scholarly journals Quiescent Gap Solitons in Coupled Nonuniform Bragg Gratings with Cubic-Quintic Nonlinearity

2021 ◽  
Vol 11 (11) ◽  
pp. 4833
Author(s):  
Afroja Akter ◽  
Md. Jahedul Islam ◽  
Javid Atai
Keyword(s):  
Numerical Stability ◽  
Bragg Gratings ◽  
Stability Boundaries ◽  
Quintic Nonlinearity ◽  
Numerical Stability Analysis ◽  
Gap Solitons ◽  
The Stability ◽  
Dual Core

We study the stability characteristics of zero-velocity gap solitons in dual-core Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity. The model supports two disjointed families of gap solitons (Type 1 and Type 2). Additionally, asymmetric and symmetric solitons exist in both Type 1 and Type 2 families. A comprehensive numerical stability analysis is performed to analyze the stability of solitons. It is found that dispersive reflectivity improves the stability of both types of solitons. Nontrivial stability boundaries have been identified within the bandgap for each family of solitons. The effects and interplay of dispersive reflectivity and the coupling coefficient on the stability regions are also analyzed.

Sensitivity Analysis and Numerical Stability Analysis of the Algorithms for Predicting the Performance of Turbines

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
Ming Wei ◽  
Yonghong Wang ◽  
Huafen Song
Keyword(s):  
Numerical Stability ◽  
Rounding Error ◽  
One Dimensional ◽  
Flow Models ◽  
Numerical Stability Analysis ◽  
Last Stage ◽  
The Stability ◽  
Performance Calculation ◽  
Poor Stability ◽  
Input Error

Sensitivity and numerical stability of an algorithm are two of the most important criteria to evaluate its performance. For all published turbine flow models, except Wang method, can be named the “top-down” method (TDM) in which the performance of turbines is calculated from the first stage to the last stage row by row; only Wang method originally proposed by Yonghong Wang can be named the “bottom-up” method (BUM) in which the performance of turbines is calculated from the last stage to the first stage row by row. To find the reason why the stability of the two methods is of great difference, the Wang flow model is researched. The model readily applies to TDM and BUM. How the stability of the two algorithms affected by input error and rounding error is analyzed, the error propagation and distribution in the two methods are obtained. In order to explain the problem more intuitively, the stability of the two methods is described by geometrical ideas. To compare with the known data, the performance of a particular type of turbine is calculated through a series of procedures based on the two algorithms. The results are as follows. The more the calculating point approaches the critical point, the poorer the stability of TDM is. The poor stability can even cause failure in the calculation of TDM. However, BUM has not only good stability but also high accuracy. The result provides an accurate and reliable method (BUM) for estimating the performance of turbines, and it can apply to all one-dimensional performance calculation method for turbine.

Influence of Gravity and Taper on the Vibration of a Standing Column

2012 ◽  
Vol 4 (04) ◽  
pp. 483-495 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Cross Section ◽  
Numerical Stability ◽  
Natural Vibration ◽  
Vibration Frequencies ◽  
Stability Criteria ◽  
Initial Value ◽  
Vertical Column ◽  
Stability Boundaries ◽  
Section Shape ◽  
The Stability

AbstractThe stability and natural vibration of a standing tapered vertical column under its own weight are studied. Exact stability criteria are found for the pointy column and numerical stability boundaries are determined for the blunt tipped column. For vibrations we use an accurate, efficient initial value numerical method for the first three frequencies. Four kinds of columns with linear taper are considered. Both the taper and the cross section shape of the column have large influences on the vibration frequencies. It is found that gravity decreases the frequency while the degree of taper may increase or decrease frequency. Vibrations may occur in two different planes.

Cordierite in felsic igneous rocks: a synthesis

1995 ◽  
Vol 59 (395) ◽  
pp. 311-325 ◽  
Author(s):  
D. B. Clarke
Keyword(s):  
Grain Size ◽  
Common Type ◽  
Igneous Rocks ◽  
Spatial Proximity ◽  
Stability Conditions ◽  
High Grade ◽  
The Stability ◽  
Type 3

AbstractCordierite is a characteristic mineral of many peraluminous felsic igneous rocks. A combination of T-P-X parameters, which overlap the stability conditions for felsic magmas, control its formation. Critical among these parameters are relatively low T, low P, and typically high (Mg+Fe2+), Mg/Fe2+, A/CNK, aAl2O3, and fO2. Spatial and textural information indicate that cordierite may originate in one of three principal ways in felsic igneous rocks: Type 1 Metamorphic: (a) xenocrystic (generally anhedral, many inclusions, spatial proximity to country rocks and pelitic xenoliths); (b) restitic (generally anhedral, high-grade metamorphic inclusions); Type 2 Magmatic: (a,b) peritectic (subhedral to euhedral, associated with leucosomes in migmatites or as reaction rims on garnet); (c) cotectic (euhedral, grain size compatibility with host rock, few inclusions); (d) pegmatitic (large subhedral to euhedral grains, associated with aplite-pegmatite contacts or pegmatitic portion alone); and Type 3 Metasomatic (spatially related to structural discontinuities in host, replacement of feldspar and/or biotite, intergrowths with quartz). Of these, Type 2a (peritectic) and Type 2c (cotectic) predominate in granitic and rhyolitic rocks derived from fluid-undersaturated peraluminous magmas, and Type 2d (pegmatitic) may be the most common type in fluid-saturated systems.

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