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RE: A toy example of molecule aggregation to familiarize with LAMMPS software

in #steemstem4 years ago

I think you are confusing reducing dimensions with making dimensionless :P

With dimension reduction I mean: If you have an N-dimensional system (for example with states in \mathbb{R}^N ) then there could be symmetries present which allow you to move the system to an M-dimensional system with M < N. This is a useful trick in the study of Hamiltonian systems.

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Hi @mathowl : Sorry for the confusion. Okay so coarse-grained simulations are indeed "dimensionally reduced" versions of original systems. Yes, a real lipid will access more configurations, but our 3 particle coarse-grained models will not have high frequency - low energy motions. Those motions are filtered out effectively. But still you can study many important phenomena. Also speed up certainly!

But is it possible to reduce the dimension of the coarse-grained simulation using symmetries in the governing equations?

You asking about reducing the dimension of already dimensionally reduced coarse grained system? I think we will lose lot of information then. But I don't know if there will be any symmetry existing in the system. It might depend on specific systems I guess. Maybe we can discuss on it if I am understanding your query in a wrong way.

If there is a symmetry or some conserved quantity then you can reduce the system without losing any of the dynamics. I am not sure if that is the case for your set of equations. We can discuss it at a later time :o)