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汕头大学海洋科学接受调剂
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fyc802

金虫 (著名写手)


[求助] 自相关函数为什么最终会接近于0

一般的自相关函数有类似的表达式:A(t)=/.其中,B(t)为t时刻的物理量,如速度、均方末端距、偶极矩等等,有的是矢量,有的是标量。<>为系综平均。当t很小的时候,A(t)接近于1,这个很好理解。但为什么当t很大的时候,A(t)接近于0?请大家帮帮忙,谢谢!
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lsloneil

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7楼: Originally posted by fyc802 at 2013-04-24 01:48:48
感谢您!可不可以说一下“系综平均”的概念或者公式,我对这个还是不太了解。之前找过资料,也问过老师。理解“系综平均”后,估计就能解决问题了。谢谢!...

I mean, you should refer to some Stat Mech textbooks for the definition of ensemble and ensemble average. Briefly speaking an ensemble is a set of points chosen in phase space, different ensembles have different probability distributions ( in NVE it's uniform and in NVT it's Boltzmann distribution). With these probability distributions you can calculating the ensemble average by sampling over the ensemble.

In an MD simulation, after the system has reached equilibrium, you just sample N copies of quantity A, add them together and divide by N, and that is the ensemble average.
8楼2013-04-25 13:18:09
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lsloneil

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fyc802: 金币+20, ★★★很有帮助 2013-04-26 09:22:43
Not always zero. It depends on the ensemble average . At t=infinity, = ^2, so if is not equal to zero, then A(t) won't go to zero at infinite time.

For velocity-velocity auto TCF or dipole-dipole TCF in uniform liquid, it should decay to zero since =0. However, at some interfaces or in confinement, the dipole-dipole TCF might not decay to zero since molecule's orientations are not uniformly distributed.
2楼2013-04-22 13:32:16
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fyc802

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引用回帖:
2楼: Originally posted by lsloneil at 2013-04-22 13:32:16
Not always zero. It depends on the ensemble average <B>. At t=infinity, <B(0)*B(t)> = <B>^2, so if <B> is not equal to zero, then A(t) won't go to zero at infinite time.

F ...

At t=infinity, = ^2,为什么?我刚刚跟老师讨论过了,可能是我们对“系综平均”的概念理解有误。我想通过编程计算自相关函数。请问您有没有关于“系综平均”的相关资料或公式?最好是关于偶极矩的。
3楼2013-04-22 17:01:04
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luqing6879

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3楼: Originally posted by fyc802 at 2013-04-22 17:01:04
At t=infinity, <B(0)*B(t)> = <B>^2,为什么?我刚刚跟老师讨论过了,可能是我们对“系综平均”的概念理解有误。我想通过编程计算自相关函数。请问您有没有关于“系综平均”的相关资料或公式?最好是 ...

Personally, I don't think "At t=infinity, = ^2". The integral should approximate to 0 at t=infinity.
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4楼2013-04-23 05:29:25
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