scholarly journals Shaping Single Offset Reflector Antennas Using Local Axis-Displaced Confocal Quadrics

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Rafael A. Penchel ◽  
José R. Bergmann ◽  
Fernando J. S. Moreira
Keyword(s):  
Differential Equation ◽  
Nonlinear Partial Differential Equation ◽  
Numerical Procedure ◽  
Reflector Antenna ◽  
Physical Optics ◽  
Exact Formulation ◽  
Reflector Antennas ◽  
Conservation Of Energy ◽  
Reflector Surface ◽  
Monge Ampere

This work investigates a novel numerical procedure for the solution of an exact formulation for the Geometrical Optics synthesis of a single reflector antenna by simultaneously imposing Snell’s Law and Conservation of Energy in a tube of rays, yielding a second-order nonlinear partial differential equation of Monge-Ampère type, which can be solved as a boundary value problem. The investigation explores the interpolating properties of confocal quadrics to locally represent the shaped reflector surface. It allows the partial derivatives involved in the formulation to be analytically expressed. To illustrate the method, two examples of offset single reflectors shaped to radiate a Gaussian power density within a superelliptical contoured beam are presented. The results are validated by Physical Optics analysis with equivalent edge currents.

HE–ELZAKI METHOD FOR SPATIAL DIFFUSION OF BIOLOGICAL POPULATION

Fractals ◽  
2019 ◽  
Vol 27 (05) ◽  
pp. 1950069 ◽  
Author(s):  
JAMSHAID UL RAHMAN ◽  
DIANCHEN LU ◽  
MUHAMMAD SULEMAN ◽  
JI-HUAN HE ◽  
MUHAMMAD RAMZAN
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Population Model ◽  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Partial Differential Equation ◽  
Numerical Procedure ◽  
Spatial Diffusion ◽  
Homotopy Perturbation ◽  
Biological Population

The foremost purpose of this paper is to present a valuable numerical procedure constructed on Elzaki transform and He’s Homotopy perturbation method (HPM) for nonlinear partial differential equation arising in spatial flow characterizing the general biological population model for animals. The actions are made usually by mature animals driven out by intruders or by young animals just accomplished maturity moving out of their parental region to initiate breeding region of their own. He–Elzaki method is a blend of Elzaki transform and He’s HPM. The results attained are compared with Sumudu decomposition method (SDM). The numerical results attained by suggested method specify that the procedure is easy to implement and precise. These outcomes reveal that the proposed method is computationally very striking.

Reflector antenna pattern improvement using optimized array feed

1995 ◽  
Vol 73 (7-8) ◽  
pp. 407-411 ◽  
Author(s):  
Birsen Saka ◽  
Erdem Yazgan
Keyword(s):  
Radiation Pattern ◽  
Reflector Antenna ◽  
Physical Optics ◽  
Excitation Condition ◽  
Reflector Antennas ◽  
Minimization Method ◽  
Rotationally Symmetric ◽  
Planar Array ◽  
Excitation Conditions ◽  
Least Squares Minimization

A method to optimize the radiation pattern of rotationally symmetric reflector antennas with an array feed is introduced. The optimization of the radiation pattern for the purpose of beam scanning is achieved by adjusting the excitation condition of each element of the planar array. The radiation-pattern calculation is based on the physical optics radiation integral. The excitation conditions (amplitude and phase) of the array elements are calculated using the least-squares minimization method.

Reflector antenna analysis using physical optics on Graphics Processing Units

2014 ◽  
Author(s):  
Oscar Borries ◽  
Hans Henrik Brandenborg Sorensen ◽  
Bernd Dammann ◽  
Erik Jorgensen ◽  
Peter Meincke ◽  
...  
Keyword(s):  
Graphics Processing Units ◽  
Reflector Antenna ◽  
Physical Optics ◽  
Graphics Processing

scholarly journals Nonlocal Symmetry, Painlevé Integrable and Interaction Solutions for CKdV Equations

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1268
Author(s):  
Yarong Xia ◽  
Ruoxia Yao ◽  
Xiangpeng Xin ◽  
Yan Li
Keyword(s):  
Differential Equation ◽  
Nonlinear Partial Differential Equation ◽  
Three Dimensional ◽  
Dynamical Evolution ◽  
Symmetry Transformation ◽  
Nonlocal Symmetry ◽  
Similarity Reduction ◽  
Nonlocal Symmetries ◽  
Interaction Solutions ◽  
Dependent Variables

In this paper, we provide a method to construct nonlocal symmetry of nonlinear partial differential equation (PDE), and apply it to the CKdV (CKdV) equations. In order to localize the nonlocal symmetry of the CKdV equations, we introduce two suitable auxiliary dependent variables. Then the nonlocal symmetries are localized to Lie point symmetries and the CKdV equations are extended to a closed enlarged system with auxiliary dependent variables. Via solving initial-value problems, a finite symmetry transformation for the closed system is derived. Furthermore, by applying similarity reduction method to the enlarged system, the Painlevé integral property of the CKdV equations are proved by the Painlevé analysis of the reduced ODE (Ordinary differential equation), and the new interaction solutions between kink, bright soliton and cnoidal waves are given. The corresponding dynamical evolution graphs are depicted to present the property of interaction solutions. Moreover, With the help of Maple, we obtain the numerical analysis of the CKdV equations. combining with the two and three-dimensional graphs, we further analyze the shapes and properties of solutions u and v.

A physical optics based near-field analysis method for the design of dual polarized fan beam shaped reflector antennas

2016 ◽  
Vol 70 (2) ◽  
pp. 132-137 ◽  
Author(s):  
E. Bagheri-Korani ◽  
K. Mohammadpour-Aghdam ◽  
M. Ahmadi-Boroujeni ◽  
E. Arbabi ◽  
M. Nemati
Keyword(s):  
Near Field ◽  
Field Analysis ◽  
Physical Optics ◽  
Analysis Method ◽  
Reflector Antennas ◽  
Dual Polarized

scholarly journals The Rayleigh quotient and dynamic programming

1978 ◽  
Vol 1 (4) ◽  
pp. 401-405
Author(s):  
Richard Bellman
Keyword(s):  
Differential Equation ◽  
Dynamic Programming ◽  
Nonlinear Partial Differential Equation ◽  
Rayleigh Quotient ◽  
Programming Approach ◽  
Nonlinear Characteristic ◽  
Dynamic Programming Approach ◽  
Computational Aspects ◽  
Characteristic Values ◽  
Matrix Problems

The purpose of this paper is to derive a nonlinear partial differential equation for whichλgiven by (1.3), is one value of the solution. In Section 2, we derive this equation using a straightforward dynamic programming approach. In Section 3, we discuss some computational aspects of derermining the solution of this equation. In Section 4, we show that the same method may be applied to the nonlinear characteristic value problem. In Section 5, we discuss how the method may by applied to find the higher characteristic values. In Section 5, we discuss how the same method may be applied to some matrix problems. Finally, in Section 7, we discuss selective computation.

Sign in / Sign up

Export Citation Format

Share Document