A perturbative analysis of dispersion-managed solitons

We study soliton solutions of the path-averaged propagation equation governing the transmission of dispersion-managed (DM) optical pulses in the (practical) limit when residual dispersion and nonlinearity only slightly affect the pulse dynamics over one compensation period. In the case of small dispersion map strengths, the averaged pulse dynamics is governed by a perturbed form of the nonlinear Schrödinger equation; applying a perturbation theory – elsewhere developed – based on inverse scattering theory, we derive an analytic expression for the envelope of the DM soliton. This expression correctly predicts the power enhancement arising from the dispersion management. Theoretical results are verified by direct numerical simulations.

Seasonal variations of EPG levels in gastro-intestinal parasitic infection in a southeast asian controlled locale:a statistical analysis

We present a data based statistical study on the effects of seasonal variations in the growth rates of the gastro-intestinal (GI) parasitic infection in livestock. The alluded growth rate is estimated through the variation in the number of eggs per gram (EPG) of faeces in animals. In accordance with earlier studies, our analysis too shows that rainfall is the dominant variable in determining EPG infection rates compared to other macro-parameters like temperature and humidity. Our statistical analysis clearly indicates an oscillatory dependence of EPG levels on rainfall fluctuations. Monsoon recorded the highest infection with a comparative increase of at least 2.5 times compared to the next most infected period (summer). A least square fit of the EPG versus rainfall data indicates an approach towards a super diffusive (i. e. root mean square displacement growing faster than the square root of the elapsed time as obtained for simple diffusion) infection growth pattern regime for low rainfall regimes (technically defined as zeroth level dependence) that gets remarkably augmented for large rainfall zones. Our analysis further indicates that for low fluctuations in temperature (true on the bulk data), EPG level saturates beyond a critical value of the rainfall, a threshold that is expected to indicate the onset of the nonlinear regime. The probability density functions (PDFs) of the EPG data show oscillatory behavior in the large rainfall regime (greater than 500 mm), the frequency of oscillation, once again, being determined by the ambient wetness (rainfall, and humidity). Data recorded over three pilot projects spanning three measures of rainfall and humidity bear testimony to the universality of this statistical argument. © 2013 Chattopadhyay and Bandyopadhyay.

Population pharmacokinetic and pharmacogenetic analysis of 6-mercaptopurine in paediatric patients with acute lymphoblastic leukaemia

WHAT IS ALREADY KNOWN ABOUT THIS SUBJECT • The cytotoxic effects of 6-mercaptopurine (6-MP) were found to be due to drug-derived intracellular metabolites (mainly 6-thioguanine nucleotides and to some extent 6-methylmercaptopurine nucleotides) rather than the drug itself. • Current empirical dosing methods for oral 6-MP result in highly variable drug and metabolite concentrations and hence variability in treatment outcome. WHAT THIS STUDY ADDS • The first population pharmacokinetic model has been developed for 6-MP active metabolites in paediatric patients with acute lymphoblastic leukaemia and the potential demographic and genetically controlled factors that could lead to interpatient pharmacokinetic variability among this population have been assessed. • The model shows a large reduction in interindividual variability of pharmacokinetic parameters when body surface area and thiopurine methyltransferase polymorphism are incorporated into the model as covariates. • The developed model offers a more rational dosing approach for 6-MP than the traditional empirical method (based on body surface area) through combining it with pharmacogenetically guided dosing based on thiopurine methyltransferase genotype. AIMS - To investigate the population pharmacokinetics of 6-mercaptopurine (6-MP) active metabolites in paediatric patients with acute lymphoblastic leukaemia (ALL) and examine the effects of various genetic polymorphisms on the disposition of these metabolites. METHODS - Data were collected prospectively from 19 paediatric patients with ALL (n = 75 samples, 150 concentrations) who received 6-MP maintenance chemotherapy (titrated to a target dose of 75 mg m−2 day−1). All patients were genotyped for polymorphisms in three enzymes involved in 6-MP metabolism. Population pharmacokinetic analysis was performed with the nonlinear mixed effects modelling program (nonmem) to determine the population mean parameter estimate of clearance for the active metabolites. RESULTS - The developed model revealed considerable interindividual variability (IIV) in the clearance of 6-MP active metabolites [6-thioguanine nucleotides (6-TGNs) and 6-methylmercaptopurine nucleotides (6-mMPNs)]. Body surface area explained a significant part of 6-TGNs clearance IIV when incorporated in the model (IIV reduced from 69.9 to 29.3%). The most influential covariate examined, however, was thiopurine methyltransferase (TPMT) genotype, which resulted in the greatest reduction in the model's objective function (P < 0.005) when incorporated as a covariate affecting the fractional metabolic transformation of 6-MP into 6-TGNs. The other genetic covariates tested were not statistically significant and therefore were not included in the final model. CONCLUSIONS - The developed pharmacokinetic model (if successful at external validation) would offer a more rational dosing approach for 6-MP than the traditional empirical method since it combines the current practice of using body surface area in 6-MP dosing with a pharmacogenetically guided dosing based on TPMT genotype.

Breakup of a multisoliton state of the linearly damped nonlinear Schrödinger equation

We address the breakup (splitting) of multisoliton solutions of the nonlinear Schrödinger equation (NLSE), occurring due to linear loss. Two different approaches are used for the study of the splitting process. The first one is based on the direct numerical solution of the linearly damped NLSE and the subsequent analysis of the eigenvalue drift for the associated Zakharov-Shabat spectral problem. The second one involves the multisoliton adiabatic perturbation theory applied for studying the evolution of the solution parameters, with the linear loss taken as a small perturbation. We demonstrate that in the case of strong nonadiabatic loss the evolution of the Zakharov-Shabat eigenvalues can be quite nontrivial. We also demonstrate that the multisoliton breakup can be correctly described within the framework of the adiabatic perturbation theory and can take place even due to small linear loss. Eventually we elucidate the occurrence of the splitting and its dependence on the phase mismatch between the solitons forming a two-soliton bound state. © 2007 The American Physical Society.

Design and analysis of an all-optical processor for modular arithmetic

We present a logical design of an all-optical processor that performs modular arithmetic. The overall design is based a set of interconnected modules that use all-optical gates to perform simple logical functions. The all-optical logic gates are based on the semiconductor optical amplifier nonlinear loop. Simulation results are presented and some practical design issues are discussed.

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.

Stochastic Solution of a KPP-Type Nonlinear Fractional Differential Equation

Mathematics Subject Classification: 26A33, 76M35, 82B31

Nonlinear Time-Fractional Differential Equations in Combustion Science

MSC 2010: 34A08 (main), 34G20, 80A25

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.

Stability and Instability of Solitary Wave Solutions of a Nonlinear Dispersive System of Benjamin-Bona-Mahony Type

2000 Mathematics Subject Classification: 35B35, 35B40, 35Q35, 76B25, 76E30.

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.

Asymptotic Analysis of a Schrödinger-Poisson System with Quantum Wells and Macroscopic Nonlinearities in Dimension 1

2000 Mathematics Subject Classification: 35Q02, 35Q05, 35Q10, 35B40.