Re: want to modify NDSolve--molecular dynamics with mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg26365] Re: want to modify NDSolve--molecular dynamics with mathematica
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Wed, 13 Dec 2000 02:41:24 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <90v82t\$79m@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

you can write your equation with Mod[x[t],a0]
but it will make the InterpolatingFunction[]s
returned by NDSolve[] unusable. Because
x[t] will jump back to for x>a0 and the
interpolation is useless.

You must write your own initial value solver.

Regards
Jens

"Toshiyuki (Toshi) Meshii" wrote:
>
> Hello,
>
> I was wondering whether I can apply NDSolve to molecular dynamics, on the
> standpoint of periodical boundary condition.
>
> The eqation I want to solve is the simple Newton equation (Let me simplify
> the problem).
>   m D[x, {x,2}] == F
> However, periodical boundary condition makes it difficult to apply NDSolve.
> That is, once
>   0<x[t]<a0
> is not satisfied (a0 is a constant), I have to move the atom so that this
> condition is satisfied.
> In concrete,
>   if x[t]<0  --->  x[t]=x[t]+a0
>   if x[t]>a0  --->  x[t]=x[t]-a0
> and then restart to solve the equation.
>
> Is there any way to realize this by directly applying NDSolve?
> If not, how can I modify NDSolve?
>
> -Toshi

```

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