[gmx-users] "Angular" Vs. "Linear" in NVE simulation

[Antonio Baptista]

On Mon, 7 Nov 2005, Antonio Baptista wrote:

> On Fri, 4 Nov 2005, David wrote:
>
>> On Fri, 2005-11-04 at 23:32 +0800, Xiaobing Feng wrote:
>>> Dear everyone,
>>> 
>>>     When I run a NVE simulation with "Angular" the
>>> total energy decreased very rapidly, though the
>>> system is equilibrated with NPT. Once "Angular" was
>>> replaced by "Linear" the total energy is well
>>> conserved.
>>> 
>>>    "Angular" removes the drifts of both center-of-mass
>>> and angular, so, it seems better to use "Angular".
>>> 
>>>    Could anybody give me an explanation why "Angular"
>>> is bad in NVE?
>> 
>> Not sure. It could be a precision problem, but I think we have tried it
>> in double as well. Have you tried that?
>
> If you are using periodic boundary conditions (pbc) in your NVE simulation, 
> angular momentum _should_ not be conserved, regardless of the precison you 
> use.  Conserved quantities are a consequence of symmetry properties: linear 
> momentum is conserved when space is homogeneous (invariant under 
> translation); angular momentum is conserved when space is isotropic 
> (invariant under rotation). Now, the use of pbc does not mess you the 
> homogenity of space, but kills its isotropy because it does not have 
> spherical symmetry. When you don't use pbc (eg, when simulating a cluster) 
> the space is sperically symmetric and angular momentum _should_ be conserved.
>
> This issue is mentioned in most simulation textbooks (Allen & Tildesley,
> Leach, etc). If you are curious about these symmetry matters you can have
> a look at the Feynman Lectures for a nice overview, or even at Goldstein
> (classical) or Messiah (quantum) for the heavy stuff.

I've realized that, in these previous comments I ended up forgeting to 
mention the implications for your practical question: Since angular 
momentum is not conserved with pbc, its removal by using "Angular" is not 
a mere correction of a truncation-error drift, as for linear momentum. 
Thus, while the removal of linear momentum probably takes place in the 
truncation-error range, without resulting in energy dissipation, the 
removal of angular momentum is much more drastic and probably involves 
significant energy dissipation. That could perhaps explain your results.

Regards,
Antonio


>
> Regards,
> Antonio
>
>> 
>>> 
>>>     Many thanks in advance
>>> 
>>>       Xiaobing
>>> 
>>> 
>>> 
>>> 
>>> 
>>> 
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>> -- 
>> David.
>> ________________________________________________________________________
>> David van der Spoel, PhD, Assoc. Prof., Molecular Biophysics group,
>> Dept. of Cell and Molecular Biology, Uppsala University.
>> Husargatan 3, Box 596,          75124 Uppsala, Sweden
>> phone:  46 18 471 4205          fax: 46 18 511 755
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>> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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>
> --
> Antonio M. Baptista
> Instituto de Tecnologia Quimica e Biologica, Universidade Nova de Lisboa
> Av. da Republica, EAN, ITQB II, Apartado 127
> 2781-901 Oeiras, Portugal
> phone: +351-214469619         email: baptista at itqb.unl.pt
> fax:   +351-214411277         WWW:   http://www.itqb.unl.pt/~baptista
> --------------------------------------------------------------------------

--
Antonio M. Baptista
Instituto de Tecnologia Quimica e Biologica, Universidade Nova de Lisboa
Av. da Republica, EAN, ITQB II, Apartado 127
2781-901 Oeiras, Portugal
phone: +351-214469619         email: baptista at itqb.unl.pt
fax:   +351-214411277         WWW:   http://www.itqb.unl.pt/~baptista
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