Sets Of Parametric Conditions Research Articles

Lipase immobilised carbonaceous catalyst assisted enzymatic transesterification of Mesua ferrea oil

The study investigates biodiesel synthesis from waste seeds derived Mesua ferrea oil (MFO) using indigenously developed biocatalyst via lipase immobilisation on coconut shells derived microporous activated carbon (AC). The carbonaceous support was developed through steam activation of carbonised char at optimised activation conditions to attain maximum porous properties. The hydrolytic enzyme i.e. lipase was immobilised on prepared AC through adsorption process at different functional variables. The enzyme loading or uptake of carbonaceous support and enzymatic activity of respective sample at each set of parametric conditions were estimated. The adsorption assisted immobilisation was optimised employing Taguchi method and significant factors affecting highly both the responses were identified through estimation of statistical constraints. The optimised conditions derived using 3FI model were: Initial protein concentration 500 mg/L, time 270 min, temperature 15 °C, and solution pH 6 for achieving maximum adsorption capacity of 10.04 mg/g and biodiesel yield 67.5%. Moreover, statistical parameters revealed, immobilisation temperature and initial protein concentration influence the catalytic activity considerably and optimised immobilisation helps in attaining highly active and stable biocatalyst. Furthermore, the chosen model was effective in predicting the optimised conditions with high precision for maximising the responses. Thus, the developed biocatalyst through lipase immobilisation on indigenously prepared microporous carbon support is effective in transesterification of MFO at 3FI model derived optimised conditions.

Pulse Amplification in Dispersion-Decreasing Fibers with Symbolic Computation

The pulse amplification in the dispersion–decreasing fiber (DDF) is investigated via symbolic computation to solve the variable-coefficient higher-order nonlinear Schrödinger equation with the effects of third-order dispersion, self-steepening, and stimulated Raman scattering. The analytic one-soliton solution of this model is obtained with a set of parametric conditions. Based on this solution, the fundamental soliton is shown to be amplified in the DDF. The comparison of the amplitude of pulses for different dispersion profiles of the DDF is also performed through the graphical analysis. The results of this paper would be of certain value to the study of signal amplification and pulse compression.

Analytic study on soliton-effect pulse compression in dispersion-shifted fibers with symbolic computation

The soliton-effect pulse compression of ultrashort solitons in a dispersion-shifted fiber (DSF) is investigated based on solving the higher-order nonlinear Schrödinger equation with the effects of third-order dispersion (TOD), self-steepening (SS) and stimulated Raman scattering (SRS). By using Hirota's bilinear method with a set of parametric conditions, the analytic one-, two- and three-soliton solutions of this model are obtained. According to those solutions, the higher-order soliton is shown to be compressed in the DSF for the pulse with width in the range of a few picoseconds or less. An appealing feature of the soliton-effect pulse compression is that, in contrast to the second-order soliton compression due to the combined effects of negative TOD and SRS, the third-order soliton can significantly enhance the soliton compression in the DSF with small values of the group-velocity dispersion (GVD) at the operating wavelength.

Analytic Multi-Solitonic Solutions of Variable-Coefficient Higher-Order Nonlinear Schrödinger Models by Modified Bilinear Method with Symbolic Computation

In this paper, the physically interesting variable-coefficient higher-order nonlinear Schr¨odinger models in nonlinear optical fibers with varying higher-order effects such as third-order dispersion, self-steepening, delayed nonlinear response and gain or absorption are investigated. The bilinear transformation method is modified for constructing the analytic solutions of these models directly with sets of parametric conditions. With the aid of symbolic computation, the explicit analytic multisolitonic solutions of the variable-coefficient higher-order nonlinear Schr¨odinger models are presented by employing the modified bilinear transformation method. The one- and two-solitonic solutions in explicit form are given in detail. Finally, solutions are illustrated and discussed through adjusting the parameters, so different dispersion management systems can be obtained.

Exact multisoliton solutions of the higher-order nonlinear Schrödinger equation with variable coefficients

We investigate the generalized higher-order nonlinear Schrödinger equation with variable coefficients under two sets of parametric conditions. The exact one-soliton solution is presented by the ansatz method for one set of parametric conditions. For the other, exact multisoliton solutions are presented by employing the Darboux transformation based on the Lax pair. As an example, we consider a soliton control system, and the results show that the soliton control system may relax the limitations to parametric conditions. The stability of the solution is discussed numerically; the results reveal that finite initial perturbations, such as amplitude, chirp, or white noise, could not influence the main character of the solution. In addition, the evolution of a quite arbitrary Gaussian pulse and the interaction between neighboring pulses have been studied in detail.