[Ifeffit] Cumulant expansion fittings

[Matthew Marcus]

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" <frenkel at bnl.gov>
To: "XAFS Analysis using Ifeffit" <ifeffit at millenia.cars.aps.anl.gov>
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 at 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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