scholarly journals Nonlinear Membrane Circuit Loaded on a Lossy Transmission Line without the Heaviside’s Condition

2019 ◽  
Vol 4 (10) ◽  
pp. 190-197 ◽  
Author(s):  
Vasil Angelov
Keyword(s):  
Fixed Point ◽  
Mixed Problem ◽  
Transmission Lines ◽  
Generalized Solution ◽  
Existence Of Solution ◽  
Nonlinear Circuit ◽  
In Series ◽  
Lossy Transmission ◽  
Kirchhoff’S Laws ◽  
Lossy Transmission Line

The paper deals with transmission lines terminated by a nonlinear circuit describing a simplified model of membrane. This means that all elements of the membrane circuit are nonlinear ones as follows: in series connected LR-loads parallel to C-load. Using the Kirchhoff’s laws we formulate boundary conditions. For lossy transmission lines systems with the Heaviside’s condition, the mixed problem is considered in previous papers. The main goal of the present paper is to investigate the same problem for lossy transmission lines without the Heaviside’s condition. We reduce the existence of solution of the more complicated mixed problem for such a system to the existence of fixed point of an operator acting on a suitable function space. Then by ensuring the existence of this fixed point we obtain conditions for existence of a generalized solution of the mixed problem. The obtained conditions are easily verifiable. We demonstrate the advantages of our method by a numerical example.

scholarly journals ОN THE QUALITATIVE ANALYSIS OF CERTAIN FLOTATION PROCESSES

2020 ◽  
Vol 9 (11) ◽  
pp. 91-99
Keyword(s):  
Fixed Point ◽  
Qualitative Analysis ◽  
Mixed Problem ◽  
Hyperbolic System ◽  
Transmission Lines ◽  
Generalized Solution ◽  
Fixed Point Method ◽  
Successive Approximations ◽  
First Order ◽  
Operator Form

The present paper is devoted to the qualitative analysis of certain flotation processes describing by a first order hyperbolic system of partial differential equations. The system in question is like telegrapher equations. That is why, we use the methods for examining the transmission lines set out in the papers mentioned in the References. We formulate a mixed problem for this system with boundary conditions corresponding to the processes in the flotation cameras. We present the mixed problem for the hyperbolic system in a suitable operator form and prove an existence of generalized solution by fixed point method. One can obtain an explicit approximated solution as a step in the sequence of successive approximations.

scholarly journals Analysis of Lossy Transmission Lines Terminated by Schottky Diode Circuit

2018 ◽  
Vol 2 (6) ◽  
Author(s):  
Vasil G. Angelov
Keyword(s):  
Transmission Line ◽  
Mixed Problem ◽  
Schottky Diode ◽  
Transmission Lines ◽  
Oscillatory Solution ◽  
System Of Differential Equations ◽  
Initial Value ◽  
Line System ◽  
Lossy Transmission ◽  
Lossy Transmission Line

In the present paper we consider a lossy transmission line terminated by a circuit corresponding to a Schottky diode. On the base of Kirchhoff’s law boundary conditions are derived. Then a mixed problem for the lossy transmission line system is formulated. We reduce the mixed problem for the hyperbolic transmission line system to an initial value problem for a system of differential equations with delays on the boundary. We prove existence-uniqueness theorem for oscillatory solution. The paper ends with numerical example with real values of the Schottky diode parameters.

scholarly journals LOSSY TRANSMISSION LINES TERMINATED BY PARALLEL CONNECTED RLC-ELEMENTS WITHOUT THE HEAVISIDE’S CONDITION

2019 ◽  
pp. 1-13
Author(s):  
Vasil G. Angelov
Keyword(s):  
Transmission Line ◽  
Mixed Problem ◽  
Hyperbolic System ◽  
Transmission Lines ◽  
Electromagnetic Waves ◽  
Neutral Type ◽  
Generalized Solution ◽  
Line System ◽  
Lossy Transmission ◽  
Transverse Electromagnetic

The paper deals with analysis of propagation of transverse electromagnetic waves along lossy transmission lines terminated by a circuit consisting of parallel connected RLCelements. Using the Kirchhoff’s laws we derive boundary conditions and formulate the mixed problem for hyperbolic system describing the lossy transmission line. Without the Heaviside's condition, we cannot guarantee the distortionless propagation of waves and hence we cannot apply the known methods. That is why we apply a different method and obtain conditions for existence-uniqueness of generalized solution. We change variables and formulate a mixed problem for the hyperbolic system with respect to the new variables. The nonlinear characteristics of the RLC-elements generate nonlinearity in the equations of neutral type on the boundary. We propose an operator presentation of the mixed problem for transmission line system and by means of fixed point technique we prove existence-uniqueness of a generalized solution.

scholarly journals LOSSY TRANSMISSION LINES TERMINATED BY PARALLEL CONNECTED RLC-ELEMENTS WITHOUT THE HEAVISIDE’S CONDITION

2019 ◽  
pp. 1-13 ◽  
Author(s):  
Vasil G. Angelov
Keyword(s):  
Transmission Line ◽  
Mixed Problem ◽  
Hyperbolic System ◽  
Transmission Lines ◽  
Electromagnetic Waves ◽  
Neutral Type ◽  
Generalized Solution ◽  
Line System ◽  
Lossy Transmission ◽  
Transverse Electromagnetic

The paper deals with analysis of propagation of transverse electromagnetic waves along lossy transmission lines terminated by a circuit consisting of parallel connected RLCelements. Using the Kirchhoff’s laws we derive boundary conditions and formulate the mixed problem for hyperbolic system describing the lossy transmission line. Without the Heaviside's condition, we cannot guarantee the distortionless propagation of waves and hence we cannot apply the known methods. That is why we apply a different method and obtain conditions for existence-uniqueness of generalized solution. We change variables and formulate a mixed problem for the hyperbolic system with respect to the new variables. The nonlinear characteristics of the RLC-elements generate nonlinearity in the equations of neutral type on the boundary. We propose an operator presentation of the mixed problem for transmission line system and by means of fixed point technique we prove existence-uniqueness of a generalized solution.

Оn the Analysis of Certain Flotation Processes with Velocities Depending on Time and Height of the Column

2021 ◽  
Vol 6 (6) ◽  
pp. 8-13
Author(s):  
Daniela D. Parashkevova
Keyword(s):  
Fixed Point ◽  
Transmission Lines ◽  
Sedimentation Rate ◽  
Generalized Solution ◽  
Fixed Point Method ◽  
Successive Approximations ◽  
Particle Sedimentation ◽  
Flotation Column ◽  
Operator Form ◽  
Column Dynamics

— The present paper is an extension of the previous paper of the author where the flotation column dynamics has been investigated. Here we consider the case when particle sedimentation rate and bubble lifting speed depend on time and position in the column. We use the methods for examining the transmission lines set out in the papers mentioned in the References. We formulate a mixed problem for the system describing the processes in the column and present it in a suitable operator form. Then we prove an existence - uniqueness of generalized solution by the fixed point method. We show an explicit approximated solution as a step in the sequence of successive approximations.

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