複雜系統之簡介(梁鈞泰) - 中研院物理研究所- Academia Sinica
複雜系統之簡介(梁鈞泰) - 中研院物理研究所- Academia Sinica
複雜系統之簡介(梁鈞泰) - 中研院物理研究所- Academia Sinica
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Random walk of a drunkard<br />
∆x<br />
Move one step at each time,<br />
equal chance to the left or right<br />
Statistics:<br />
after many realizations, regularities emerge when<br />
we compute their averages:<br />
time t<br />
X(t) = x 1 + x 2 + x 3 +…+ x n<br />
= 0<br />
X 2 (t) = x 1<br />
2<br />
+ x 2<br />
2<br />
+ x 3<br />
2<br />
+…+ x n<br />
2<br />
+ x 1 x 2 + x 1 x 3 +…+ x 1 x n<br />
+ x 2 x 1 + x 2 x 3 +…+ x 2 x n +…<br />
+ x n x 1 + x n x 2 +…+ x n x n-1<br />
X<br />
= + + +…+ + 0<br />
= n = (∆x) 2 n<br />
= [ (∆x) 2 /∆t ] (n ∆t)<br />
= C t<br />
where C≣ (∆x) 2 /∆t is called the diffusion constant