<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">Hi Patrick,<div><br></div><div>There is a fast decay of the hbond acf for liquid water on a 100-200 fs timescale that traditionally is associated with the librational motion of water molecules. There's a good paper by Omer Markovich and Noam Agmon in J. Chem. Phys. 129 084505 2008 where this effect is discussed, although it's not the main focus of that paper. Then, after 10 ps or so, there's a regime where the acf falls of as a power law. As a consequence the correlation time is not really derived from a purely exponential acf and the interpretation might be misleading to some extent if you imply exponential behaviour.</div><div><br></div><div>Best,</div><div><br></div><div>Erik</div><div><br><div><div>21 maj 2012 kl. 14.07 skrev Patrick Fuchs:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div>Hi Erik,<br>your examples on H-bond acfs are interesting. I'm wondering about the "distinct features which are non-exponential" in your examples. What do you mean exactly? Could these features be due to rare (H-bonding) events, or in other words to poor sampling?<br>Intuitively, I'd say that the interpretation of the acf (at least for the decay and the decorelation) is always valid unless maybe if you have very poor statistics.<br>Ciao,<br><br>Patrick<br><br>Le 20/05/2012 16:12, Erik Marklund a écrit :<br><blockquote type="cite">Dear Chris,<br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite">As I see it there one can interpret the acf and correlatation time<br></blockquote><blockquote type="cite">further for certain types of data. I'll use the h-bond autocorrelation<br></blockquote><blockquote type="cite">function as an example. Here the data is time series of logical true and<br></blockquote><blockquote type="cite">false, represented as ones and zeros. This type of acf can be direcly<br></blockquote><blockquote type="cite">interpreted as a probablity, and some quantities derived from the acf<br></blockquote><blockquote type="cite">can bear further meaning because of this.<br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite">I also thought that the nature of the data may be such there is a<br></blockquote><blockquote type="cite">non-exponential part, which makes the autocorreltaion time less valid,<br></blockquote><blockquote type="cite">or less connected to other intuitive concepts. Again, the h-bond acf has<br></blockquote><blockquote type="cite">distinct features which are non-exponential and the autocorreltaion time<br></blockquote><blockquote type="cite">derived from such acfs may in fact be misleading when the h-bond<br></blockquote><blockquote type="cite">kinetics is to be determined.<br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite">Hope that makes sense. I's be happy to hear from you if you disagree.<br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite">Best,<br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite">Erik<br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite">19 maj 2012 kl. 04.01 skrev Christopher Neale:<br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite"><blockquote type="cite">Dear Erik:<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">I thought about your comment for a while and I have come to understand<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">that you are correct. The exponential (or integral) autocorrelation<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">time is a mathematical construct and is defined as such. What I was<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">looking for was an interpretation of the autocorrelation time in terms<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">of the time required to decorrelate the sampling.<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">As to whether or not this will depend on the nature of the data, I<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">don't really understand your conjecture. If the interpretation of the<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">autocorrelation time depends on the nature of the data, then that<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">implies to me that a single scalar value is useless in this case. I<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">don't understand how it could be useful to represent the<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">autocorrelation time by a single number if that number does not mean<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">anything on its own. If you have time, I would appreciate if you could<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">elaborate on this point.<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">Thank you,<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">Chris.<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">-- original message --<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">Aren't you looking for an interpretation rather than a definition? And<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">will this not depend on the nature of the data?<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">Best,<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">Erik<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">--<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">gmx-users mailing list <a href="mailto:gmx-users@gromacs.org">gmx-users@gromacs.org</a><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><<a href="mailto:gmx-users@gromacs.org">mailto:gmx-users@gromacs.org</a>><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><a href="http://lists.gromacs.org/mailman/listinfo/gmx-users">http://lists.gromacs.org/mailman/listinfo/gmx-users</a><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">Please search the archive at<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><a href="http://www.gromacs.org/Support/Mailing_Lists/Search">http://www.gromacs.org/Support/Mailing_Lists/Search</a> before posting!<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">Please don't post (un)subscribe requests to the list. Use the<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">www interface or send it to <a href="mailto:gmx-users-request@gromacs.org">gmx-users-request@gromacs.org</a>.<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">Can't post? Read <a href="http://www.gromacs.org/Support/Mailing_Lists">http://www.gromacs.org/Support/Mailing_Lists</a><br></blockquote></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite">-----------------------------------------------<br></blockquote><blockquote type="cite">Erik Marklund, PhD<br></blockquote><blockquote type="cite">Dept. of Cell and Molecular Biology, Uppsala University.<br></blockquote><blockquote type="cite">Husargatan 3, Box 596, 75124 Uppsala, Sweden<br></blockquote><blockquote type="cite">phone: +46 18 471 6688 fax: +46 18 511 755<br></blockquote><blockquote type="cite"><a href="mailto:erikm@xray.bmc.uu.se">erikm@xray.bmc.uu.se</a> <<a href="mailto:erikm@xray.bmc.uu.se">mailto:erikm@xray.bmc.uu.se</a>><br></blockquote><blockquote type="cite"><a href="http://www2.icm.uu.se/molbio/elflab/index.html">http://www2.icm.uu.se/molbio/elflab/index.html</a><br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite"><br></blockquote><br>-- <br>_______________________________________________________________________<br>Patrick FUCHS<br>Dynamique des Structures et Interactions des Macromolécules Biologiques<br>INTS, INSERM UMR-S665, Université Paris Diderot,<br>6 rue Alexandre Cabanel, 75015 Paris<br>Tel : +33 (0)1-44-49-30-57 - Fax : +33 (0)1-43-06-50-19<br>E-mail address: <a href="mailto:patrick.fuchs@univ-paris-diderot.fr">patrick.fuchs@univ-paris-diderot.fr</a><br>Web Site: <a href="http://www.dsimb.inserm.fr/~fuchs">http://www.dsimb.inserm.fr/~fuchs</a><br>-- <br>gmx-users mailing list <a href="mailto:gmx-users@gromacs.org">gmx-users@gromacs.org</a><br><a href="http://lists.gromacs.org/mailman/listinfo/gmx-users">http://lists.gromacs.org/mailman/listinfo/gmx-users</a><br>Please search the archive at http://www.gromacs.org/Support/Mailing_Lists/Search before posting!<br>Please don't post (un)subscribe requests to the list. Use the www interface or send it to gmx-users-request@gromacs.org.<br>Can't post? Read http://www.gromacs.org/Support/Mailing_Lists<br></div></blockquote></div><br><div>
<span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; font-size: medium; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; font-size: medium; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; font-size: medium; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div>-----------------------------------------------</div><div>Erik Marklund, PhD</div><div>Dept. of Cell and Molecular Biology, Uppsala University.</div><div>Husargatan 3, Box 596, 75124 Uppsala, Sweden</div><div>phone: +46 18 471 6688 fax: +46 18 511 755</div><div><a href="mailto:erikm@xray.bmc.uu.se">erikm@xray.bmc.uu.se</a></div><div><a href="http://www2.icm.uu.se/molbio/elflab/index.html">http://www2.icm.uu.se/molbio/elflab/index.html</a></div></div></span></div></span></span>
</div>
<br></div></body></html>