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fyc802

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lsloneil

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7Â¥: Originally posted by fyc802 at 2013-04-24 01:48:48
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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.
8Â¥2013-04-25 13:18:09
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fyc802: ½ð±Ò+20, ¡ï¡ï¡ïºÜÓаïÖú 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.
2Â¥2013-04-22 13:32:16
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fyc802

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ÒýÓûØÌû:
2Â¥: 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£¬ÎªÊ²Ã´£¿ÎÒ¸Õ¸Õ¸úÀÏʦÌÖÂÛ¹ýÁË£¬¿ÉÄÜÊÇÎÒÃǶԡ°Ïµ×ÛÆ½¾ù¡±µÄ¸ÅÄîÀí½âÓÐÎó¡£ÎÒÏëͨ¹ý±à³Ì¼ÆËã×ÔÏà¹Øº¯Êý¡£ÇëÎÊÄúÓÐûÓйØÓÚ¡°Ïµ×ÛÆ½¾ù¡±µÄÏà¹Ø×ÊÁÏ»ò¹«Ê½£¿×îºÃÊǹØÓÚż¼«¾ØµÄ¡£
3Â¥2013-04-22 17:01:04
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luqing6879

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ÒýÓûØÌû:
3Â¥: Originally posted by fyc802 at 2013-04-22 17:01:04
At t=infinity, <B(0)*B(t)> = <B>^2£¬ÎªÊ²Ã´£¿ÎÒ¸Õ¸Õ¸úÀÏʦÌÖÂÛ¹ýÁË£¬¿ÉÄÜÊÇÎÒÃǶԡ°Ïµ×ÛÆ½¾ù¡±µÄ¸ÅÄîÀí½âÓÐÎó¡£ÎÒÏëͨ¹ý±à³Ì¼ÆËã×ÔÏà¹Øº¯Êý¡£ÇëÎÊÄúÓÐûÓйØÓÚ¡°Ïµ×ÛÆ½¾ù¡±µÄÏà¹Ø×ÊÁÏ»ò¹«Ê½£¿×îºÃÊÇ ...

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