臺灣博碩士論文加值系統

我們考慮在 $(M+1) times (2N+1)$ 的三角晶格上一個定向滲流的模型，
賦予此三角晶格垂直方向的機率值 $p_y$ ， 對角方向的機率值 $p_d$ ，水平方向偶數列的機率值 $1$ 、 奇數列的機率值 $p_x$ ， 將討論此滲流從晶格中的左下角 $(0,0)$ 流到右上角 $(M, 2N)$ 的機率值 $P_{p_x, p_y, p_d}(M, 2N)$ ，且證明存在一個臨界的縱橫比 $alpha_c$ ，使得
$lim_{N

rightarrow infty}P((0, 0)

rightarrow(2 alpha N, 2N))$ 在 $alpha=alpha_c$ 時不連續。

We consider a directed percolation model on $(M+1) times (2N+1)$ triangular
lattices with vertical edges directed northward with an occupation
probability $p_y$, diagonal edges directed northeastward with an occupation probability $p_d$,
and horizontal edges directed eastward with occupation probabilities $p_x$ and $1$
in alternate rows. We deduce a closed-form expression for the percolation probability
$P_{p_x, p_y, p_d}(M, 2N)$, the probability that one or more directed paths connect
the lower-left and upper-right corner sites of the lattices.
We will show that there exists a critical aspect ratio $alpha_c$ such that
$lim_{N
rightarrow infty}P((0, 0)
rightarrow(2 alpha N, 2N))$
is discontinuous at $alpha=alpha_c$.}

1 Introduction 1
2 Main Theorem 5
3 Proof of Main Theorem 6
4 Proof of Proposition 15
5 Proof of Lemmas 20

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