Modeling lossy anisotropic dielectric waveguides with the method of lines

1996 ◽  
Vol 44 (5) ◽  
pp. 749-759 ◽  
Author(s):  
P. Berini ◽  
Ke Wu
Keyword(s):  
Method Of Lines ◽  
Dielectric Waveguides ◽  
Anisotropic Dielectric ◽  
The Method Of Lines

SOLUTION OF THE RICHARDS EQUATION IN A SOIL PROFILE WITH TWO LAYERS USING THE METHOD OF LINES

2020 ◽  
Author(s):  
Diego Sousa Lopes ◽  
Augusto Cezar Cordeiro Jardim ◽  
Diego Estumano ◽  
Emanuel Macêdo ◽  
João Quaresma
Keyword(s):  
Soil Profile ◽  
Method Of Lines ◽  
Richards Equation ◽  
The Method Of Lines

TRAVELLING WAVES AND OSCILLATIONS IN SAL’NIKOV’S COMBUSTION REACTION IN A COMPRESSIBLE GAS

2015 ◽  
Vol 56 (3) ◽  
pp. 233-247 ◽  
Author(s):  
RHYS A. PAUL ◽  
LAWRENCE K. FORBES
Keyword(s):  
Asymptotic Solution ◽  
Multiple Scales ◽  
Travelling Waves ◽  
Method Of Lines ◽  
Travelling Wave ◽  
Reaction Scheme ◽  
Compressible Viscous Gas ◽  
The Method Of Lines ◽  
Temperature Waves ◽  
Parameter Values

We consider a two-step Sal’nikov reaction scheme occurring within a compressible viscous gas. The first step of the reaction may be either endothermic or exothermic, while the second step is strictly exothermic. Energy may also be lost from the system due to Newtonian cooling. An asymptotic solution for temperature perturbations of small amplitude is presented using the methods of strained coordinates and multiple scales, and a travelling wave solution with a sech-squared profile is derived. The method of lines is then used to approximate the full system with a set of ordinary differential equations, which are integrated numerically to track accurately the evolution of the reaction front. This numerical method is used to verify the asymptotic solution and investigate behaviours under different conditions. Using this method, temperature waves progressing as pulsatile fronts are detected at appropriate parameter values.

Enhanced Reactor Performance with Pressure and Vacuum Swing Reaction

2004 ◽  
Vol 2 (1) ◽  
Author(s):  
Vincent G Gomes
Keyword(s):  
Method Of Lines ◽  
Fixed Bed ◽  
Downstream Processing ◽  
Operating Conditions ◽  
Reactor Performance ◽  
Orthogonal Collocation ◽  
The Method Of Lines ◽  
Dynamic Experiments ◽  
Product Separation ◽  
Pressure Swing

Product separation and regeneration of sorbent was accomplished in a novel pressure swing reactor through pressurisation, adsorption, blowdown and purge steps. The switching from sorption to reaction to regeneration was tested in a two bed sorption/reaction apparatus. Models developed for the mass and momentum transfer in the catalyst bed and sorber, were solved using orthogonal collocation within the method of lines. The effects of operating conditions and cycle configurations on performance were assessed. The results from dynamic experiments with propene metathesis to produce ethene and 2-butene in a fixed-bed catalytic reactor were in agreement with model predictions. Both pressure and vacuum swing demonstrated that conversion and product quality can be enhanced by periodic cycling with greater separation obtained with vacuum swing. The separation of products help reduce the downstream processing costs of exit mixtures, enable reactant utilisation by recycling and improve product handling at subsequent stages. The efficacy of the periodic separating reactor in terms of conversion, product purity and recovery were investigated.

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