A Study of Current-Dependent Resistors in Nonlinear Circuits
Nonlinear electrical circuits can be used to model fluid flow in pipe networks when the resistance of any element in the network is assumed to be dependent on the flow rate through that element. This relationship is often assumed in classical models of pressure drops at orifices and through valves. More recently, it has also been used to model blood flow through vessels, and may potentially have applications in nano-fluid systems. Motivated by these applications, in this thesis we investigate circuits where the resistors have linear and affine (linear plus offset) dependence on current. Rules for their reduction in series and parallel are derived for the general case as well as for special cases of their linear coefficients and offset terms. Other adapted circuit analysis and manipulation techniques are also discussed, including mesh current analysis and delta-wye transformation, and avenues for further investigation of this topic are illuminated. The methods developed in this thesis may have potential
applications in simplifying the analysis of complex nonlinear flow networks in cardiovascular systems, especially those at the nano-scale.
Advisor:Dr. Marwan A. Simaan; Dr. Luis F. Chaparro; Dr. J. Robert Boston
School:University of Pittsburgh
School Location:USA - Pennsylvania
Source Type:Master's Thesis
Date of Publication:05/08/2003