OK, here's my alternative for modeling asymmetric distributions: I use for the effective RDF a Gaussian-broadened exponential tail
function. The tail function is defined as:
t(r) = (1/|w|)*exp(-r/w) r*sign(w) >0
0 r*sign(w) <= 0
This limits to a delta function for w->0. The complete function is the tail function convolved with a gaussian. The result has an
analytically-simple FT, so fitting in k-space is
easy. It adds in a string of cumulants with just one extra parameter. It has no physical significance, except that it looks sort
of like RDF's from asymmetric potentials.
mam
----- Original Message -----
From: "Frenkel, Anatoly"
To: "XAFS Analysis using Ifeffit"
Sent: Wednesday, January 21, 2009 7:39 PM
Subject: Re: [Ifeffit] Cumulant expansion fittings
Hi Scott,
It could be an interesting direction, to use these type of lattice calculations to predict, as you suggested, what type of
structures (or host compounds, for dopands), will, if not make it zero, which is probably impossible, but minimize third cumulant.
Thus, it may be a rational way to design materials, at least hypothetically, with controlled thermal expansion, or even the lack of
thereof.
I do not care that someone may jump in and patent it, but I will appreciate a Porsche, if possible, when it is licensed.
Anatoly
________________________________
From: ifeffit-bounces@millenia.cars.aps.anl.gov on behalf of Scott Calvin
Sent: Wed 1/21/2009 10:30 PM
To: XAFS Analysis using Ifeffit
Subject: Re: [Ifeffit] Cumulant expansion fittings
Anatoly,
You're right--3 dimensions ruins my symmetry argument. My mistake.
On the other hand, I still suspect that there exists a realistic case
where forcing the third cumulant to zero cause a much smaller increase
in chi-square than forcing the fourth cumulant to zero; e.g., a broad,
flat radial distribution function.
For those of you out there who are relative novices, this is an
entertaining and informative discussion, but I don't want to lose
track of the practical point:
It is very rare to find a system where the fourth cumulant is both
necessary and sufficient. Either the potentials are close enough to
harmonic that the fourth cumulant makes little difference, or they are
so far from harmonic that the fourth cumulant alone is not enough.
--Scott Calvin
Sarah Lawrence College
On Jan 21, 2009, at 10:11 PM, Frenkel, Anatoly wrote:
Thus, I am pretty much convinced, unless there is some mistake in my
reasoning, that no case exists in 3D with a zero third cumulant.
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