# [lammps-users] Fix thermal/conductivity with different atoms (mass)

Dear Sreekant,

I think I’ve solved this as what I’ve demonstrated in the following emails:
Please check it for me, thanks

Best wishes

Xiaoliang Zhang

CAS, China

****************

Dear Aidian,

energy but not for linear momentum conservation.
My solution I showed yesterday considerred conservation of the total energy and momentum of the two atoms with two equations in the following.
m1
v1
2 + m2
v2
2 = m1
v3
2 + m2
v4
2 (1)
m1
v1 + m2 v2 = m1 * v3 + m2 * v4 (2)
in the two equations above, v1, v2 are the old velocities of the hot and cold atoms, and v3, v4 are the new associated velocities.
Through the equations I got v3 and v4 being the funcions of v1, v2, and m1, m2
09年6月16日，周二, [email protected] [email protected] 写道：

> 发件人: aidan.thompson@…92… [email protected]
> 主题: Re: [lammps-users] Muller Plathe method applied to atoms of different types
> 收件人: “剑心 张” <zhxlhdd2008@…215…>
> 日期: 2009年6月16日,周二,下午11:43
>
> This seems like a rather complicated formula, and does not appear to conserve energy. I suggest that for atoms of unequal mass, instead of swapping velocities, you should swap kinetic energyies This preserves the intent of the original method.
>
> This will require you to change the velocities in the following way:
>
> v1 = v2_old
beta
> v2 = v1_old / beta
>
> where beta = sqrt(m2/m1)
>
> check:
>
> KE1 = m1
v1^2 = m2
v2_old^2 = KE2_old
> KE2 = m2
v2^2 = m1
v1_old^2 = KE1_old
>
> Aidan
>
> On Jun 15, 2009 6:42pm, 剑心 张 <zhxlhdd2008@…215…> wrote:
> > Morning every one,
> >
> >
> >
> > First of all, I want to say Muller Plathe method is a good method. however, I find it only to be applied to atoms of same types, so I tried to modify it to be applied to atoms of different types days ago.
> >
> > I only made the Muller Plathe to satisfy the momentum and energy conservation with different mass, and I got the formula which can be used to different types, and I find it work well.
> >
> > So here I want to enjoy it with every one, of cource ,maybe it’s wrong, so would you please check it for me? thanks
> >
> > the formula i got is as follows:
> >
> > I suppose the mass of the hot atom is m1, whose velocity is v1; and for the cold one is m2 and v2. After velocity interchange, i change the v1 to be v1 + 2
beta/(beta+1)
(v2 - v1) and v2 to be (2
v1 + (beta - 1)*v2 ) / (beta+1)
> > where beta = m2/m1

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