Paul,

This is a bit more lengthy version of the first email.

For the neighbor list "skin" (neighbor <skin> bin), is there somewhere a list with recommondations, for different densities / temperatures?

Regarding the temp/rescale problem: I did not use the most recent version. In my version the temp/rescale was still like

fix ID group-ID temp/rescale Tstart Tstop N window fraction

I should have changed this in the version that I had sent to you. I have no upgraded to the newest version.

The "atom_style energy" is something that I have put in. It just defines an extra field for the potential energy of each atom. This field is updated during the normal force

calculation. I need it, because I work on hybrid MD-Continuum methods. For this I have to calculate cell averages of density, momentum and total energy for the continuum solver. To get the total energy of the cell, I obviously need Epot of each atom.

Naturally, the cell averages are subject fluctuation in time. In order to obtain an averages that are within a limit (like 5%) from the "true" value, one has to choose two parameters:

- Number of atoms within one cell

- the sample frequency (what is the optimal number time step between each measurment)

- time average over how many measurements

The number of atoms for my cases is quite low (100 -1000). This is mainly because I test a lot and want to the system to run fast.

As far as I know the sample frequency should be based on the correlation time of the variable of interest.

To find the optimal sample frequency I have used the block method, that is described in Allen&Tildesley (from a paper by Flyberg et. al . I think).

From the block method one should get a curve that converges to a plateau, which shows a useful sample frequency.

So I applied this method to cell averaged variables(density, momentum), but the result was not clear.

When I tried to find out why, I realised that there were quite low frequent flucutations.

Calculating the the time correlation function directly I obtain a correlation time of around 40,000 time steps. This seemed very long and is not practicle to use, because I would have to run for a very long time in order to calculate reliable averages.

So I performed a discrete fourier transformation to obtain the power spectrum.

I may be wrong, and please correct in that case: For random fluctuations the power spectra should look random as well, and energies should be distributed over the entire frequency range and not only at low frequencies. But here, all the energy is in low frequent waves and not "uniformly" distributed over the spectrum.

I have put together the graphs for the some example runs. My basic idea was to use small free flow cases to test the method. So all the setups are periodic in y and z direction and with "continuum boundary conditions" in x directions. For fluid at rest, I just used walls to confine the fluid, which are later replaced by the continuum boundary conditions. However, the long time fluctuations are also present for peridicity in all directions (so the boundary is not the problem).

gas (r=0.01) at T=2, simulation box based on a lattice of 200x5x5 simulated over 10,000,000 time steps:

1a) velocity of the entire channel: www.cranfield.ac.uk/~ei2989/lammps/vx/Powerapectra_r0.01_T2_all_460x23x23.jpg

1b) velocity of the entire channel: www.cranfield.ac.uk/~ei2989/lammps/vx/Powerapectra_r0.01_T2_cell_460x23x23.jpg

A 2D case of the same system (simulation box based on a lattice of 200x200x5), 1,000,000 time steps:

2) velocity of a cell: www.cranfield.ac.uk/~ei2989/lammps/vx/PowerSpectra_r0.01_T2_vx_cell_465x465x46.jpg

A smaller case with r=0.1 and T=2 , simulation based on a lattice of 100x5x5 time steps:

3a) velocitity of the entire channel: www.cranfield.ac.uk/~ei2989/lammps/vx/PowerSpectra_r0.1_T2_vx_all_215x23x23.jpg

3b) velocitity of a cell in the middle: www.cranfield.ac.uk/~ei2989/lammps/vx/PowerSpectra_r0.1_T2_vx_cell_215x23x23.jpg

The most extrem is 3a), as here almost the entire energy is contained in one wave length. But for all other cases the fluctuations are low frequent.