  博碩士論文 104221004 詳細資訊

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(A comparison of methods to determine effective resistances in a grid)

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determine resistance distances between two nodes on a grid.
First, we show how to compute the effective resistances by using the spectrum of Laplacian L of a graph G. Then, we describe how to compute the effective resistances by using the pseudo inverse L^+ of a Laplacian L. Next, we use the the series, parallel and Y-Delta transformations to compute the effective resistances between two nodes in a grid. At last, we introduce the celebrated Kirchhoff′s Theorem and use it to compute the effective resistances in a resistance network.

★ 網格圖

★ grid

Method A: Using the spectrum of Laplacian L....4

Method B: Using the pseudoinverse L^+ of a Laplacian L...............6

Method C: Using series, parallel and Y-Delta transformations...................8

Method D: Using Kirchhoff′s Theorem.................12

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