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## Re: [h5md-user] fields of observable group

 From: Konrad Hinsen Subject: Re: [h5md-user] fields of observable group Date: Wed, 7 Sep 2011 11:03:19 +0200

```On 6 Sep, 2011, at 11:00 , Felix Höfling wrote:

> If we restrict to isometric transformations, the matrix shall be
> orthogonal. This appears to be pretty general already, see
> http://en.wikipedia.org/wiki/Euclidean_group.

Indeed. I don't see any point in going beyond isometric transformations for
atomic systems.

> It think about two optional attributes "transformation" and "shift"
> attached to the "box" group. They hold datasets of ranks 3 and 2,
> respectively: a square matrix and a vector for each copy of the stored
> particle coordinates.

For the applications I can think off, it would be excessive to store
transformations for each configuration (i.e. each time step). The situation of
variable box size and shape can be solved by storing the transformations in
fractional coordinates, as it is the habit in crystallography. A truncated
octahedral, for example, would have a symmetry transformation saying "translate
by 1/2 of each lattice vector".

> One problem appears here: if the box size fluctuates, the shift vector has
> to be adjusted as the simulation progresses. If the matrix is orthognonal,
> i.e., of norm unity, it is unaffected. Maybe the shift vector should be
> unified with 'offset'?

Even an orthogonal matrix must be adjusted for changes in box size. Take for
example a rotation around the center of the box: even if the orthogonal matrix
always stands for a rotation, its axis would be wrong after a change of box
size. But fractional coordinate rotations take care of all that.

> Shall the boundary conditions of the box be stored in an H5MD file? I can
> think of open boundaries, periodic boundaries and (a bit weird)
> Klein-bottle boundaries (a torus plus a twist). The same question arises
> for the velocities in case of Lee-Edwards boundaries.

There's also 2D-periodic systems (for surface simulations). I don't know if
1D-periodic is used in real life, but it is possible in principle. And yes, I
think that information needs to be stored in order to make the coordinate data
interpretable.

> The role of the offset may change with the inclusion of Euclidean
> transformations, see above. Just one remark: for studies of transport in
> liquids, it is desirable to store the unwrapped trajectory of each
> particle in periodic space, otherwise the displacements after long time
> lags get unphysically truncated. Thus the positions should definitely not
> be enforced to be within the unit cell, leaving it open to the writer
> whether to reduce them or not.

That makes sense.

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