalizer (W-H/E) to LTE standard for compensation of both linear and nonlinear effects induced by power amplifiers and multipath channels. We evaluate the performance of the W-H/E for a Downlink LTE system in terms of BLER, EVM and Throughput versus SNR. Afterwards, we compare the results with a traditional Least-Mean Square (LMS) equalizer. It is shown that W-H/E can significantly reduce both linear and nonlinear distortions compared to LMS and improve LTE Downlink system performance.

PMD tolerant nonlinear compensation using in-line phase conjugation

In this paper, we numerically investigate the impact of polarisation mode dispersion on the efficiency of compensation of nonlinear transmission penalties for systems employing one of more inline phase conjugation devices. We will show that reducing the spacing between phase conjugations allows for significantly improved performance in the presence polarisation mode dispersion or a significant relaxation in the acceptable level of polarization mode dispersion. We show that these results are consistent with previously presented full statistical analysis of nonlinear transmission appropriately adjusted for the reduced section length undergoing compensation.

Analysis and interpretation of serial position data

The representation of serial position in sequences is an important topic in a variety of cognitive areas including the domains of language, memory, and motor control. In the neuropsychological literature, serial position data have often been normalized across different lengths, and an improved procedure for this has recently been reported by Machtynger and Shallice (2009). Effects of length and a U-shaped normalized serial position curve have been criteria for identifying working memory deficits. We present simulations and analyses to illustrate some of the issues that arise when relating serial position data to specific theories. We show that critical distinctions are often difficult to make based on normalized data. We suggest that curves for different lengths are best presented in their raw form and that binomial regression can be used to answer specific questions about the effects of length, position, and linear or nonlinear shape that are critical to making theoretical distinctions. © 2010 Psychology Press.

Serum α-tocopherol has a nonlinear inverse association with periodontitis among US adults

Previous experimental models suggest that vitamin E may ameliorate periodontitis. However, epidemiologic studies show inconsistent evidence in supporting this plausible association. We aimed to investigate the association between serum α-tocopherol (αT) and γ-tocopherol (γT) and periodontitis in a large cross-sectional US population. This study included 4708 participants in the 1999–2001 NHANES. Serum tocopherols were measured by HPLC and values were adjusted by total cholesterol (TC). Periodontal status was assessed by mean clinical attachment loss (CAL) and probing pocket depth (PPD). Total periodontitis (TPD) was defined as the sum of mild, moderate, and severe periodontitis. All measurements were performed by NHANES. Means ± SDs of serum αT:TC ratio from low to high quartiles were 4.0 ± 0.4, 4.8 ± 0.2, 5.7 ± 0.4, and 9.1 ± 2.7 μmol/mmol. In multivariate regression models, αT:TC quartiles were inversely associated with mean CAL (P-trend = 0.06), mean PPD (P-trend < 0.001), and TPD (P-trend < 0.001) overall. Adjusted mean differences (95% CIs) between the first and fourth quartile of αT:TC were 0.12 mm (0.03, 0.20; P-difference = 0.005) for mean CAL and 0.12 mm (0.06, 0.17; P < 0.001) for mean PPD, whereas corresponding OR for TPD was 1.65 (95% CI: 1.26, 2.16; P-difference = 0.001). In a dose-response analysis, a clear inverse association between αT:TC and mean CAL, mean PPD, and TPD was observed among participants with relatively low αT:TC. No differences were seen in participants with higher αT:TC ratios. Participants with γT:TC ratio in the interquartile range showed a significantly lower mean PPD than those in the highest quartile. A nonlinear inverse association was observed between serum αT and severity of periodontitis, which was restricted to adults with normal but relatively low αT status. These findings warrant further confirmation in longitudinal or intervention settings.

Suppression of nonlinear distortion in few-mode fibres using strong mode coupling

In this paper, we investigate the impact of linear mode coupling on the efficiency of intermodal four-wave mixing and on the group delay statistics in few-mode fibres. The investigation will include not only the weak or strong linear coupling regimes, but also the transition region between them, the intermediate coupling regime. This analysis will allow to assess the level of coupling strength require to suppress the nonlinear distortion in a few-mode fibre below the level of distortion for single-mode propagation without mode coupling.

Dynamics of spatial heterogeneity in a landfill with interacting phase densities:a stochastic analysis

A landfill represents a complex and dynamically evolving structure that can be stochastically perturbed by exogenous factors. Both thermodynamic (equilibrium) and time varying (non-steady state) properties of a landfill are affected by spatially heterogenous and nonlinear subprocesses that combine with constraining initial and boundary conditions arising from the associated surroundings. While multiple approaches have been made to model landfill statistics by incorporating spatially dependent parameters on the one hand (data based approach) and continuum dynamical mass-balance equations on the other (equation based modelling), practically no attempt has been made to amalgamate these two approaches while also incorporating inherent stochastically induced fluctuations affecting the process overall. In this article, we will implement a minimalist scheme of modelling the time evolution of a realistic three dimensional landfill through a reaction-diffusion based approach, focusing on the coupled interactions of four key variables - solid mass density, hydrolysed mass density, acetogenic mass density and methanogenic mass density, that themselves are stochastically affected by fluctuations, coupled with diffusive relaxation of the individual densities, in ambient surroundings. Our results indicate that close to the linearly stable limit, the large time steady state properties, arising out of a series of complex coupled interactions between the stochastically driven variables, are scarcely affected by the biochemical growth-decay statistics. Our results clearly show that an equilibrium landfill structure is primarily determined by the solid and hydrolysed mass densities only rendering the other variables as statistically "irrelevant" in this (large time) asymptotic limit. The other major implication of incorporation of stochasticity in the landfill evolution dynamics is in the hugely reduced production times of the plants that are now approximately 20-30 years instead of the previous deterministic model predictions of 50 years and above. The predictions from this stochastic model are in conformity with available experimental observations.