scholarly journals AN NUMERICAL METHOD BASED ITERATIVE PROCESS TO CHARACTERIZE MICROWAVE PLANAR CIRCUITS

2014 ◽  
pp. 86-94
Author(s):  
Mohamed Tellache ◽  
Youcef Lamhene ◽  
Brahim Haraoubia ◽  
Henri Baudrand
Keyword(s):  
Iterative Method ◽  
Iterative Process ◽  
Original Method ◽  
Simulation Software ◽  
Patch Antennas ◽  
Two Dimensional ◽  
Quarter Wavelength ◽  
Planar Circuits ◽  
Coplanar Technology ◽  
The Waves

In the present work, the modeling of microwaves planar circuits is proposed with an original method based on the Waves Concept Iterative Process (WCIP). It consists in the development of simulation software based on an iterative method. The iterative method is developed from the fast modal transform on a two-dimensional fast Fourier transform (FFT) algorithm. The method has been applied to the characterization and the modeling of patch antennas with notches in microstrip and coplanar technology and the quarter wavelength directive coupler. The obtained results are very powerful and successfully compared to others methods in term of time and reliability of convergence and particularly the accuracy of the results obtained in comparison with previous works.

Effects of plane progressive irrotational waves on thermal boundary layers

1971 ◽  
Vol 50 (2) ◽  
pp. 321-334 ◽  
Author(s):  
James Witting
Keyword(s):  
Boundary Layers ◽  
Deep Water ◽  
Maximum Amplitude ◽  
Capillary Waves ◽  
Temperature Gradients ◽  
Two Dimensional ◽  
Inviscid Incompressible Fluid ◽  
Mean Temperature ◽  
The Waves ◽  
Thermal Boundary Layers

The average changes in the structure of thermal boundary layers at the surface of bodies of water produced by various types of surface waves are computed. the waves are two-dimensional plane progressive irrotational waves of unchanging shape. they include deep-water linear waves, deep-water capillary waves of arbitrary amplitude, stokes waves, and the deep-water gravity wave of maximum amplitude.The results indicate that capillary waves can decrease mean temperature gradients by factors of as much as 9·0, if the average heat flux at the air-water interface is independent of the presence of the waves. Irrotational gravity waves can decrease the mean temperature gradients by factors no more than 1·381.Of possible pedagogical interest is the simplicity of the heat conduction equation for two-dimensional steady irrotational flows in an inviscid incompressible fluid if the velocity potential and the stream function are taken to be the independent variables.

Internal waves in a viscous atmosphere

1975 ◽  
Vol 72 (4) ◽  
pp. 773-786 ◽  
Author(s):  
W. L. Chang ◽  
T. N. Stevenson
Keyword(s):  
Energy Source ◽  
Incompressible Fluid ◽  
Internal Waves ◽  
Infinite Number ◽  
Similarity Solution ◽  
Small Amplitude ◽  
Horizontal Plane ◽  
Two Dimensional ◽  
The Waves ◽  
Isothermal Atmosphere

The way in which internal waves change in amplitude as they propagate through an incompressible fluid or an isothermal atmosphere is considered. A similarity solution for the small amplitude isolated viscous internal wave which is generated by a localized two-dimensional disturbance or energy source was given by Thomas & Stevenson (1972). It will be shown how summations or superpositions of this solution may be used to examine the behaviour of groups of internal waves. In particular the paper considers the waves produced by an infinite number of sources distributed in a horizontal plane such that they produce a sinusoidal velocity distribution. The results of this analysis lead to a new small perturbation solution of the linearized equations.

Dispersion relations of dust lattice waves in two-dimensional honeycomb configuration

2013 ◽  
Vol 79 (5) ◽  
pp. 629-633
Author(s):  
B. FAROKHI
Keyword(s):  
Dispersion Relation ◽  
Group Velocity ◽  
Hexagonal Lattice ◽  
Dispersion Relations ◽  
Two Dimensional ◽  
The Third ◽  
Lattice Waves ◽  
The Waves

AbstractThe linear dust lattice waves propagating in a two-dimensional honeycomb configuration is investigated. The interaction between particles is considered up to distance 2a, i.e. the third-neighbor interactions. Longitudinal and transverse (in-plane) dispersion relations are derived for waves in arbitrary directions. The study of dispersion relations with more neighbor interactions shows that in some cases the results change physically. Also, the dispersion relation in the different direction displays anisotropy of the group velocity in the lattice. The results are compared with dispersion relations of the waves in the hexagonal lattice.

scholarly journals Reliable Iterative Method for solving Volterra - Fredholm Integro Differential Equations

2021 ◽  
Vol 26 (2) ◽  
Author(s):  
Samaher Marez
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Iterative Method ◽  
Iterative Process ◽  
Initial Conditions ◽  
High Accuracy ◽  
Series Solutions ◽  
Math Program ◽  
The Right

  The aim of this paper, a reliable iterative method is presented for resolving many types of Volterra - Fredholm Integro - Differential Equations of the second kind with initial conditions. The series solutions of the problems under consideration are obtained by means of the iterative method.  Four various problems are resolved with high accuracy to make evident the enforcement of the iterative method on such type of integro differential equations. Results were compared with the exact solution which exhibit that this technique has compatible with the right solutions, simple, effective and easy for solving such problems. To evaluate the results in an iterative process the MATLAB is used as a math program for the calculations.

scholarly journals THE MATHEMATICAL MODELLING METHODS APPLYING TO ESTIMATE THE PIPELINES TECHNICAL STATE AND ENVIRONMENT SITUATION

2019 ◽  
pp. 97-103
Author(s):  
A. P. Oliinyk ◽  
G. V. Grigorchuk ◽  
R. M. Govdyak
Keyword(s):  
Boundary Conditions ◽  
Oil And Gas ◽  
Equation System ◽  
Technical Condition ◽  
Original Method ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Emergency Situations ◽  
Negative Impacts ◽  
The Impact

In the context of providing trouble-free operation of oil and gas pipelines and preventing possible negative impacts on the environment, the issues of constructing an integrated mathematical model for assessing the technical condition of pipelines and the impact of emergency situations on the state of the environment in the course of hydrocarbon leakage are considered. The model of the evaluation of the stress-strain state of the pipeline according to the data on the displacement of surface points for the above ground and underground sections is given by constructing the law of motion of the site by known displacements of a certain set of surface points using assumptions about the type of deformation of the sections and reproduction of the deformations and stresses tensors components   on the basis of different models of deformed solid body. The specified model does not require information on the whole complex of forces and loads acting on the investigated object during operation. The flow model has been refined in a pipeline with a violation of its tightness by recording a special type of boundary conditions for a Navier-Stokes equation system in a two-dimensional formulation and developing an original method for its solution on the basis of the finite difference method. In the article the stability conditions of the proposed numerical schemes on basis of the spectral sign of stability are presented. In order to assess possible negative impacts on the environment, a model of propagation of matter at its leakage from the pipeline was developed by solving two-dimensional diffusion equations taking into account the variables and different types of boundary conditions that take into account the number of sources of pollution and their intensity. The results of computations based on computational algorithms implemented by these models and graphic material illustrating these calculations are presented, peculiarities of distribution of harmful substances in the environment near the pipeline are analyzed. Directions of further researches for successful practical realization of the offered models are established.

scholarly journals To the Solution of Geometric Inverse Heat Conduction Problems

2021 ◽  
Vol 24 (1) ◽  
pp. 6-12
Author(s):  
Yurii M. Matsevytyi ◽  
◽  
Valerii V. Hanchyn ◽  
Keyword(s):  
Heat Conduction ◽  
Iterative Process ◽  
Regularization Parameter ◽  
Outer Boundary ◽  
Linear Equations ◽  
The Body ◽  
Two Dimensional ◽  
Inverse Heat Conduction ◽  
System Of Linear Equations ◽  
Inverse Heat Conduction Problems

On the basis of A. N. Tikhonov’s regularization theory, a method is developed for solving inverse heat conduction problems of identifying a smooth outer boundary of a two-dimensional region with a known boundary condition. For this, the smooth boundary to be identified is approximated by Schoenberg’s cubic splines, as a result of which its identification is reduced to determining the unknown approximation coefficients. With known boundary and initial conditions, the body temperature will depend only on these coefficients. With the temperature expressed using the Taylor formula for two series terms and substituted into the Tikhonov functional, the problem of determining the increments of the coefficients can be reduced to solving a system of linear equations with respect to these increments. Having chosen a certain regularization parameter and a certain function describing the shape of the outer boundary as an initial approximation, one can implement an iterative process. In this process, the vector of unknown coefficients for the current iteration will be equal to the sum of the vector of coefficients in the previous iteration and the vector of the increments of these coefficients, obtained as a result of solving a system of linear equations. Having obtained a vector of coefficients as a result of a converging iterative process, it is possible to determine the root-mean-square discrepancy between the temperature obtained and the temperature measured as a result of the experiment. It remains to select the regularization parameter in such a way that this discrepancy is within the measurement error. The method itself and the ways of its implementation are the novelty of the material presented in this paper in comparison with other authors’ approaches to the solution of geometric inverse heat conduction problems. When checking the effectiveness of using the method proposed, a number of two-dimensional test problems for bodies with a known location of the outer boundary were solved. An analysis of the influence of random measurement errors on the error in identifying the outer boundary shape is carried out.

Nonlinear Aspects of Subcritical Shallow-Water Flow Past Two-Dimensional Obstructions

1978 ◽  
Vol 22 (04) ◽  
pp. 203-211
Author(s):  
Nils Salvesen ◽  
C. von Kerczek
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Flow Problem ◽  
Free Stream ◽  
The Body ◽  
Two Dimensional ◽  
Third Order ◽  
Submerged Body ◽  
The Mean ◽  
The Waves

Some nonlinear aspects of the two-dimensional problem of a submerged body moving with constant speed in otherwise undisturbed water of uniform depth are considered. It is shown that a theory of Benjamin which predicts a uniform rise of the free surface ahead of the body and the lowering of the mean level of the waves behind it agrees well with experimental data. The local steady-flow problem is solved by a numerical method which satisfies the exact free-surface conditions. Third-order perturbation formulas for the downstream free waves are also presented. It is found that in sufficiently shallow water, the wavelength increases with increasing disturbance strength for fixed values of the free-stream-Froude number. This is opposite to the deepwater case where the wavelength decreases with increasing disturbance strength.

scholarly journals I. On the waves produced by a single impulse in water of any depth, or in a dispersive medium

1887 ◽  
Vol 42 (251-257) ◽  
pp. 80-83 ◽  
Keyword(s):  
Wave Velocity ◽  
Dispersive Medium ◽  
Wave Length ◽  
Periodic Waves ◽  
Two Dimensional ◽  
Group A ◽  
Two Sides ◽  
The Waves

For brevity and simplicity consider only the case of two-dimensional motion . All that it is necessary to know of the medium is the relation between the wave-velocity and the wave-length of an endless procession of periodic waves. The result of our work will show us that the velocity of progress of a zero, or maximum, or minimum, in any part of a varying group of waves, is equal to the velocity of progress of periodic waves of wave-length equal to a certain length, which may be defined as the wave-length in the neighbourhood of the particular point looked to in the group (a length which will generally be intermediate between the distances from the point considered to its next-neighbour corresponding points on its two sides).

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