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,
Thanks for your reply. And I find your solution is good to conserve the total kinetic
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 v12 + m2 v22 = m1 v32 + m2 v42 (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: [email protected]…92… [email protected]
> 主题: Re: [lammpsusers] Muller Plathe method applied to atoms of different types
> 收件人: “剑心 张” <[email protected]…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_oldbeta
> v2 = v1_old / beta
>
> where beta = sqrt(m2/m1)
>
> check:
>
> KE1 = m1v1^2 = m2v2_old^2 = KE2_old
> KE2 = m2v2^2 = m1v1_old^2 = KE1_old
>
> Aidan
>
> On Jun 15, 2009 6:42pm, 剑心 张 <[email protected]…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 + 2beta/(beta+1)(v2  v1) and v2 to be (2v1 + (beta  1)*v2 ) / (beta+1)
> > where beta = m2/m1
