scholarly journals Mode Coupling in the Solar Corona. II. Oblique Incidence

1974 ◽  
Vol 27 (1) ◽  
pp. 43 ◽  
Author(s):  
DB Melrose
Keyword(s):  
Physical Interpretation ◽  
Mode Coupling ◽  
Present Method ◽  
Iterative Procedure ◽  
Oblique Incidence ◽  
Explicit Solutions ◽  
Finite Range ◽  
Coupling Coefficients ◽  
Magnetic Structures ◽  
One Step

Previous discussions of mode coupling at a QT region have assumed vertical incidence and have hus invoked magnetic structures which violate div B = o. A new method is developed here for alculating the coupling coefficients for oblique incidence so that coupling at a QT region can be reated without invoking nonphysical magnetic structures. The method involves solving the Booker uartic equation implicitly in terms of the familiar formulae of magnetoionic theory. A coupling pproximation is introduced which involves one step in an iterative procedure to find explicit solutions rom the implicit ones. The approximation is necessarily valid in a finite range about the critical oupling points. The present method is used to generalize the results of Cohen to allow oblique ncidence. The results of the existing discussions of mode coupling for vertical incidence and nonphysical agnetic structures can be justified both qualitatively and semiquantitatively (although ith a slightly different physical interpretation).

scholarly journals Choosing the Optimal Multi-Point Iterative Method for the Colebrook Flow Friction Equation

Processes ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 130 ◽  
Author(s):  
Pavel Praks ◽  
Dejan Brkić
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Iterative Procedure ◽  
Accurate Solution ◽  
Final Solution ◽  
Worst Case ◽  
Flow Friction ◽  
One Step ◽  
Newton Raphson ◽  
Number Of Iterations

The Colebrook equation is implicitly given in respect to the unknown flow friction factor λ; λ = ζ ( R e , ε * , λ ) which cannot be expressed explicitly in exact way without simplifications and use of approximate calculus. A common approach to solve it is through the Newton–Raphson iterative procedure or through the fixed-point iterative procedure. Both require in some cases, up to seven iterations. On the other hand, numerous more powerful iterative methods such as three- or two-point methods, etc. are available. The purpose is to choose optimal iterative method in order to solve the implicit Colebrook equation for flow friction accurately using the least possible number of iterations. The methods are thoroughly tested and those which require the least possible number of iterations to reach the accurate solution are identified. The most powerful three-point methods require, in the worst case, only two iterations to reach the final solution. The recommended representatives are Sharma–Guha–Gupta, Sharma–Sharma, Sharma–Arora, Džunić–Petković–Petković; Bi–Ren–Wu, Chun–Neta based on Kung–Traub, Neta, and the Jain method based on the Steffensen scheme. The recommended iterative methods can reach the final accurate solution with the least possible number of iterations. The approach is hybrid between the iterative procedure and one-step explicit approximations and can be used in engineering design for initial rough, but also for final fine calculations.

Analysis and design of TEM-TE11 coaxial waveguide bend mode converters

2019 ◽  
Vol 12 (3) ◽  
pp. 198-204 ◽  
Author(s):  
Qiang Zhang ◽  
Xuhao Zhao ◽  
Chengwei Yuan ◽  
Jiande Zhang
Keyword(s):  
Mode Coupling ◽  
Theoretical Calculations ◽  
Coaxial Waveguide ◽  
Coupling Coefficients ◽  
Electromagnetic Mode ◽  
Analysis And Design ◽  
Mode Converters ◽  
Transverse Electromagnetic ◽  
Conversion Efficiencies ◽  
Waveguide Bend

AbstractTwo coaxial waveguide bend mode converters that transform coaxial transverse electromagnetic mode to TE11 coaxial waveguide mode are presented in this paper. Both converters are designed and optimized on the basis of the strictly derived mode coupling coefficients. Conversion efficiencies of both converters are over 99% and the power-handling capacities reach a gigawatt level. The combined dual-bend mode converter is fabricated and tested. The experimental results coincide well with the theoretical calculations and simulations, which demonstrates the feasibility of the designed converter.

The Determination of Mode Coupling Coefficients

1985 ◽  
Vol 32 (6) ◽  
pp. 635-637 ◽  
Author(s):  
E. Popov ◽  
L. Mashev
Keyword(s):  
Mode Coupling ◽  
Coupling Coefficients

Flow Interaction Near the Tail of a Body of Revolution—Part 1: Flow Exterior to Boundary Layer and Wake

1976 ◽  
Vol 98 (3) ◽  
pp. 531-537 ◽  
Author(s):  
A. Nakayama ◽  
V. C. Patel ◽  
L. Landweber
Keyword(s):  
Boundary Layer ◽  
Integral Equation ◽  
Potential Flow ◽  
Present Method ◽  
Iterative Procedure ◽  
The Body ◽  
Body Of Revolution ◽  
Near Wake ◽  
Momentum Integral ◽  
Good Agreement

An iterative procedure for the calculation of the thick attached turbulent boundary layer near the tail of a body of revolution is presented. The procedure consists of the potential-flow calculation by a method of integral equation of the first kind and the calculation of the development of the boundary layer and the wake using an integral method with the condition that the velocity remains continuous across the edge of the boundary layer and the wake. The additional terms that appear in the momentum integral equation for the thick boundary layer and the near wake are taken into account and the pressure difference between the body surface and the edge of the boundary layer and the wake can be determined. The results obtained by the present method are in good agreement with the experimental data. Part 1 of this paper deals with the potential flow, while Part 2 [1] describes the boundary layer and wake calculations, and the overall iterative procedure and results.

scholarly journals An Analytical Investigation of Fractional-Order Biological Model Using an Innovative Technique

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Hassan Khan ◽  
Adnan Khan ◽  
Maysaa Al Qurashi ◽  
Dumitru Baleanu ◽  
Rasool Shah
Keyword(s):  
Fractional Order ◽  
Present Method ◽  
Iterative Procedure ◽  
Laplace Transformation ◽  
Small Volume ◽  
Analytical Investigation ◽  
Form Solution ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Closed Contact

In this paper, a new so-called iterative Laplace transform method is implemented to investigate the solution of certain important population models of noninteger order. The iterative procedure is combined effectively with Laplace transformation to develop the suggested methodology. The Caputo operator is applied to express the noninteger derivative of fractional order. The series form solution is obtained having components of convergent behavior toward the exact solution. For justification and verification of the present method, some illustrative examples are discussed. The closed contact is observed between the obtained and exact solutions. Moreover, the suggested method has a small volume of calculations; therefore, it can be applied to handle the solutions of various problems with fractional-order derivatives.

Couplings in GaAs/AlGaAs/Metal Photonic Waveguides with Metallic Variations

2012 ◽  
Vol 1396 ◽  
Author(s):  
Meng-Mu Shih
Keyword(s):  
Mode Coupling ◽  
Hybrid Structure ◽  
Wave Mode ◽  
Photonic Devices ◽  
Coupling Coefficients ◽  
Light Emitting ◽  
Photonic Waveguides ◽  
And Performance ◽  
Metal Gratings ◽  
Future Work

ABSTRACTTo have better light-emitting performance, semiconductor-metal periodic photonic waveguides can generate stable wavelengths. This work constructs a multi-parameter model to compute the backward-wave mode-coupling coefficients, which are important to the analysis and performance of photonic devices. For such a semiconductor-metal hybrid structure, a proper photonic technique needs to be utilized to solve this computational complexity.Numerical results demonstrate how the materials of metal gratings, the corrugation amplitudes of metal gratings, and the metallic aluminum mole fraction can affect the coupling coefficients. Further physical interpretation and discussion can support and explain the above results. The results can help engineers decide the values of parameters used in fabrication. Future work and applications will be proposed.

Numerical Solution of Stream Function Equations in Transonic Flows

1987 ◽  
Vol 109 (4) ◽  
pp. 508-512 ◽  
Author(s):  
J. Z. Xu ◽  
W. Y. Ni ◽  
J. Y. Du
Keyword(s):  
Stream Function ◽  
Present Method ◽  
Iterative Procedure ◽  
The Other ◽  
Transonic Flows ◽  
Cascade Flow ◽  
Function Formulation ◽  
Function Calculation ◽  
Stream Function Formulation ◽  
Transonic Cascade

In order to develop the transonic stream function approach, in this paper one of the momentum equations is employed to form the principal equation of the stream function which does not contain vorticity and entropy terms, and the other one is used to calculate the density directly. Since the density is uniquely determined, the problem that the density is a double-valued function of mass flux in the stream function formulation disappears and the entropy increase across the shock is naturally included. The numerical results for the transonic cascade flow show that the shock obtained from the present method is slightly weaker and is placed farther downstream compared to the irrotational stream function calculation, and is closer to the experimental data. From a standpoint of computation the iterative procedure of this formulation is simple and the alternating use of two momentum equations makes the calculation more effective.

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