Efficient Green’s-function approach to finding the currents in a random resistor network

1994 ◽  
Vol 49 (2) ◽  
pp. 1712-1725 ◽  
Author(s):  
Kang Wu ◽  
R. Mark Bradley
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Approach ◽  
Random Resistor Network ◽  
Resistor Network

On the perturbation of a uniform tiling with resistors

2016 ◽  
Vol 30 (24) ◽  
pp. 1650166 ◽  
Author(s):  
M. Q. Owaidat ◽  
J. H. Asad ◽  
Zhi-Zhong Tan
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Square Lattice ◽  
Resistor Network ◽  
Theoretical Results

The perturbation of a uniformly tiled resistor network by adding an edge (a resistor) to the network is considered. The two-point resistance on the perturbed tiling in terms of that on the perfect tiling is obtained using Green’s function. Some theoretical results are presented for an infinite modified square lattice. These results are confirmed experimentally by constructing an actual resistor lattice of size 13 × 13.

scholarly journals Analysis of the interaction of thermoacoustic modes with a Green’s function approach

2018 ◽  
Vol 10 (4) ◽  
pp. 326-336 ◽  
Author(s):  
Alessandra Bigongiari ◽  
Maria Heckl
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Initial Perturbation ◽  
Time History ◽  
Function Approach ◽  
Stability Maps ◽  
Flame Describing Function ◽  
The Stability ◽  
Dynamics Simulations ◽  
Fast Prediction

In this paper, we will present a fast prediction tool based on a one-dimensional Green's function approach that can be used to bypass numerically expensive computational fluid dynamics simulations. The Green’s function approach has the advantage of providing a clear picture of the physics behind the generation and evolution of combustion instabilities. In addition, the method allows us to perform a modal analysis; single acoustic modes can be treated in isolation or in combination with other modes. In this article, we will investigate the role of higher-order modes in determining the stability of the system. We will initially produce the stability maps for the first and second mode separately. Then the time history of the perturbation will be computed, where both the modes are present. The flame will be modelled by a generic Flame Describing Function, i.e. by an amplitude-dependent Flame Transfer Function. The time-history calculations show the evolution of the two modes resulting from an initial perturbation; both transient and limit-cycle oscillations are revealed. Our study represents a first step towards the modelling of nonlinearity and non-normality in combustion processes.

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